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Prisoner's dilemma

The prisoner's dilemma is a game theory thought experiment that involves two rational agents, each of whom can cooperate for mutual benefit or betray their partner ("defect") for individual reward. This dilemma was originally framed by Merrill Flood and Melvin Dresher in 1950 while they worked at the RAND Corporation. Albert W. Tucker later formalized the game by structuring the rewards in terms of prison sentences and named it the "prisoner's dilemma".

The prisoner's dilemma models many real-world situations involving strategic behavior. In casual usage, the label "prisoner's dilemma" may be applied to any situation in which two entities could gain important benefits from cooperating or suffer from failing to do so, but find it difficult or expensive to coordinate their activities.

Premise
William Poundstone described this "typical contemporary version" of the game in his 1993 book Prisoner's Dilemma:

"Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If both prisoners testify against each other, both will be sentenced to two years in jail. The prisoners are given a little time to think this over, but in no case may either learn what the other has decided until he has irrevocably made his decision. Each is informed that the other prisoner is being offered the very same deal. Each prisoner is concerned only with his own welfare—with minimizing his own prison sentence."

This leads to four different possible outcomes for prisoners A and B:
 * 1) If A and B both remain silent, they will each serve one year in prison.
 * 2) If A testifies against B but B remains silent, A will be set free while B serves three years in prison.
 * 3) If A remains silent but B testifies against A, A will serve three years in prison and B will be set free.
 * 4) If A and B testify against each other, they will each serve two years.

Strategy for the prisoner's dilemma
Two prisoners are separated into individual rooms and cannot communicate with each other. It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside of the game. The normal game is shown below:

Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves analyzing both players' best responses: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So, either way, A should defect since defecting is A's best response regardless of B's strategy. Parallel reasoning will show that B should defect.

Defection always results in a better payoff than cooperation, so it is a strictly dominant strategy for both players. Mutual defection is the only strong Nash equilibrium in the game. Since the collectively ideal result of mutual cooperation is irrational from a self-interested standpoint, this Nash equilibrium is not Pareto efficient.

Generalized form
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue and that each player chooses to either "cooperate" or "defect".

If both players cooperate, they both receive the reward $$R$$ for cooperating. If both players defect, they both receive the punishment payoff $$P$$. If Blue defects while Red cooperates, then Blue receives the temptation payoff $$T$$, while Red receives the "sucker's" payoff, $$S$$. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff $$S$$, while Red receives the temptation payoff $$T$$.

This can be expressed in normal form:

and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:

The payoff relationship $T > R > P > S$ implies that mutual cooperation is superior to mutual defection, while the payoff relationships $R > P$ and $T > R$ imply that defection is the dominant strategy for both agents.

The iterated prisoner's dilemma
If two players play the prisoner's dilemma more than once in succession, remember their opponent's previous actions, and are allowed to change their strategy accordingly, the game is called the iterated prisoner's dilemma.

In addition to the general form above, the iterative version also requires that $P > S$, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.

The iterated prisoner's dilemma is fundamental to some theories of human cooperation and trust. Assuming that the game effectively models transactions between two people that require trust, cooperative behavior in populations can be modeled by a multi-player iterated version of the game. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma is also called the "peace-war game".

General strategy
If the iterated prisoner's dilemma is played a finite number of times and both players know this, then the dominant strategy and Nash equilibrium is to defect in all rounds. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.

For cooperation to emerge between rational players, the number of rounds must be unknown or infinite. In that case, "always defect" may no longer be a dominant strategy. As shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain cooperation. Specifically, a player may be less willing to cooperate if their counterpart did not cooperate many times, which causes disappointment. Conversely, as time elapses, the likelihood of cooperation tends to rise, owing to the establishment of a "tacit agreement" among participating players. Another aspect of the iterated prisoner's dilemma is that this tacit agreement between players has always been established successfully even when the number of iterations is made public to both sides.

According to a 2019 experimental study in the American Economic Review that tested what strategies real-life subjects used in iterated prisoner's dilemma situations with perfect monitoring, the majority of chosen strategies were always to defect, tit-for-tat, and grim trigger. Which strategy the subjects chose depended on the parameters of the game.

Axelrod's tournament and successful strategy conditions
Interest in the iterated prisoner's dilemma was kindled by Robert Axelrod in his 1984 book The Evolution of Cooperation, in which he reports on a tournament that he organized of the N-step prisoner's dilemma (with N fixed) in which participants have to choose their strategy repeatedly and remember their previous encounters. Axelrod invited academic colleagues from around the world to devise computer strategies to compete in an iterated prisoner's dilemma tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.

Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behavior from mechanisms that are initially purely selfish, by natural selection.

The winning deterministic strategy was tit for tat, developed and entered into the tournament by Anatol Rapoport. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness": when the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%, depending on the lineup of opponents). This allows for occasional recovery from getting trapped in a cycle of defections.

After analyzing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to succeed:

 * Nice: The strategy will not be the first to defect (this is sometimes referred to as an "optimistic" algorithm), i.e., it will not "cheat" on its opponent for purely self-interested reasons first. Almost all the top-scoring strategies were nice.
 * Retaliating: The strategy must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate, a very bad choice that will frequently be exploited by "nasty" strategies.
 * Forgiving: Successful strategies must be forgiving. Though players will retaliate, they will cooperate again if the opponent does not continue to defect. This can stop long runs of revenge and counter-revenge, maximizing points.
 * Non-envious: The strategy must not strive to score more than the opponent.

In contrast to the one-time prisoner's dilemma game, the optimal strategy in the iterated prisoner's dilemma depends upon the strategies of likely opponents, and how they will react to defections and cooperation. For example, if a population consists entirely of players who always defect, except for one who follows the tit-for-tat strategy, that person is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy is to defect every time. More generally, given a population with a certain percentage of always-defectors with the rest being tit-for-tat players, the optimal strategy depends on the percentage and number of iterations played.

Other strategies
Deriving the optimal strategy is generally done in two ways: In the strategy called win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.
 * Bayesian Nash equilibrium: If the statistical distribution of opposing strategies can be determined an optimal counter-strategy can be derived analytically.
 * Monte Carlo simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a genetic algorithm for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit-for-tat players, but no analytic proof exists that this will always occur.

Although tit-for-tat is considered the most robust basic strategy, a team from Southampton University in England introduced a more successful strategy at the 20th-anniversary iterated prisoner's dilemma competition. It relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the competing program's score. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places (and a number of positions towards the bottom), despite having fewer wins and many more losses than the GRIM strategy. The Southampton strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that a team's performance was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing).

Because of this new rule, this competition also has little theoretical significance when analyzing single-agent strategies as compared to Axelrod's seminal tournament. But it provided a basis for analyzing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise.

Long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but remarked that Axelrod would most likely not have allowed them if they had been submitted. It also relies on circumventing the rule that no communication is allowed between players, which the Southampton programs arguably did with their preprogrammed "ten-move dance" to recognize one another, reinforcing how valuable communication can be in shifting the balance of the game.

Even without implicit collusion between software strategies, tit-for-tat is not always the absolute winner of any given tournament; more precisely, its long-run results over a series of tournaments outperform its rivals, but this does not mean it is the most successful in the short term. The same applies to tit-for-tat with forgiveness and other optimal strategies.

This can also be illustrated using the Darwinian ESS simulation. In such a simulation, tit-for-tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit-for-tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Dawkins showed that here, no static mix of strategies forms a stable equilibrium, and the system will always oscillate between bounds.

Stochastic iterated prisoner's dilemma
In a stochastic iterated prisoner's dilemma game, strategies are specified in terms of "cooperation probabilities". In an encounter between player X and player Y, X's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: $$P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}$$, where Pcd is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by X cooperating and Y defecting. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit-for-tat strategy written as $$P=\{1,0,1,0\}$$, in which X responds as Y did in the previous encounter. Another is the win-stay, lose switch strategy written as $$P=\{1,0,0,1\}$$. It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy that gives the same statistical results, so that only memory-1 strategies need be considered.

If $$P$$ is defined as the above 4-element strategy vector of X and $$Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}$$ as the 4-element strategy vector of Y (where the indices are from Y 's point of view), a transition matrix M may be defined for X whose ij-th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to $$M_{cd,cd}=P_{cd}(1-Q_{dc})$$. Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.

One result of stochastic theory is that there exists a stationary vector v for the matrix v such that $$v\cdot M=v$$. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij-th entry in $$M^n$$ will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j independent of i. In other words, the rows of $$M^\infty$$ will be identical, giving the long-term equilibrium result probabilities of the iterated prisoner's dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for $$M^n$$ and particularly $$M^\infty$$, so that each row of $$M^\infty$$ will be equal to v. Thus, the stationary vector specifies the equilibrium outcome probabilities for X. Defining $$S_x=\{R,S,T,P\}$$ and $$S_y=\{R,T,S,P\}$$ as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (from X's point of view), the equilibrium payoffs for X and Y can now be specified as $$s_x=v\cdot S_x$$ and $$s_y=v\cdot S_y$$, allowing the two strategies P and Q to be compared for their long-term payoffs.

Zero-determinant strategies

In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: $$s_x = D(P, Q, S_x)$$ and $$s_y = D(P, Q, S_y)$$, which do not involve the stationary vector v. Since the determinant function $$s_y = D(P, Q, f)$$ is linear in $$f$$, it follows that $$\alpha s_x + \beta s_y + \gamma = D(P, Q, \alpha S_x + \beta S_y + \gamma U)$$ (where $$U =\{1,1,1,1 \}$$). Any strategies for which $$D(P, Q, \alpha S_x + \beta S_y + \gamma U) = 0$$ are by definition a ZD strategy, and the long-term payoffs obey the relation $$\alpha s_x + \beta s_y + \gamma = 0$$.

Tit-for-tat is a ZD strategy which is "fair", in the sense of not gaining advantage over the other player. But the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect, but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which $$D(P, Q, \beta S_y + \gamma U) = 0$$, unilaterally setting sy to a specific value within a particular range of values, independent of Y's strategy, offering an opportunity for X to "extort" player Y (and vice versa). But if X tries to set sx to a particular value, the range of possibilities is much smaller, consisting only of complete cooperation or complete defection.

An extension of the iterated prisoner's dilemma is an evolutionary stochastic iterated prisoner's dilemma, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly because they reduce each other's surplus).

Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.

While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. When the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Ethan Akin to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.

Continuous iterated prisoner's dilemma
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. In a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit-for-tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit-for-tat-like cooperation are extremely rare even though tit-for-tat seems robust in theoretical models.

Real-life examples
Many instances of human interaction and natural processes have payoff matrices like the prisoner's dilemma's. It is therefore of interest to the social sciences, such as economics, politics, and sociology, as well as to the biological sciences, such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma.

Environmental studies
In environmental studies, the dilemma is evident in crises such as global climate change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide emissions. The immediate benefit to any one country from maintaining current behavior is perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.

An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by governments is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.

Thomas Osang and Arundhati Nandy provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.

Animals
Cooperative behavior of many animals can be understood as an example of the iterated prisoner's dilemma. Often animals engage in long-term partnerships; for example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.

Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior.

Psychology
In addiction research and behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal prisoner's dilemma problem between the present and future selves of the addict. In this case, "defecting" means relapsing, where not relapsing both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome: in some sense, the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where they started and will have to start over. Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining tomorrow, has the problem that (as in other prisoner's dilemmas) there is an obvious benefit to defecting "today", but tomorrow one will face the same prisoner's dilemma, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.

In The Science of Trust, John Gottman defines good relationships as those where partners know not to enter into mutual defection behavior, or at least not to get dynamically stuck there in a loop. In cognitive neuroscience, fast brain signaling associated with processing different rounds may indicate choices at the next round. Mutual cooperation outcomes entail brain activity changes predictive of how quickly a person will cooperate in kind at the next opportunity; this activity may be linked to basic homeostatic and motivational processes, possibly increasing the likelihood of short-cutting into mutual cooperation.

Economics
The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good.

Advertising is sometimes cited as a real example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium.

Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry.

Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. "Cooperating" typically means agreeing to a price floor, while "defecting" means selling under this minimum level, instantly taking business from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.

Sport
Doping in sport has been cited as an example of a prisoner's dilemma. Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over the competitor, reduced by the legal and/or medical dangers of having taken the drug. But if both athletes take the drug, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had doped.

International politics
In international relations theory, the prisoner's dilemma is often used to demonstrate why cooperation fails in situations when cooperation between states is collectively optimal but individually suboptimal. A classic example is the security dilemma, whereby an increase in one state's security (such as increasing its military strength) leads other states to fear for their own security out of fear of offensive action. Consequently, security-increasing measures can lead to tensions, escalation or conflict with one or more other parties, producing an outcome which no party truly desires. The security dilemma is particularly intense in situations when it is hard to distinguish offensive weapons from defensive weapons, and offense has the advantage in any conflict over defense.

The prisoner's dilemma has frequently been used by realist international relations theorists to demonstrate the why all states (regardless of their internal policies or professed ideology) under international anarchy will struggle to cooperate with one another even when all benefit from such cooperation.

Critics of realism argue that iteration and extending the shadow of the future are solutions to the prisoner's dilemma. When actors play the prisoner's dilemma once, they have incentives to defect, but when they expect to play it repeatedly, they have greater incentives to cooperate.

Multiplayer dilemmas
Many real-life dilemmas involve multiple players. Although metaphorical, Garrett Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the prisoner's dilemma: each villager makes a choice for personal gain or restraint. The collective reward for unanimous or frequent defection is very low payoffs and the destruction of the commons.

The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma, describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting), but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best-case outcome for prisoner's dilemma.

Academic settings
The prisoner's dilemma has been used in various academic settings to illustrate the complexities of cooperation and competition. One notable example is the classroom experiment conducted by sociology professor Dan Chambliss at Hamilton College in the late 1980s. Chambliss proposed that if no student took the final exam, everyone would receive an A, but if even one student took it, those who didn't would receive a zero. John Werner, a first-year student, successfully organized his classmates to boycott the exam, demonstrating a practical application of game theory and the prisoner's dilemma concept.

Nearly 25 years later, a similar incident occurred at Johns Hopkins University in 2013. Professor Peter Fröhlich's grading policy scaled final exams according to the highest score, meaning that if everyone received the same score, they would all get an A. Students in Fröhlich's classes organized a boycott of the final exam, ensuring that no one took it. As a result, every student received an A, successfully solving the prisoner's dilemma in a mutually optimal way without iteration. These examples highlight how the prisoner's dilemma can be used to explore cooperative behavior and strategic decision-making in educational contexts.

Closed-bag exchange
Douglas Hofstadter suggested that people often find problems such as the prisoner's dilemma problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange": "Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag."

Friend or Foe?
Friend or Foe? is a game show that aired from 2002 to 2003 on the Game Show Network in the US. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings, and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.

This is the rewards matrix:

This payoff matrix has also been used on the British television programs Trust Me, Shafted, The Bank Job and Golden Balls, and on the American game shows Take It All, as well as for the winning couple on the reality shows Bachelor Pad and Love Island. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world but were comparatively low in the context of the game.

Iterated snowdrift
Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations, although this model is actually a chicken game. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.

This may better reflect real-world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn't do any work, it's probably better for you to do all the work yourself. You'll still end up with a completed project."

Coordination games
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.

Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.

Asymmetric prisoner's dilemmas
A more general set of games is asymmetric. As in the prisoner's dilemma, the best outcome is cooperation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, hence the term "alibi game".

In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X game, while the other always co-operates. Such behavior may depend on the experiment's social norms around fairness.

Software
Several software packages have been created to run simulations and tournaments of the prisoner's dilemma, some of which have their source code available:
 * The source code for the second tournament run by Robert Axelrod (written by Axelrod and many contributors in Fortran) is available online
 * Prison, a library written in Java, last updated in 1998
 * Axelrod-Python, written in Python
 * Evoplex, a fast agent-based modeling program released in 2018 by Marcos Cardinot

In fiction
Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.

A game modeled after the iterated prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.

In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later, they become actual prisoners and escape once again.

In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.

In the 8th novel from the author James S. A. Corey Tiamat's Wrath, Winston Duarte explains the prisoner's dilemma to his 14-year-old daughter, Teresa, to train her in strategic thinking.

The 2008 film The Dark Knight includes a scene loosely based on the problem in which the Joker rigs two ferries, one containing prisoners and the other containing civilians, arming both groups with the means to detonate the bomb on each other's ferries, threatening to detonate them both if they hesitate.

In moral philosophy
The prisoner's dilemma is commonly used as a thinking tool in moral philosophy as an illustration of the potential tension between the benefit of the individual and the benefit of the community.

Both the one-shot and the iterated prisoner's dilemma have applications in moral philosophy. Indeed, many of the moral situations, such as genocide, are not easily repeated more than once. Moreover, in many situations, the previous rounds' outcomes are unknown to the players, since they are not necessarily the same (e.g. interaction with a panhandler on the street).

The philosopher David Gauthier uses the prisoner's dilemma to show how morality and rationality can conflict.

Some game theorists have criticized the use of the prisoner's dilemma as a thinking tool in moral philosophy. Kenneth Binmore argued that the prisoner's dilemma does not accurately describe the game played by humanity, which he argues is closer to a coordination game. Brian Skyrms shares this perspective.

Steven Kuhn suggests that these views may be reconciled by considering that moral behavior can modify the payoff matrix of a game, transforming it from a prisoner's dilemma into other games.

Pure and impure prisoner's dilemma
A prisoner's dilemma is considered "impure" if a mixed strategy may give better expected payoffs than a pure strategy. This creates the interesting possibility that the moral action from a utilitarian perspective (i.e., aiming at maximizing the good of an action) may require randomization of one's strategy, such as cooperating with 80% chance and defecting with 20% chance.

title: Prisoner's dilemma


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Sport of athletics

Athletics is a group of sporting events that involves competitive running, jumping, throwing, and walking. The most common types of athletics competitions are track and field, road running, cross-country running, and racewalking.

The results of racing events are decided by finishing position (or time, where measured), while the jumps and throws are won by the athlete that achieves the highest or furthest measurement from a series of attempts. The simplicity of the competitions, and the lack of a need for expensive equipment, makes athletics one of the most common types of sports in the world. Athletics is mostly an individual sport, with the exception of relay races and competitions which combine athletes' performances for a team score, such as cross country.

Organized athletics are traced back to the Ancient Olympic Games from 776 BC. The rules and format of the modern events in athletics were defined in Western Europe and North America in the 19th and early 20th century, and were then spread to other parts of the world. Most modern top level meetings are held under the auspices of World Athletics, the global governing body for the sport of athletics, or its member continental and national federations.

The athletics meeting forms the backbone of the Summer Olympics. The foremost international athletics meeting is the World Athletics Championships, which incorporates track and field, marathon running and race walking. Other top level competitions in athletics include the World Athletics Cross Country Championships and the World Athletics Road Running Championships. Athletes with a physical disability compete at the Summer Paralympics and the World Para Athletics Championships.

The word athletics is derived from the Ancient Greek ἀθλητής (athlētēs, "combatant in public games") from ἆθλον (athlon, "prize") or ἆθλος (athlos, "competition"). Initially, the term described athletic contests in general – i.e. sporting competition based primarily on human physical feats. In the 19th century, the term athletics acquired a more narrow definition in Europe and came to describe sports involving competitive running, walking, jumping and throwing. This definition continues to be prominent in the United Kingdom and the former British Empire. Related words in Germanic and Romance languages also have a similar meaning.

In many parts of North America, athletics is commonly understood as encompassing sports in general, aligning with its historical usage. The term "athletics" is seldom used specifically to denote the sport of athletics in this region. Instead, track and field is the preferred term used in the United States and Canada to describe athletics events, which include race-walking and marathon running (although cross-country running is typically categorized as a distinct sport).

Ancient
Athletic contests in running, walking, jumping and throwing are among the oldest of all sports and their roots are prehistoric. Athletics events were depicted in the Ancient Egyptian tombs in Saqqara, with illustrations of running at the Heb Sed festival and high jumping appearing in tombs from as early as of 2250 BC. The Tailteann Games were an ancient Celtic festival in Ireland, founded c. 1800 BC, and the thirty-day meeting included running and stone-throwing among its sporting events. The original and only event at the first Olympics in 776 BC was a stadium-length running event known as the stadion. This later expanded to include throwing and jumping events within the ancient pentathlon. Athletics competitions also took place at other Panhellenic Games, which were founded later around 500 BC.

Modern era
The Cotswold Olympic Games, a sports festival which emerged in 17th century England, featured athletics in the form of sledgehammer throwing contests. Annually, from 1796 to 1798, L'Olympiade de la République was held in revolutionary France, and is an early forerunner to the modern Olympic Games. The premier event of this competition was a running event, but various ancient Greek disciplines were also on display. The 1796 Olympiade marked the introduction of the metric system into the sport.

Athletics competitions were held about 1812 at the Royal Military College, Sandhurst, and in 1840 in Shrewsbury, Shropshire at the Royal Shrewsbury School Hunt. The Royal Military Academy at Woolwich held an organised competition in 1849, and a regular series of closed meetings open only to undergraduates, was held by Exeter College, Oxford, from 1850. The annual Wenlock Olympian Games, first held in 1850 in Wenlock, England, incorporated athletics events into its sports programme.

The first modern-style indoor athletics meetings were recorded shortly after in the 1860s, including a meet at Ashburnham Hall in London which featured four running events and a triple jump competition.

The Amateur Athletic Association (AAA) was established in England in 1880 as the first national body for the sport of athletics and began holding its own annual athletics competition – the AAA Championships. The United States also began holding an annual national competition – the USA Outdoor Track and Field Championships – first held in 1876 by the New York Athletic Club. Athletics became codified and standardized via the English AAA and other general sports organisations in the late 19th century, such as the Amateur Athletic Union (founded in the US in 1888) and the Union des sociétés françaises de sports athlétiques (founded in France in 1889).

An athletics competition was included in the first modern Olympic Games in 1896 and it has been as one of the foremost competitions at the quadrennial multi-sport event ever since. Originally for men only, the 1928 Olympics saw the introduction of women's events in the athletics programme. Athletics is part of the Paralympic Games since the inaugural Games in 1960. Athletics has a very high-profile during major championships, especially the Olympics, but otherwise is less popular.

An international governing body, the International Amateur Athletics Federation (IAAF), was founded in 1912. It enforced amateur sport status on competitions during much of the 20th century. Professional competition continued at a low level, becoming increasingly more common as the century progressed. The International Track Association briefly formed a professional track and field circuit in the United States in the 1970s. Athletes used their increasing status to push for remuneration and the IAAF responded with the IAAF Golden Events series and the establishment an outdoor World Championships in 1983, including track and field, racewalking and a marathon event. In modern times, athletes can receive money for racing, putting an end to the so-called "amateurism" that existed before. The global body updated the name to the International Association of Athletics Federations in 2001, moving away from its amateur origins, before taking on its current name World Athletics in 2019.

The Comité International Sports des Sourds had been formed by 1922, to govern international deaf sports, including athletics.

The first organized international competitions for athletes with a physical disability (not deaf) began in 1952, when the first international Stoke Mandeville Games were organized for World War II veterans. This only included athletes in a wheelchair. This inspired the first Paralympic Games, held in 1960. Competitions would over time be expanded to include mainly athletes with amputation, cerebral palsy and visual impairment, in addition to wheelchair events.

Events
World Athletics, the sport's governing body, defines athletics in six disciplines: track and field, road running, race walking, cross country running, mountain running, and trail running. Mountain running was added in 2003 and trail running was added in 2015.

All forms of athletics are individual sports with the exception of relay races. However, athletes' performances are often tallied together by country at international championships, and, in the case of cross country and road races, finishing positions or times of the top athletes from a team may be combined to declare a team victor.

Several further forms of competitive running exist outside of the governance of World Athletics. The International Skyrunning Federation (ISF) governs high-altitude mountain running, defined as skyrunning, and is affiliated with the International Climbing and Mountaineering Federation rather than World Athletics. Competitive stair climbing events, usually hosted in skyscrapers, has two common names: vertical running (as described by the ISF) and tower running (as described by the Towerrunning World Association). Snowshoe running is a winter sport governed by the World Snowshoe Federation, which is similarly to cross country running but has athletes wearing snowshoes to race over deep snow on an obstacle-free course. The International Association of Ultrarunners organises ultra running as an affiliate of World Athletics, but these long-distance forms of competition fit within World Athletics disciplines, albeit with additional distance.

Track and field

Track and field competitions emerged in the late 19th century and were typically contested between athletes who were representing rival educational institutions, military organisations and sports clubs. Participating athletes may compete in one or more events, according to their specialities. Men and women compete separately. Track and field comes in both indoor and outdoor formats, with most indoor competitions occurring in winter, while outdoor events are mostly held in summer. The sport is defined by the venue in which the competitions are held – the athletics stadium.

A variety of running events are held on the track which fall into three broad distance categories: sprints, middle-distance, and long-distance track events. Relay races feature teams comprising four runners each, who must pass a baton to their teammate after a specified distance with the aim of being the first team to finish. Hurdling events and the steeplechase are a variation upon the flat running theme in that athletes must clear obstacles on the track during the race. The field events come in two types – jumping and throwing competitions. In throwing events, athletes are measured by how far they hurl an implement, with the common events being the shot put, discus, javelin, and hammer throw. There are four common jumping events: the long jump and triple jump are contests measuring the horizontal distance an athlete can jump, while the high jump and pole vault are decided on the height achieved. Combined events, which include the decathlon (typically competed by men) and heptathlon (typically competed by women), are competitions where athletes compete in a number of different track and field events, with each performance going toward a final points tally.

The most prestigious track and field contests occur within athletics championships and athletics programmes at multi-sport events. The Olympic athletics competition and World Championships in Athletics, and the Paralympic athletics competition and World Para Athletics Championships, are the highest and most prestigious levels of competition in track and field. Track and field events have become the most prominent part of major athletics championships and many famous athletes within the sport of athletics come from this discipline. Discrete track and field competitions are found at national championships-level and also at annual, invitational track and field meets. Meetings range from elite competitions – such as those in the IAAF Diamond League series – to basic all comers track meets, inter-sports club meetings and schools events, which form the grassroots of track and field.

Road running
Road running competitions are running events (predominantly long distance) which are mainly conducted on courses of paved or tarmac roads, although major events often finish on the track of a main stadium. In addition to being a common recreational sport, the elite level of the sport – particularly marathon races – are one of the most popular aspects of athletics. Road racing events can be of virtually any distance, but the most common and well known are the marathon, half marathon, 10 km and 5 km. The marathon is the only road running event featured at the IAAF World Championships in Athletics and the Summer Olympics, although there is also an annual IAAF World Half Marathon Championships. The marathon is also the only road running event featured at the World Para Athletics Championships and the Summer Paralympics. The World Marathon Majors series includes the six most prestigious marathon competitions at the elite level – the Berlin, Boston, Chicago, London, New York City and Tokyo Marathons.

The sport of road running finds its roots in the activities of footmen: male servants who ran alongside the carriages of aristocrats around the 18th century, and who also ran errands over distances for their masters. Foot racing competitions evolved from wagers between aristocrats, who pitted their footman against that of another aristocrat in order to determine a winner. The sport became professionalised as footmen were hired specifically on their athletic ability and began to devote their lives to training for the gambling events. The amateur sports movement in the late 19th century marginalised competitions based on the professional, gambling model. The 1896 Summer Olympics saw the birth of the modern marathon and the event led to the growth of road running competitions through annual events such as the Boston Marathon (first held in 1897) and the Lake Biwa Marathon and Fukuoka Marathons, which were established in the 1940s. The 1970s running boom in the United States made road running a common pastime and also increased its popularity at the elite level.

Ekiden contests – which originated in Japan and remain very popular there – are a relay race variation on the marathon, being in contrast to the typically individual sport of road running.

Cross country running
Cross country running is the most naturalistic of the sports in athletics as competitions take place on open-air courses over surfaces such as grass, woodland trails, and earth. It is both an individual and team sport, as runners are judged on an individual basis and a points scoring method is used for teams. Competitions are typically long distance races of 3 km or more which are usually held in autumn and winter. Cross country's most successful athletes often compete in long-distance track and road events as well.

The Crick Run in England in 1838 was the first recorded instance of an organised cross country competition. The sport gained popularity in British, then American schools in the 19th century and culminated in the creation of the first International Cross Country Championships in 1903. The annual IAAF World Cross Country Championships was inaugurated in 1973 and this remains the highest level of competition for the sport. A number of continental cross country competitions are held, with championships taking place in Asia, Europe, North America and South America. The sport has retained its status at the scholastic level, particularly in the United Kingdom and United States. At the professional level, the foremost competitions come under the banner of the IAAF Cross Country Permit Meetings.

While cross country competitions are no longer held at the Olympics, having featured in the athletics programme from 1912 to 1924, it has been present as one of the events within the modern pentathlon competition since the 1912 Summer Olympics. One variation on traditional cross country is mountain running, which incorporates significant uphill and/or downhill sections as an additional challenge to the course. Fell running and Orienteering are other competitive sports similar to cross country, although they feature an element of navigation which is absent from the set courses of cross country.

Racewalking
Racewalking is a form of competitive walking that usually takes place on open-air roads, although running tracks are also occasionally used. Racewalking is the only sport in athletics in which judges monitor athletes on their technique. Racewalkers must always have a foot in contact with the ground and their advancing leg must be straightened, not bent at the knee – failure to follow these rules results in disqualification from the race.

Racewalking finds its roots in the sport of pedestrianism which emerged in the late 18th century in England. Spectators would gamble on the outcome of the walking competitions. The sport took on an endurance aspect and competitions were held over long distances or walkers would have to achieve a certain distance within a specified time frame, such as Centurion contests of walking 100 mi within 24 hours. During this period, racewalking was frequently held on athletics tracks for ease of measurement, and the 1908 Summer Olympics in London saw the introduction of the 3500-metre and 10-mile walks. Racewalking was briefly dropped from the Olympic programme in 1928, but the men's 50 kilometres race walk has been held at every Olympic Games but one since 1932. The men's 20 kilometres race walk was added to the Olympic athletics schedule in 1956 and the women's event was first held in 1992. The most common events in modern competition are over 10 km, 20 km and 50 km on roads, although women's 3 km and men's 5 km are held on indoor tracks.

The highest level racewalking competitions occur at the IAAF World Championships in Athletics and at the Summer Olympics, although the sport also has its own separate major competition – the IAAF World Race Walking Cup – which has been held since 1961. The IAAF World Race Walking Challenge forms the primary seasonal competition – athletes earn points for their performances at ten selected racewalking competitions and the highest scoring walkers are entered into that year's IAAF Race Walking Challenge Final.

Categories

The significant variation in people's abilities in the sport of athletics has led to the creation of numerous competitive categories, in order that athletes are pitted against rivals of a similar kind or ability, and to include groups of people who would otherwise not be competitive in open-to-all events. The eligibility of athletes for a given category is occasionally a source of controversy among the sport's participants, officials and spectators, with disputes typically being rooted in deliberate cheating in order to gain a competitive advantage or differing cultural perspectives over the eligibility of a category.

Beyond the primary categories based on physical attributes, some competitions have further eligibility criteria based on nationality, community membership or occupation.

Men's and women's divisions
The foremost division of this kind is by sex[ling]: in athletics, men and women almost exclusively compete against people of the same sex. In contrast to the men's division, the development of the women's division has caused regular dispute in terms of eligibility. Several intersex athletes had success in the women's division in the early 20th century, such as Stanisława Walasiewicz and Mary Weston (later Mark), and the IAAF responded by introducing sex verification for all athletes in the women's category, beginning with the disqualification of sprinter Foekje Dillema in 1950 after she refused to be tested. Olympic champion Ewa Kłobukowska became the first athlete to publicly fail the test in 1967 and the humiliation she suffered as a result of the announcement led to sex tests becoming a confidential process. Hurdler Maria José Martínez-Patiño failed a test and was disqualified in 1985, but publicly fought the ban in court and was reinstated in 1988. In 1991, the IAAF replaced the sex chromatin test with general medical tests for athletes of all divisions, due to changes in ethical and scientific viewpoints.

The question of eligibility for the women's division continued to be a contentious and public issue into the 21st century, with Caster Semenya and Dutee Chand bearing periods of ineligibility and taking the IAAF to the Court of Arbitration for Sport over their bans under the hyperandrogenism rules. An increasing number of trans men and trans women began to compete in the women's division in the 2010s, which caused other athletes in the division to raise questions of fairness in competition.

The dispute reached new heights in 2019 with the United Nations Human Rights Council issuing a statement that the IAAF was breaching "international human rights norms and standards" through its practice of allowing some athletes to compete in the women's division only once they had lowered their testosterone levels through medical intervention. The IAAF and several prominent women athletes, such as Paula Radcliffe, said this was required in order to prevent a situation where countries deliberately sought out athletes who were intersex, transgender or had a difference in sex development in order to succeed in women's sport. Others have argued for the abolition of gender verification testing, with academic Maren Behrensen citing the harm to tested athletes' social and emotional well-being, the inaccuracy of the medical tests, the difficulty of determining the exact performance advantage provided by a given condition, and the moral risk of "gender-engineering" by setting a biological definition for a female athlete.

Age
Age is a significant determiner of ability to compete in athletics, with athletic ability generally increasing through childhood and adolescence, peaking in early adulthood, then gradually declining from around the age of 30 onwards. As a result, numerous age categories have been created to encourage younger and older athletes to engage in competition. At international level, there are three major categories for young athletes: under-23, under-20 (formerly junior), and under-18 (formerly youth). Beyond international rules, different youth categories are in use in the sport, often in the form of two-year or single age groupings. Age categories are more extensive for older athletes and these are commonly organised under the umbrella of masters athletics, which has age groups spanning five years for all athletes aged 35 and above. There is no limit to the number of age groupings, hence Stanisław Kowalski holds a world record for men aged 105 years and over. For competitions where age is not taken into account, this is known as senior or open class athletics; in international rules there remain some restrictions on younger people competing in endurance events for health reasons.

Athletes' eligibility for a competitive age grouping is typically assessed through official documentation, such as birth records or passports. Instances of age cheating have occurred at all of the IAAF's global age category championships. One prominent incident was Olympic medalist Thomas Longosiwa, who provided a falsified passport to compete at the 2006 World Junior Championships in Athletics at age 24. Age falsification for youth categories is mostly limited to less developed parts of the world, such as Africa and South Asia, which have less stringent controls on official documentation and many mature athletes engaging in high school competition due to disruptions to education. The same regions of the world also present issues with age verification in masters age categories, with examples such as Indian distance runners Dharampal Singh Gudha and Fauja Singh (both claiming to be over 100 years old) reaching mainstream attention.

Athletes with disabilities
Athletes with physical disabilities have competed at separate international events since 1952. The International Paralympic Committee governs the competitions in athletics, and hosts the Paralympic Games, which have continued since 1960.

Competitors at elite level competitions, are classified by disability, to arrange athletes with a similar disability in the same event. A classified T12 athlete for example, is a track athlete with a visual impairment.
 * F = Field athletes
 * T = Track athletes
 * 11–13 – visual impairment. Compete with a sighted guide.
 * 20 – Intellectual disability
 * 31–38 – cerebral palsy
 * 40–46 – amputation, and others (including athletes with dwarfism)
 * 51–58 – Wheelchair

Operating independently of the Paralympic movement, deaf athletes have a long-established tradition of organised athletics, with the first major world competition being included at the 1924 Deaflympics. The primary impediments to the inclusion of deaf athletes in mainstream athletics are sound based elements of the sport, such as the starter's pistol. This can be a disadvantage even in Paralympic sport, as shown in by the example of Olivia Breen who failed to hear a false start in a cerebral palsy class race at the 2012 Paralympics.

In wheelchair racing athletes compete in lightweight racing chairs. Most major marathons have wheelchair divisions and the elite racers consistently beat the runners on foot. The speed of wheel chair racers has caused difficulties for race organisers in properly staggering their start times compared to runners. A collision between Josh Cassidy (a wheelchair racer) and Tiki Gelana (a leading female marathoner) at the 2013 London Marathon brought the issue into the spotlight again.

Occasionally, athletes with a disability reach a level at which they can compete against able-bodied athletes. Legally blind Marla Runyan ran in the 2000 and 2004 Olympics and won a gold medal in the 1500 metres at the 1999 Pan American Games. Oscar Pistorius, a double amputee, was a semi-finalist at the 2011 World Championships and won a silver medal as part of South Africa's 4 × 400 metres relay team. In masters athletics it is far more common to make an accommodation for athletes with a disability. Blind Ivy Granstrom set numerous Masters world records while being guided around the track.

The disability categories have caused dispute among athletes, with some athletes being accused of exaggerating their level of disability in order to compete in less challenging categories. Athletes with intellectual disabilities were banned from competition in all Paralymic sports in response to verification issues and cheating at the 2000 Summer Paralympics and the intellectual disability athletics programme was only restored twelve years later at the 2012 Summer Paralympics.

Venues
Professional athletics almost exclusively takes place in one of three types of venue: stadiums, set courses on grass or woodland, and road-based courses. Such venues ensure that events take place in a relatively standardised manner, as well as improving the safety of athletes and enjoyment for spectators. At a more basic level, many forms of athletics demand very little in terms of venue requirements; almost any open space or area of field can provide a suitable venue for basic running, jumping and throwing competitions.

Athletics stadium
A standard outdoor track is in the shape of a stadium, 400 metres in length, and has at least eight lanes 1.22 m in width (small arenas might have six lanes). Older track facilities may have nonstandard track lengths, such as 440 yards (402.3 m; 1/4 mile) (common in the United States). Historically, tracks were covered by a dirt running surface. Modern All-weather running tracks are covered by a synthetic weather-resistant running surface, which typically consists of rubber (either black SBR or colored EPDM granules), bound by polyurethane or latex resins. Older tracks may be cinder-covered. The facilities can be called track and field stadiums or athletics stadiums.

A standard indoor track is designed similarly to an outdoor track, but is only 200 metres in length and has between four and eight lanes, each with width between 0.90 m and 1.10 m. Often, the bends of an indoor track will be banked to compensate for the small turning radius. However, because of space limitations, indoor tracks may have other nonstandard lengths, such as 160-yard (146.3 m) indoor track at Madison Square Garden used for the Millrose Games. Because of space limitations, meetings held at indoor facilities do not hold many of athletics events typically contested outdoors.

Cross country courses
There is no standardised form of cross country course and each venue is significantly defined by the environment it contains – some may be relatively flat and featureless, while others may be more challenging with natural obstacles, tight turns, and undulating ground. While a small number of purpose-built courses exist, the vast majority of cross country running courses are created by cordoning a specific area within any open natural land, typically a park, woodland or greenspace near a settlement.

At the elite and professional level, courses must be looped and each lap must be between 1750 m and 2000 m in length. Severe obstacles such as deep ditches, high barriers and thick undergrowth not normally present; the course should be able to be completed whilst remaining on foot throughout. In order to maintain the sport's distinction from road running, the usage of unnatural or macadamised surfaces is generally kept to a minimum or avoided entirely.

Because the majority of races take place on areas of grass, soil, mud or earth, weather conditions can significantly affect the difficulty of cross country courses, as snow and rain reduces traction and can create areas of standing water.

Road courses
The surface of road races is highly important and the IAAF dictate that the courses must be along man-made roads, bicycle paths or footpaths. Courses set along major roads of cities are typical of road running events, and traffic is usually cordoned off from the area during the competition. While soft ground, such as grass, is generally avoided, races may start and finish on soft ground or within an athletics stadium. Road racing courses come in two primary types: looped and point-to-point. Courses may be measured and designed to cover a standardised distance, such as 10 km, or they may simply follow a set route between two landmarks.

Road running courses over 5 km usually offer drinks or refreshment stations for runners at designated points alongside the course and medical professionals are present at the courses of major races due to the health risks involved with long-distance running.

Elite road walks are conducted on closed loop courses (usually loops of 2,000 or 2,500 meters). Refreshment stations are also present over long distance walking competitions, with drinks being available on every lap for races longer than 10 km.

Organizations
In 1912, the formation of the international governing body for athletics, the International Amateur Athletics Federation, began. In recognition of the movement of the sport from amateurism towards professionalism that began in the late 1970s, the word amateur was dropped from the name, and the organization was rebranded as the International Association of Athletics Federations in 2001. In late 2019, another rebranding began, with World Athletics as the new title of the governing body.

World Athletics has 215 member nations and territories, which are divided into six continental areas (or area associations). The six association areas are for Asia, Africa, Europe, Oceania, North and Central America and Caribbean and South America. The sports within athletics do not have their own independent governing bodies at either international or continental level; instead, all fall under the athletics authorities.

 * AAA – Asian Athletics Association
 * CAA – Confederation of African Athletics
 * CONSUDATLE – South American Athletics Confederation
 * NACACAA – North America, Central America and Caribbean Athletic Association
 * EAA – European Athletics Association
 * OAA – Oceania Athletics Association

National level athletics organisations are responsible for the regulation of the sport within their respective countries and most major competitions have some form of permit or approval from their national body.

Competitions
Athletics competitions can be broadly divided into three types: international championships, national championships, and annual meetings and races. Athletics at international championships, or Games, represent the pinnacle of competition within the sport, and they are contested between athletes representing their country or region. The organisation of these competitions is usually overseen by either a world, continental, or regional athletics governing body. Athletes gain entry into these competitions by earning selection from their national athletics governing body, which is generally done by assessing athletes via their past achievements or performances at a national selection event. National championships are annual competitions endorsed by a national governing body which serve the purpose of deciding the country's best athlete in each event. Annual one-day meetings and races form the most basic level of competition and are the most common format of athletics contests. These events are often invitational and are organised by sports organisations, sports promoters, or other institutions.

Competitions typically feature only one of the sports within athletics. However, major outdoor international athletics championships and athletics competitions held as part of multi-sport events usually feature a combination of track and field, road running and racewalking events

Multi-sport events
The modern Summer Olympics was the first event at which a global athletics competition took place. All the four major sports within athletics have featured in the Olympic athletics programme since its inception in 1896, although cross country has since been dropped. The Olympic competition is the most prestigious athletics contest, and many athletics events are among the most watched events at the Summer Olympics. A total of 47 athletics events are held at the Olympics, 24 for men and 23 for women (as of London 2012). The events within the men's and women's programmes are either identical or have a similar equivalent, with the sole exception being that men contest the 50 km race walk.

Following the model of the Olympics, various other multi-sport events arose during the 20th century, which included athletics as a core sport within the programme from the outset. These included the Commonwealth Games, the Central American and Caribbean Games, Universiade, and many others.

The Summer Paralympics include athletes with a physical disability. Track and field, and road events have featured in the Paralympic athletics programme since its inception in 1960. The Paralympic competition is the most prestigious athletics contest where athletes with a physical disability compete. Athletics at the Paralympic Games also include wheelchair racing where athletes compete in lightweight racing chairs. Athletes with a visual impairment compete with a sighted guide. At the 2012 Summer Paralympics in London, for the first time at an international athletics event, the guides received medals, such as the pilots in cycling, and the guides at the Paralympic Winter Games have done for a while.

World championships
The World Athletics Championships is the primary global athletics championships held by World Athletics. The biennial competition was first held in 1983 and now features an event programme which is identical to the Olympics. Thus, road running, racewalking and track and field are the sports which feature at the competition. Cross country running has its own discrete global championships – the World Athletics Cross Country Championships – which has been held annually since 1973. The World Athletics Indoor Championships is a biennial athletics championships which features solely indoor track and field events. The foremost separate road running event is the annual World Athletics Half Marathon Championships (formerly IAAF World Half Marathon Championships). While not having official world championship status, the biennial World Athletics Race Walking Team Championships fulfils a similar role for the sport of racewalking. Outdoor track and field is the only sport in athletics that does not have a its own distinct global championship which is separate from other types of athletics, although the IAAF Continental Cup (a quadrennial competition between continental teams) is composed entirely of outdoor track and field events.

Other world championships include the World Athletics U20 Championships and the 2017 defunct World Youth Championships in Athletics, which are for athletes under-19 and under-17, respectively. World Masters Athletics conducts the World Masters Athletics Championships for athletes in 5-year age divisions over the age of 35. The now defunct IAAF World Road Relay Championships served as the global event for ekiden marathon relay races.

Elite athletes with a physical disability compete at the World Para Athletics Championships.

Area/Continental championships
African, Asian, European, North & Central and Caribbean (NACAC), Oceania and South American Athletics Championships are held regularly in a variety of configurations. For example, the Oceania Area Championships in Athletics are combined with the Oceania U20 Athletics Championships. Most of the main regions hold separate cross-country, road-running and marathon championships.

There is the Pan American Combined Events Cup. Central American and Caribbean Championships are organised by the Central American and Caribbean Athletic Confederation (the CACAC)).

Culture and media
Athletics, and its athletes in particular, has been artistically depicted since ancient times – one of the surviving instances include runners and high jumpers in the motifs of Ancient Egyptian tombs dating from 2250 BC. Athletics was much respected in Ancient Greece and the events within the ancient pentathlon provided inspiration for large statues such as the Discobolus and Discophoros, and for motifs on countless vase and pottery works. Aristotle discussed the significance of the pentathlon in his treatise Rhetoric and reflected on the athlete aesthetic of the period: "a body capable of enduring all efforts, either of the racecourse or of bodily strength...This is why the athletes in the pentathlon are most beautiful".

Films about athletics are overwhelmingly focused on running events: the 1962 film The Loneliness of the Long Distance Runner (based on the book of the same name) explores cross country running as a means of escape. Chariots of Fire, perhaps one of the most well-known athletics films, is a fictionalised account of Eric Liddell and Harold Abrahams's chase for sprint gold medals at the 1924 Olympics. Track and field has been the subject of American films such as Personal Best (1981) and Across the Tracks (1991). Biopics are found within the genre, including Prefontaine (regarding Steve Prefontaine) and Jim Thorpe – All-American (1951) featuring Burt Lancaster as Thorpe. Documentaries are also common with examples such as 2007 film Spirit of the Marathon, which follows runners' preparations for the 2005 Chicago Marathon.

Books on the subject are predominantly non-fiction, and tend towards the forms of training manuals and historical accounts of athletics. The story of the four-minute mile has been a particularly popular subject, spawning books such as The Perfect Mile and 3:59.4: The Quest to Break the Four Minute Mile.

Athletics journalism has spawned a number of dedicated periodicals including Athletics Weekly and Race Walking Record, both of which were first published in England in the early 1940s, and Track & Field News which was first published in the United States in 1948. Runner's World has been in print since 1966 and the Track & Field Magazine of Japan (Rikujyo Kyogi Magazine) is another long-running publication.

Athletics events have been selected as a main motif in numerous collectors' coins. One of the recent samples is the €10 Greek Running commemorative coin, minted in 2003 to commemorate the 2004 Summer Olympics. In the obverse of the coin, a modern athlete figure appears in the foreground, shown in the starting position, while in the background two ancient runners are carved in a manner that gives the appearance of a coin that is "worn" by time. This scene originally appeared on a black-figure vase of the 6th century BC.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Sport of athletics


text:
Hammer throw

The hammer throw is one of the four throwing events in regular outdoor track and field competitions, along with the discus throw, shot put and javelin.

The "hammer" used in this sport is not like any of the tools also called by that name. It consists of a metal ball attached by a steel wire to a grip. These three components are each separate and can move independently. Both the size and weight of the ball vary between men's and women's events. The women's hammer weighs 4 kg for college and professional meets while the men's hammer weighs 7.26 kg.

History
The exact origins of the hammer throw are a mystery to modern historians. According to legend, at the Tailteann Games in Tara, Ireland, as far back as 2000 BC the Celtic warrior Culchulainn took a chariot axle with a wheel still attached and spun it around and hurled it. The wheel was later replaced by a rock with a wooden handle attached. A sledgehammer began to be used for the sport in Scotland and England during the Middle Ages. In current times, the hammer has changed to the more modern 7.26 kg ball attached to a wire and a handle, but the Scottish Highland Games still feature the older style of hammer throw with the rock and the solid wood handle. Today the Hammer throw is one of four throwing events featured in the Olympics alongside discus, shot put, and javelin.

While the men's hammer throw has been part of the Olympics since 1900, the International Association of Athletics Federations did not start ratifying women's marks until 1995. Women's hammer throw was first included in the Olympics at the 2000 summer games in Sydney, Australia, after having been included in the World Championships a year earlier.

Competition
The men's hammer weighs 16 lb and measures 3 ft in length, and the women's hammer weighs 4 kg and 3 ft in length. Like the other throwing events, the competition is decided by who can throw the implement the farthest.

The throwing motion starts with the thrower swinging the hammer back-and-forth about two times to generate momentum. The thrower then makes three, four or (rarely) five full rotations using a complex heel-toe foot movement, spinning the hammer in a circular path and increasing its angular velocity with each rotation. Rather than spinning the hammer horizontally, it is instead spun in a plane that angles up towards the direction in which it will be launched. The thrower releases the hammer as its velocity is upward and toward the target.

Throws are made from a throwing circle. The thrower is not allowed to step outside the throwing circle before the hammer has landed and may only enter and exit from the rear of the throwing circle. The hammer must land within a 34.92º throwing sector that is centered on the throwing circle. The sector angle was chosen because it provides a sector whose bounds are easy to measure and lay out on a field (10 metres out from the center of the ring, 6 metres across). A violation of the rules results in a foul and the throw not being counted.

the men's hammer world record is held by Yuriy Sedykh, who threw at the 1986 European Athletics Championships in Stuttgart, West Germany on 30 August. The world record for the women's hammer is held by Anita Włodarczyk, who threw during the Kamila Skolimowska Memorial on 28 August 2016. Sedykh's 1986 world record has been noted for its longevity, and for dating from "a time when track and field was starting to realize the scale of performance-enhancing drug use" (AP). According to Russian doping whistleblower Grigory Rodchenkov, Sedykh was a heavy user of steroids, which Sedykh denied.

The throwing distance depends on the velocity and height at which the hammer is released, but also on other factors that are not under the athlete's control. In particular, Earth's rotation affects it via the location's latitude (due to the centrifugal force, the hammer will fly a bit further in a location closer to the equator) and to a lesser extent also via the throw's azimuth (i.e. its compass direction, due to Coriolis forces). According to a 2023 study, such effects are large enough that the top 20 world-record rankings for both men and women at the time could somewhat change if they were adjusted for latitude and azimuth.

Safety issues
Hammer throwing has been described as involving "inherent danger [...]. Athletes, coaches, and spectators participating in the event are at risk; steel hammers [...] are hurled through the air at great speeds, [travel] far distances, and [are] sometimes difficult to spot in flight." For example, hammer throws resulted in four deaths in Europe in 2000 alone, and have caused deaths and permanent brain damage injuries in the United States too.

To mitigate such risks, a C-shaped "hammer cage" was introduced, which is built around the throwing circle, preventing the hammer from flying off in unwanted directions. In 2004, the IAAF changed its rules to increase the mandatory height of hammer cages to 10m and reduce their "danger zone" angle to around 53°. The change also moved the cage gates further away from the throwing circle, thus reducing the risk of a misdirected hammer bouncing back on the thrower.

Men

 * Correct as of April 2024.

Annulled marks

 * Ivan Tsikhan of Belarus also threw 86.73 in Brest on 3 July 2005. This performance was annulled due to doping offences.

Women

 * Correct as of May 2024.

Annulled marks
The following athletes had their performances (over 77.00 m) annulled due to doping offences:
 * Tatyana Lysenko (Russia) 78.80 (2013) and 78.15 (2013).
 * Aksana Miankova (Belarus) 78.69 and 78.19 (both 2012).
 * Gulfiya Agafonova (Russia) 77.36 (2007).

title: Hammer throw


text:
Decathlon

The decathlon is a combined event in athletics consisting of 10 track and field events. The word "decathlon" was formed, in analogy to the word "pentathlon", from Greek δέκα (déka, meaning "ten") and ἄθλος (áthlos, or ἄθλον, áthlon, meaning "contest" or "prize"). Events are held over two consecutive days and the winners are determined by the combined performance in all. Performance is judged on a points system in each event, not by the position achieved. The decathlon is contested mainly by male athletes, while female athletes typically compete in the heptathlon.

Traditionally, the title of "World's Greatest Athlete" has been given to the person who wins the decathlon. This began when Gustav V of Sweden told Jim Thorpe, "Sir, you are the world's greatest athlete" after Thorpe won the decathlon at the Stockholm Olympics in 1912.

The event is similar to the pentathlon held at the ancient Greek Olympics, and also similar to a competition called an "all-around", which was contested at the United States amateur championships in 1884. Another all-around was held at the 1904 Summer Olympics. The modern decathlon first appeared at the 1912 Games.

In modern athletics, the 10 events are: 100 metres, 400 metres, 1500 metres, 110 metre hurdles, long jump, high jump, pole vault, discus throw, javelin throw, and shotput. The current official decathlon world record holder is French athlete Kevin Mayer, who scored a total of 9,126 points at the 2018 Décastar in France.

Historical background
The decathlon developed from the ancient pentathlon competitions held at the ancient Greek Olympics. Pentathlons involved five disciplines – long jump, discus throw, javelin throw, sprint and a wrestling match. Introduced in Olympia during 708 BC, this competition was extremely popular for many centuries.

A ten-event competition known as the "all-around" or "all-round" championship, similar to the modern decathlon, was first contested at the United States amateur championships in 1884 and reached a consistent form by 1890. While an all-around event was held at the 1904 Summer Olympics, whether it was an official Olympic event has been disputed.

The modern decathlon first appeared in the Olympic athletics program at the 1912 Games in Stockholm.

Men's decathlon
The vast majority of international and top-level men's decathlons are divided into a two-day competition, with the track and field events held in the order below. Traditionally, all decathletes who finish the event, rather than just the winner or medal-winning athletes, do a round of honour together after the competition. The current world record holder is Kevin Mayer from France with 9126 points which he set on September 16, 2018, in Talence, France.

 * Day 1
 * 100 metres
 * Long jump
 * Shot put
 * High jump
 * 400 metres

 * Day 2
 * 110 metres hurdles
 * Discus throw
 * Pole vault
 * Javelin throw
 * 1500 metres

Women's decathlon
At major championships, the women's equivalent of the decathlon is the seven-event heptathlon; before 1981 it was the five-event pentathlon. However, in 2001, the IAAF (now World Athletics) approved scoring tables for a women's decathlon; the current world record holder is Austra Skujytė of Lithuania, with 8,358. Women's disciplines differ from men's in the same way as for standalone events: the shot, discus, and javelin weigh less, and the sprint hurdles use lower hurdles over 100 m rather than 110 m. The points tables used are the same as for the heptathlon in the shared events. The schedule of events differs from the men's decathlon, with the field events switched between day one and day two; this is to avoid scheduling conflicts when men's and women's decathlon competitions take place simultaneously.

 * Day 1
 * 100 metres
 * Discus throw
 * Pole vault
 * Javelin throw
 * 400 metres

 * Day 2
 * 100 metres hurdles
 * Long jump
 * Shot put
 * High jump
 * 1500 metres

One hour
The one-hour decathlon is a special type of decathlon in which the athletes have to start the last of ten events (1500 m) within sixty minutes of the start of the first event. The world record holder is Czech decathlete Robert Změlík, who achieved 7,897 points at a meeting in Ostrava, Czechoslovakia, in 1992.

Masters athletics
In Masters athletics, performance scores are age graded before being applied to the standard scoring table. This way, marks that would be competitive within an age division can get rated, even if those marks would not appear on the scale designed for younger age groups. Additionally, like women, the age divisions use different implement weights and lower hurdles. Based on this system, German Rolf Geese in the M60 division and American Robert Hewitt in the M80 divisions have set their respective world records over 8,000 points. Using the same scale, Nadine O'Connor scored 10,234 points in the W65 division, the highest decathlon score ever recorded.

Points system
The 2001 IAAF points tables use the following formulae:
 * Points = $INT(A(B — P)^{C})$ for track events (faster time produces a higher score)
 * Points = $INT(A(P — B)^{C})$ for field events (greater distance or height produces a higher score)

A, B and C are parameters that vary by discipline, as shown in the table on the right, while P is the performance by the athlete, measured in seconds (running), metres (throwing), or centimetres (jumping).

The decathlon tables should not be confused with the scoring tables compiled by Bojidar Spiriev, to allow comparison of the relative quality of performances by athletes in different events. On those tables, for example, a decathlon score of 9,006 points equates to 1,265 "comparison points", the same number as a triple jump of 18 m.

Benchmarks
Split evenly between the events, the following table shows the benchmark levels needed to earn 1,000, 900, 800, and 700 points in each sport.

Records
The official decathlon world record holder is Kevin Mayer of France, with a score of 9,126 points set during the 2018 Décastar in Talence, France, which was ratified by World Athletics.

The previous record from Ashton Eaton (9,045 points):

Decathlon bests
The total decathlon score for all world records in the respective events would be 12,629. The total decathlon score for all the best performances achieved during decathlons is 10,630. The Difference column shows the difference in points between the decathlon points that the individual current world record would be awarded and the points awarded to the current decathlon record for that event. The relative differences in points are much higher in throwing events than in running and jumping events.

Decathlon bests are only recognized when an athlete completes the ten-event competition with a score of over 7,000 points.

All-time top 25 men

 * Correct as of June 2024.

All-time top performances women ≥ 8,000 pts

 * Correct as of September 2023.

Continental competitions

 * African Combined Events Championships
 * European Cup Combined Events
 * Oceania Combined Events Championships
 * Pan American Combined Events Cup

Other

 * IAAF Combined Events Challenge
 * Multistars
 * Hypo-Meeting
 * TNT - Fortuna Meeting
 * Erdgas Mehrkampf-Meeting
 * Décastar

National records
Equal or superior to 8,000 pts:
 * Updated 18 June 2024.

Under-20 records
The world decathlon under-20 record is held by Niklas Kaul, of Germany, who scored 8,435 points at the European U20 Championships in Grosseto, Italy, from 22 to 23 July 2017.

The world decathlon under-20 record using senior implements is held by Torsten Voss, of East Germany, who scored 8,397 points in Erfurt, East Germany, from 6–7 July 1982. This was the last record to be ratified because it is no longer a World Athletics under-20 record event.

Key: NWI = No Wind Indication

Key: + = Senior implements * = 6-kg shot, 1.067-m hurdles, 1.75-kg discus A = Altitude (over 1,000 m)

Decathlon under-20 bests
(Within a completed decathlon scoring more than 7,000 points)

Other multiple event contests

 * Aquathlon
 * Biathlon
 * Chess-boxing
 * CrossFit Games
 * Duathlon
 * Heptathlon
 * Icosathlon or double decathlon
 * Modern pentathlon
 * Nordic combined
 * Octathlon
 * Omnium
 * Quadrathlon
 * Triathlon

title: Decathlon