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Economic Classroom Experiments/The Wallet Game

Hand Run Version
Students bid for an object in a first-price auction. Each receives an independently drawn signal of the value of the object. The actual value is the sum of the signal.

Objectives for learning (Intended Learning Outcomes)

 * 1) Strengthening understanding of rules behind first-price auction.
 * 2) Concept of common value auction but private information about value.
 * 3) Intuition behind Bayes’ Rule. (Given that you win, the value of the others’ signals are lower.)
 * 4) Understand of the Winner’s curse.

Suitable modules.
Financial Markets and Decisions, Advanced/MSc Micro.

Level (year of programme):
Third year or MSc or MBA.

Prerequisite knowledge:
Knowledge of first price auctions.

Procedures/tips for instructors
Divide students in three groups (or how many bidders you want). Give the students index cards with randomly drawn signals [0,10] written on them. (You can get these from random numbers excel file.) Write their group (A,B or C) on the card for them (they may forget). Have them write their bids on the cards. Collect the cards and show bids, signals on the board. Determine winner and profit of the winner. Repeat one or two times.

Tip. You may want to write 4 numbers per card and randomly choose one to count. Worthwhile to write all 4 bids on the board and chose the one that counts after all numbers are displayed. (The random selection process can be done by flipping a coin twice (HH is 1, HT is 2, TH is 3, TT is 4) or writing the numbers 1 to 4 on the slips of paper and have one student select the winner.

Tip. For excitement you can pay (or get paid) for the winner. Use a conversion such as winnings are divided by 10 and given in pounds.

Tip. Group sizes should not be larger than 3 to 4 students. For larger classes, either increase the number of groups in the game or randomly select a subset of groups that count in the experiment. For instance if the class size is 60, you can have 20 groups of 3 and select 4 of these 20 groups to count (writing the bids on the board and the value is the sum of only these 4 groups).

The equilibrium bidding is described by $$b=\frac{(N+2)(N-1)}{2N}\cdot V$$ (see slides for derivation). For N=2, this is just b=V.

Topics/questions for class discussion
Can be described as a takeover battles where bidder 1 knows the value of one of the target's divisions and bidder 2 knows the value of the other division.

Myopia would have one think the value is $$N \cdot V$$ and bid $$(N-1)/N$$ times this equals $$(N-1)\cdot V$$. Actual expected value is $$(N-1)\cdot {V\over 2}+V=(N+1)\cdot {V \over 2}$$. Another possibility is that expect everyone else’s signal to be ½ times highest possible signal. Then using the above analysis expected value is $$V+{1\over 2} \cdot 10\cdot (N-1). $$ Hence, in both cases there could be a winner’s curse.

As N increases, your information becomes less useful, however, the competition becomes fiercer. If true value were average of the signals (rather than sum), then a graph of bid/V vs. N looks like. The above graph shows that competition increases bids for smaller N, Winner’s curse hurts bids more for higher N.

What happens when N is large? Your bid approaches the expected value of the object if you win.

Instructions for students.

 * You know how much money is in your wallet.
 * You do not know how much money is in the wallet of others.
 * Each wallet has money is drawn uniformly on [0,10].
 * We will run a first-price auction on the sum of three wallets (including yours).

also see slides.

Results and feedback:
Most groups bid $$3+0.8\cdot V$$, i.e., overbidding for all signals but particularly for low signals.

Computerized Experiment
Students bid for an object in a first-price auction. Each receives an independently drawn signal of the value of the object. The actual value is the average of the signals.

Procedure
This experiment is run on Charlie Holt’s website. See tip sheet for his website.

For an introduction see http://veconlab.econ.virginia.edu/cv/cv.php

To set up a session http://veconlab.econ.virginia.edu/cv/cv_admin_login.php

The equilibrium bidding is described by $$b=\frac{(N+2)\cdot(N-1)}{(2N\cdot N)} \cdot V$$ (see slides for derivation). For $$N=2$$, this is just $$b=V/2$$.

Further reading:

 * Auctions with Almost Common Values: The "Wallet Game" and its Applications European Economic Review, 1998. Paul Klemperer. http://www.nuff.ox.ac.uk/economics/papers/1998/w3/wallwebb.pdf

 * Ch. 21 of Webgames and Strategy: Recipes for Interactive Learning, Charles Holt, forthcoming, Addison-Wesley, 2006.
 * Holt and Sherman (2000), ""Risk Aversion and the Winner's Curse,"," Working Paper, University of Virginia. http://www.people.virginia.edu/~cah2k/wincurse.pdf

This page was first created by Toddkaplan 10:07, 9 April 2007 (UTC)


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Instructional design/Psychomotor behaviors/Strategies in Psychomotor Assessment

Introduction
This lesson will focus on strategies for assessment of psychomotor skills.

The Psychomotor Domain is skill based and refers to the learning of physical skills. Physical skills are the ability move, act, or manually manipulate the body to perform a physical movement. There are three instructional levels; imitation, practice, and habit that were defined in Introduction to the Psychomotor Behaviors article.

Assessment of the psychomotor domain requires an instructor to grade the activity without the use of a paper and pencil test. Psychomotor skills need to be performed and observed to determine mastery of the skill.

Learning Objectives for this lesson:

 * Learners will be able to give examples of objectives that fall into the psychomotor domain
 * Learners will be able to construct a checklist for evaluating psychomotor objectives

You will be asked to complete two Learning Activities associated with this lesson.

Begin with the Objectives
As with any learning activity, assessment begins with the learning objectives. Objectives in the psychomotor domain are created under the same criteria as objectives in the other domains. Creation of learning objectives are beyond the scope of this article.

Examples of Objectives in the Psychomotor Domain
Assessment of any of these example objectives can be accomplished through observation by the evaluator/instructor.

Sports:
 * Student will demonstrate effective technique when performing 50 bicycle crunches within 2 minutes.

Life Skills:
 * Student will prepare the proper amount of dry spaghetti pasta for 4 adults using the correct process resulting in properly prepared pasta.

Oftentimes objectives from the psychomotor domain contain certain key words like those listed in the table below.

Learning Activity 1
Print out the Psychomotor Objectives WorkSheet and place a check mark next to those objectives listed that are examples of objectives that fall into the psychomotor domain.

Self-Check

When you have completed the Psychomotor Objectives Worksheet compare your answers to the Psychomotor Objectives Answer Sheet.

Creating Assessment Checklists for the Psychomotor Domain
Using one of our example objectives from the previous section:

 * Student will demonstrate effective technique when performing 50 bicycle crunches within 2 minutes.

Using the Assessment Checklist template we will contruct a checklist that will help the instructor assess the mastery of the student in meeting the objective.

The first step is to determine the learning outcome, which has already been identified above Student will demonstrate effective technique when performing 50 bicycle crunches within 2 minutes. Now we are assuming that the evaluator or instructor is already an expert in performing bicycle crunches. However, here we will assume first that a description of the proper technique is necessary. It is also a good idea to include it in your checklist for the student so they understand the required expectation.

Description: Each individual must lie on their back and put their hands behind their head. Next they raise their legs so their thighs are perpendicular to the floor and their lower legs are parallel to the floor. The individual will curl up and bring their left elbow toward their right side while drawing their right knee in to meet it. It is like the individual is riding a bike; alternate sides, continuing the motion back and forth. The individual should not flap their elbow across their body; they actually rotate their shoulder across and squeeze their abs.

We also need to decribe the criteria that the student is being assessed.

Directions: Each individual must perform 50 bicycle crunches demonstrating effective technique. Each individual must complete the bicycle crunches within 2 minutes without pausing

Now we determine the scale and the criteria for that scale.

A common scale is outlined.

 Scale
 * 4 (excellent) – Performs the bicycle crunches flawlessly. Does not need to check. position, does not pause. Completes 50 bicycle crunches without pausing within the 2 minutes.
 * 3 – Performs the bicycle crunches but is somewhat unsteady. Completes the bicycle crunches within 2 minutes.
 * 2 – Performs the bicycle crunches but is somewhat unsteady. May pause one or more times. Takes more than 2 minutes to complete the bicycle crunches.
 * 1 – the bicycle crunches but is very unsteady, may pause one or more times, and/or takes more than 2 minutes.
 * 0 – Cannot complete a bicycle crunch correctly

The last item for the checklist outlines the conditions for assessment.

Conditions of Assessment
 * Assessment occurs only during the bicycle crunch phase.
 * The individual indicates when the assessment should begin.
 * The assessment ends as soon as the individual reaches 50 bicycle crunch count, 2 minutes has elapsed, or the individual tells the evaluator they want to stop.

To see the complete Assessment Checklist for this objective see the Bicycle Crunches article.

Learning Activity 2
Using the objective below and the Assessment Checklist template create an assessment checklist for that objective.

Student will prepare the proper amount of dry spaghetti pasta for 4 adults using the correct process resulting in properly prepared pasta.

Remember the steps to creating the checklist.

Self Check

To check your checklist click on the corresponding link below.

 * Pasta

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


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C Source Code/Functions

This page is about computer programming functions. For mathematical functions, see Functions (mathematics).

This example is on functions. With Functions you need to state the return type of the function. Either int or void. Int is value used for returning something to a call, mainly used for returning integers such as the add function in the following program. Void is used for functions that don't return a value or you don't want to return a value. You must use int or void in every function you make. Take a look at the following program:

You could have done this(it really doesn't make a difference):

title: C Source Code/Functions


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Valuation of options using lottery ticket securities

Problem. Valuation of derivatives in incomplete markets requires specification of risk tolerance of agents. The standard way of specifying this is via utility functions and indifference pricing. A one parameter utility function is derived and from this Hodges indifference prices are calculated.

The limitations of this approach are:

 * utility functions are not observable and it is difficult to derive the utility function of an investor from observable items
 * utility functions mix the concepts of utility and risk aversion
 * utility functions do not allow for risk-seeking behavior
 * using utility pricing for derivative pricing requires the derivation of a market utility. However it is unclear how this market utility function arises from the individual utility function of individual investors.  One standard assumption is to assume that all market traders have a standard utility function, but if this were the case there would be no reason for markets to exist.

We propose an alternate method of specifying risk behavior using a lottery ticket security, and use this risk profile framework to price standard European options. A lottery ticket security is a security with that has a gain or less of x with probability p. We then specify an agents risk profile by determining what the agent is willing to pay or loss for the security and we specify this with a function

$$ \pi(p, x) $$

We include the follow constraints for the lottery security function which describe the limits of the payoff in cases where there is complete certainty.

$$ \pi(0, x) = 0 $$ $$ \pi(p, 0) = 0 $$ $$ \pi(1, x) = x $$

And we include the following conditions that assert a larger payoff as either probability or payoff increases:

$$ \frac{\partial \pi}{\partial p} > 0 $$ $$ \frac{\partial \pi}{\partial x} > 0 $$

The risk-neutral payoff function can be specified as follows

$$ \pi(p, x) = px $$

and we make the assertion that payoffs become risk neutral as the value at risk becomes small.

$$ \lim_{x\rightarrow 0} \pi(p, x) = px $$

To value a payoff for a standard option, we need to derive the value of an option of f(u) given that the probability distribution function for the payoff is p(u). To do this let consider an lottery ticket security that pays one dollar if a coin reads heads and two dollars if the coin reads tails. These two securities can be represented as

$$ \pi_{head}(0.5, 1) $$ $$ \pi_{tail}(0.5, 2) $$

Combining these securities we have a certain payoff of $1 with a 0.5 probability of another $1 payoff or

$$ 1.0 + \pi_(0.5, 1) $$

Applying this argument to the continuous limit we derive the pricing function for options in the $$ \int_0^\infty \frac{\partial \pi}{\partial x}(P(0< f < x), x) dx - \int_{-\infty}^{0} \frac{\partial \pi}{\partial x}(P(x < f < 0), x) dx $$


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Exploring Intersonal Topics/Issues to Help Plan your Strategy

Introduction
Welcome to the lesson on Identifying Topics to Help Plan your Strategy! This lesson will provide information, examples, research and resources that relate to Interpersonal Topics. The purpose of the lesson is to help you define the specific issues and topics of your training; to find related ideas and research you can use to develop strategies; to take what information you have about your project, and locate resources, information and theories that are directly applicable to it.

In designing instruction, how will you know what topics and issues to include?

Perhaps you have been directed to design a course about something of a "personal" or "interpersonal" nature. Your employer may have asked you to to develop training to help people get along better, to help teams work together more effectively, or to help managers be better bosses. Perhaps your employer asked you to design an activity to decrease the arguing between sales reps, or a non-profit family group wants you to develop training to improve parent teen relationships.

The purpose of this lesson is to serve as a springboard; it will provide examples of situations and issues as they relate to interpersonal topics. You can use this lesson if you have a vague idea of what you want, but aren't sure exactly where to start. You may have an idea about a subject, but don't know what to call it, or how to do research to find strategies, activities and information. Perhaps you don't know how your ideas fit within a broader topic, or how to get more information about the subject. You may know your objective, but aren't sure what research has been done before or what ideas and theories are available on the topic. This lesson can help you in these areas.

What You will Do In This Lesson

This lesson will explore issues, topic and situations that fall within the Interpersonal Domain. You will be reading about which topics and issues are relevant or related to Interpersonal Behavior. You’ll participate in activities to match words and concepts with broad interpersonal issues and situations. For example, you may find concepts like, “insensitive boss” or “too much work” or “loneliness” or “anger management” and will see how they relate to broader topics.

You will read about research, activities and theorists who focus on Interpersonal Topics: you’ll read about a specific issue, who wrote about it, and what they discovered or developed on that topic. You’ll also have a chance to delve within yourself and your experiences, to see if you can identify any other topics, and generate information you wish to add to the Wiki to help others.

Objectives

After completing this course, you will be able to evaluate which topics/issues and situations would be most relevant to your specific objective. To do this, you will be able to distinguish between topics that fall within the Interpersonal Domain and other domains.

After identifying that your instruction is within the “interpersonal” domain, you will be able to compare and contrast various topics, and their related research, in order to select which topics and methods best meet your objectives.

If you have not been assigned a specific topic or task for your project, you will be able to generate ideas from the examples provided in the lesson, to meet your objectives.

After matching your objective with relevant issues and topics within the Interpersonal domain, you will be able to select, create, identify, develop or find activities and strategies related to the topics or issues you select.

You will also be able to integrate suitable ideas and research about Interpersonal Domain topics, into your instructional design plan.


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Wikiversity talk:Help desk/Archive 3

This is an orphan page. Sounds like it belongs in the Political Science department. Anyone? The Jade Knight 11:57, 9 April 2007 (UTC)
 * Remerged into the help desk from article space. Ottava Rima (talk) 23:05, 1 June 2010 (UTC)

title: Wikiversity talk:Help desk/Archive 3


text: User:Fubsadoo

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Economic Classroom Experiments

This page refers to information on economic classroom experiments and related material.

Numbers insist that an economic model of giving, can produce an economy of abundance in that, if all were to give consistently, a substantial amount, into, let's picture it as a river of abundance. What you do not need for right now goes to the river. And what you need when you need it comes from the river, for the most part. We see something similar to this in paying taxes to support the public welfare system. The problem is that these welfare systems that are in place, are terribly inefficient. And more money goes to paying employees of the system to manage the lesser amount of money actually going to public welfare.

I challenge anyone to run the numbers and prove the giving river wrong. Also, a challenge to anyone to say the public welfare system is not riddled with inefficiency...

Why use experiments in teaching economics?

 * 1) They help students to understand an otherwise abstract model. In the double auction experiment they experience, for example, how demand and supply drive the market towards equilibrium. It's learning by doing.
 * 2) To show that economic theory can work (for instance, in a Bertrand game). This is important because students or the general public are often sceptical about the use of mathematical analysis in economics.
 * 3) To show that economic theory might not work (for instance, in an ultimatum game). This quickly leads to questions on the current frontier of our science.
 * 4) An experiment can make it easier for students to grasp a threshold concept like Nash equilibrium.

List of Experiments

 * 1) The Twenty pound auction
 * 2) The Wallet Game
 * 3) The Ultimatum and the Dictator Bargaining Games
 * 4) The Public Good Game
 * 5) Private Value Auctions
 * 6) The Insurance Game
 * 7) Currency Attack
 * 8) Bertrand Competition
 * 9) American Call Option
 * 10) Diamond Dybvig Experiment
 * 11) Hold-Up Problem
 * 12) Kiyotaki Wright Hazlett Experiment
 * 13) Lemon Game
 * 14) Miniconomy
 * 15) Monty Hall Paradox
 * 16) Network Externalities
 * 17) Price Discrimination
 * 18) Team Draft
 * 19) Warren Buffett
 * 20) The Guessing Game
 * 21) Search
 * 22) Pit Market
 * 23) Complete List of Interactive Experiments

title: Economic Classroom Experiments


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User:Fubsadoo/Introduction to Being A Kid

Intro
Being a kid is about having a sense of awe and wonder. It's about being able to see things as they are, without any prejudices that people pick up through life.

Things To Do
Here are some fun things to do that are best done with friends who are completely stressed.

Play With Food
Get some toast and add food colouring and vanilla extract. Cut a carrot into sticks and build a model with them, sticking them together with chocolate spread. Make the biggest sandwich the world has ever seen. You'll only do it once - doing it twice ruins it - so it doesn't matter if it rots your teeth or makes you sick.

Look At The Clouds
Lie down on the ground and look up. Figure out what each cloud is, then make up ridiculous stories about them. Go bananas.

Look At The Sky
On a clear night, see how many stars you can see. Sure, find the real constellations, but they'll never be as good as the ones you make up.

Make A Dust Ball
Collect fluff. Computers are good for it, as well as the places that don't get dusted properly.

Lesson Objective

 * 1) Have a laugh. Or a smile, at least.
 * 2) Get your imagination going.

=Recommended Reading/Sources e.t.c.=

 * The Dangerous Book For Boys by Gonn Iggulden and Hal Iggulden. ISBN-9780007232741
 * "Fifty Dangerous Things (You Should Let Your Children Do)" by Gever Tulley


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User talk:Dieter

Image copyright problems

 * Your currently affected images are listed below. For each, please provide a license template and source. Thanks. – Mike.lifeguard | @en.wb 23:22, 13 February 2008 (UTC)

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User talk:Doce~enwikiversity

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Doce. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Doce~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:31, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:06, 19 April 2015 (UTC)

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Economic Classroom Experiments/Public Goods

The experiment illustrates the problem of public good provision as discussed in most microeconomics lectures or lectures on public economics. Participants experience how free riding hinders the efficient provision of a public good. We describe here a hand-run version, a computerized version is available at veconlab

Level
Any level

Prerequisite knowledge
None

Suitable modules
Microeconomics, Public Economics

Intended learning outcomes
Participants in the experiment will

 * 1) be made familiar with a simple problem of public good provision
 * 2) experience the problem of free riding and how it hinders efficient public good provision

Description of the Experiment
At the beginning of the lesson each student receives a number of identical sheets of paper, one for each round played (we conducted 3 rounds). On every page there is the same introduction and underneath a box to fill by the participants. In it each participant must choose how much to invest into a private account and how much into a public account. The total amount of investments must be equal to ten pounds. Each person in the group will receive an equal share of the money in the group investment regardless of the amount invested in the group. Every page is numbered and the first page is used for the first round out of three. The students are asked to read through the instructions and afterwards the experiment instructor/teacher will repeat the most important points.

Instructions
“You will be in a group of 10. Each of you is requested to make a decision on how to invest £10. There is a private account and a group account. For each pound invested in the private account, you will receive one pound. Each pound invested in the group account will yield 3 pounds for the group. Each person in the group will receive an equal share (one-tenth) of the money in the group account regardless of the individual contribution.

The first investment decision will be made on the decision sheet with the number 1 on top. Then, we will collect only those sheets. Ten participants will be randomly selected. They will form the group of contibuters in the first round. We will evaluate their decisions and then announce the investments made and the payoffs received. Afterwards, we will repeat this procedure with the decision sheets for the 2nd and then for the 3rd round. Thus we will play 3 rounds overall.

Out of the thirty decision sheets collected, one participant will be selected at random at the end of the lecture. He or she will be paid in cash the amount from the corresponding period. Only the name of this winner will be revealed. Everything else remains anonymous, in particular whose decision sheets have been collected in which round and how much the winner earned.

Please make your first decision now and fill it into the first decision sheet. Ensure that no-one can see your choice."

Description of the Experiment, continued
In the experiment the group of 10 people selected is only a virtual group; every student decides alone and has no opportunity to consult other students. At the end of each round 10 decision sheets are chosen randomly and their results are taken to construct one “real” group. This makes it possible to calculate the payments for the 10 different players. The results are projected onto the screen so the audience can see the results for this representative group after each round. This is important to make learning possible. The instructor should not comment on the results and thereby influence the students´ decisions in the next two rounds. For the success of the experiment it is crucial that the instructor doesn´t highlight the fact that the secure return of a private investment is obviously higher.

For a one pound group investment the player will only receive 30 pence whereas the return on a private investment is always one pound. A rational (and myopic) agent should hence only invest into the private account.

To give appropriate incentives one person will be chosen at random and paid in cash. The maximum amount someone could earn in any round is 37 Pounds, but this high amount is quite unlikely.

The box at the end of each page in which the students fill in their investment decision looks like this:

Procedure

 * 1) Distribution of the sheets to the students
 * 2) Students have 5 minutes to read the instructions
 * 3) Instructor/Teacher repeats the main information
 * 4) Participants make their decision and hand their decision sheets in
 * 5) 10 sheets are randomly chosen
 * 6) The answers of the “representative” group are filled into an Excel Spreadsheet which is projected onto a screen via a beamer (alternatively, a black or a whiteboard can used, in which case the results on the board should be carefully copied down for later class discussions.
 * 7) The sum of the group investment is calculated and then multiplied by three. This is divided by ten and is the payment each member of the group earns
 * 8) The payments of each group member are calculated as the sum of the above plus the money in the private account.
 * 9) The instructor announces the next round, which, as the last round, is played in the same fashion.
 * 10) After the third round the instructor discuss the results of the three rounds together with the students.
 * 11) At the end of the experiment one student, who is chosen by chance, receives the amount of money in cash which he has earned in one of the rounds.

Interpretation
The person who invests the lowest amount of money is the winner of the group. This result can be easily related to reality, those people who are not willing to pay for public goods and save their money reach the highest income or utility. Because some people are paying for public goods and other people can not be excluded from consuming them. The free rider makes the highest personal profit in a situation like this.

The free rider’s behaviour can be very advantageous for a handful of people but as the number of free riders increases their payments decrease. Why? Because the total sum society is willing to pay becomes smaller whilst the number of society members stays constant. This implies that people who do pay for the group are becoming worse off. They will learn this and change their behaviour and start free riding.

We are now in a situation of undersupply of public goods in a private economy where the people can decide how much they are willing to pay for the community. Obviously the sum of marginal willingness to pay for public goods is smaller than the actual demand. Thus we have an inefficient outcome which doesn´t fit the Samuelson Rule. The Samuelson Rule tells us to balance the marginal cost of public provision with the summation across households of marginal willingness to pay to reach a first best (efficient) solution.

When you compare the different rounds you can see that the number of free riders is increasing from round to round because of learning effects caused by the projection of the results from the representative group. However, the highest payment for each round is decreasing and the lowest payment is falling sharply because of a gerneal decline in contributions from round to round. That contributions are falling over time is a standard result in public good games. (Burland & Guala, 2005) Thus free riding which is rational at the micro level causes inefficiency at the macro level. All people in the group could be benefited in case that the number of free riders declines. The same outcome would result in an increase of the marginal willingness to pay of a large number of people within the group.

Students learned relatively quickly how to maximise their payment and therefore the experiment is well suited to show how free riding can cause inefficiency and influence the supply of public goods. The provided example-tables after each round have been quite inconstistent with the overall result and seem not to influence students. Because of the fact that nearly all students have been British it is not possible to see if British people free ride more than other citizens. On the whole, besides the group is consisting of hetergeneous people there is a general tendency towards lower contribution and more free-riding.

Game Theoretical Background
This experiment is set up similar to a prisoner dilemma situation. To reach the highest return everybody should cooperate and invest 10 pounds in the group. This outcome would be Pareto efficient. In a group of 10 people everybody would receive a payment of 30 pounds. However the dominant strategy is not cooperating and therefore rational players should free ride and invest all their money in private funds. In this way he/she can maximise his/her payments. But the other players will follow this strategy and the dominant strategy equilibrium would be that everybody invests nothing for the group and keeps the 10 pounds for himself. Then each player would receive only 10 pounds obviously this outcome is less for everybody. But in the long run this outcome will be reached because of learning effects of those players who invested in the group in the first rounds.

Results of the experiment
About 150 undergraduate BA and Economics students took part in the experiment in March 2006. The procedure was exactly as described above and the setup of the experiment was identical to the way described in the beginning. These are the results of the three rounds where we treated all students as one group. Answers which didn´t fit the instructions where not taken into account. Obviously the total group investment decreased constantly from the first to the second round. This means that more people decided to act as a free rider or reduced their investment for the group from round to round. Thus implies that the payment each member receives is declining also. In the third round the payment per member is only 64% of the payment in the first round.

When we have a look on the table which was showed on the blackbord after each round the results are difficult. After each round ten answer sheets have randomly been choosen and the group payments was calculated. In contrast to the overall result the group payments increased strongly from the first to the second round and thus the payments per member increased as well.

Therefore the decisions in round three have been very contrary. The value of the total group investment was halved in comparison to the second round and dropped even under the level of the overall result. Because of the controversial tables it is very hard to make any conslusions about the influence of the provided results on the decisions of the students. Burlando and Hey (1996) examined with different experiments that there is an effect on behaviour because of nationality differences. The results of this experiment do not provide an interpretation for differences in the behaviour because nearly all students have been British. To comment on this issue the same experiment must be run in other countries as well. Generally the contributions were declining and more and more students acted as free rider from round to round. This can be seen in the graph below. More and more people behaved as free rider or reduced their group investment.

First Round
How many students decided to act as a free rider in the first round? The following diagram makes it clear. About 36 students out of 156 (~23%) acted as free riders while only about 20 students (~13%) invested all their money in the group. However nearly 100 students (~65%) spent at least 5 pounds for the group. This is the reason why the overall amount of payment is so high.

Now we know how people decided to invest their 10 pounds. Leuthold (1983) pointed out that in similiar class experiments about public goods the average contribution was about 40 to 60%. This interpretation fits as well for this experiment. In the first round the average contribution to the public good was about 50% of the disposable budget. But what about the payment they got at the end of the first round? This table gives us the answer.

The highest earning in the first round was 25.61 pounds for all people who only invested privately. On the other side the lowest payment was 15.61 for everyone who spent all their money on the group investment. The ratio between the highest and the lowest payment is 164%, this means that the free rider receives 1.64 times the payment than the people who invested in the group. Recall that about 24% of the students earned 25.61 and about 14% earned only 15.61 pounds.

Second Round
The result in the second round shows that students are quick leaners. About 45 students out of 150 decided to be a free rider and the amount of people willing to pay at least 5 pounds for the group dropped dramatically.

Only about 65 students (43%) invested at least 5 pounds in the group while in the round before this amount was about 100 people. You can see the enourmous change in the behaviour of the students in the graph above. Thus the total group investment dropped and the payment per member decreased from 15.61 to 12.41 pounds per player. The difference in comparison in highest and lowest earning is even larger.

The difference increased from 164% to 183% because the lowest income fell stronger than the highest payment. The more people who behave as free riders the lower the highest possible earning will be because the total payment decreases too.

Third Round
What the experiment predicts and what happened in reality is that the players will learn to reallocate their investments. This reallocation implies that more and more players are becoming free riders or are investing less into the community.

This diagram makes it clear how the students changed their minds. In the third round only about 7% invested 10 pounds in the group while one third was investing nothing. Also the percentage of players who invested at least 5 pounds in the group dropped under 30%. However this rational behaviour implied that the payments per member decreased and thus the highest and lowest earnings decreased again.

As we can see in the little table the difference between the two antipodes had increased again due to the strong reduction of group investments. The next diagram on the other page shows us how many people (in %) invested between 0 and 10 pounds in the last round. In the first round 23% of the players where acting as free rider, in the third round this percentage rose to one third. Only about 8% invested all their money in the group while in the beginning it was 13%. About 28% of the students invested at least 5 pounds in the group whilst in the beginning 65% invested at least 5 pounds. The majority of students did not act as a free rider but reduced their amount for the group investment dramatically over the three rounds. Not only are free riders making the system inefficient it is also the behaviour of the majority who reduce the amount of money they are willing to spend for the society.

Differences between Gender
Due to the fact that the participating students signed their answer sheets we could analyse the results in more detail. First of all we looked for differences in the decision between female and male players.

As it is illustrated in the above table there was hardly any difference in the decision process between men and women. The prejudice that women care more about the welfare of the group does not hold true in this experiment.Contadictionary in similar public good experiments done in Isrealian Universities women seemed to free ride less than man. As well Israelian students free ride more than US American students taking part at the experiment (Kleiman & Rubinstein, 1996). However, we could not observe a differenct behaviour because of the sex of the students.

Differences between Programmes
Moreover we tested what was the influence on the student’s decisions in the experiment in course accordance to each student’s studies. We divided the students into three groups, Business Administration (BA), Economics and other studies. There were only few other students so we did not calculate the results for this group.

We created two new societies, one for BA students and one for Economic students only. Then we calculated the results which you can see above. At a glance there are hardly any differences between the decisions made by the two groups of students. However when we look at the results in more details we can see that the Economic students learn quicker than the other students. The reduction in the group investments in round two and three are larger. As we can see in the third round there are far more free riders from the economic students than the third round than Economics students the BA students. And BA students contribute about 20% more in the group in the third round. They pay on average about £ 10 whilst the Economics students only contribute about £ 8.

When we compare the results of the two groups with the overall, we can see that the groups do not really differ. About 40% of the Economics students behaved as free riders in the third round whilst overall only one third was perfectly selfish. The fact we can deduce is that Economic students realised earlier the advantages of free riding than the BA students.

Differences between Genders within Programmes
First we compared the results in BA between female and male students:

Business and Economics students:

The female students did an amazing job in the second round and changed their behaviour very strongly. A lot of the female students were free riding or reducing their group investment in the second round. The difference between the highest and the lowest income was already 200%. But in the third round girls changed their mind and increased their group investments. Thus the difference between the highest and lowest payment declined. The male students behaved ambiguously in the first round, a lot of them invested a high amount in the group and a large proportion of the group was free riding. Obviously the boys didn´t change their mind as fast as the girls and the results didn´t change so much in the second round. In the third round a large proportion of boys had learnt their lesson and decided to act as free rider. Therefore the inequality between highest and lowest payment was much higher than that of the girls. Female BA students obviously put a higher value on the group investment than their male collegues and reduced the inequality between highest and lowest income. Let’s see how the economics students worked. Obviously there are strong differences between female and male students. Nevertheless it was not really easy to come up to a conclusion because only 5 female students took part in the experiment while we had 15 male students.

Economics Students:

However boys and girls behaved quite differently to each other. While the majority of the girls acted as free rider in the second round they changed their behaviour like the female BA students in the third round. As you can see the investment in the group decreased enormously in the second round but increased again in the third round. The boys behaved like the average student in the overall results and more and more students acted as free rider from round to round.

Differences because of A-level math
We created two groups of economics and BA students who had A-levels (the 18+ qualification in the UK) in Mathematics and wanted to see if this had any influence on the results. In the second round the Economics students with A-levels in Mathematics seemed to be very quick learners and strongly reduced the amount invested in the group. However in the third round they decided to invest again more in the group and behaved differently to the overall results and the whole group of economic students.

Economics students

Business and Economics Students:

The BA students with A-levels behaved differently in comparison with the whole group of BA in the third round. They pay more in the third round then they did in the second round and contribute £ 12 on average whilst all BA students only contribute about £ 10. But in general, there are no significant differences from main importance. We can say that Alevels caused only a difference in the decision of Economics and BA students in the third round. In all other cases the results are pretty much the same with or without A-levels.

Statistical Testing of some Results
We examined the data with the help of the Software-program SPSS with the procedure of Regression with Optimal Scaling.

Influences on Group Investments
First we treated the dependent variables seperately (group investment 1, group investment 2, group investment 3) and we tried to identify which of the independent variables (gender, grades, and course) would have the biggest effect on the dependent variables. According to the Importance and the Beta values we can see which of the independent variables has more influence on the dependent variable (group investment 1). GCSE (Marks) with Importance=0.792 seems to have the biggest effect on group investment in round one.

In round two group investments are also strongly influenced by GCSE. With Importance= 0.616 the GCSE seems to have the major effect on the investments from the three independent variables.

In round three we can observe that the results are totally different to the two previous rounds. The independent variable (gender) seems to have the biggest influence on the group investment and the marks (GSCE), which had been in the previous rounds more important than the other independent variables, have only a very low importance=0.190.

In these three cases, which we have examined, the adjusted R square value is always close to zero. This implies that the results of the three regressions are not very reliable and we think that the impact of the independent variables on the dependent variables is relatively low. In other words, the kind of gender, programmes and the marks does not significantly influence the decisions in the experiment. We tried to find regressions which have significant results and therefore we treated the group investment in round three as the dependent variable and the group investments in previous rounds as independent variables. The adjusted R square value is 0.39 and much higher than in the regressions before, hence the result is more reliable. According to the importance values, the group investment in the second round has a strong influence on the group investment decisions in round three. The importance value is 0.8625 and the beta factor is 0.5701. Obviously the investment decisions in the second round are more important for the decisions in the third round than the investment decisions in

the first round. However this can be also the case because of similar decisions in round two and three which are linked to the learning process.

We also made a regression to predict the group investment in round two with the investment decision of round one. This linear regression shows very low R Square and Beta values and thus shows only a low statistically significance for a strong influence of the decision of round one on the decision in the next round.

Influences on Payments
We also carried out a regression where we took as the dependent variable the payments in round three and as independent variables the payments in the two rounds before. Again the adjusted R square value is 0.337 and shows us that not only these two regressors have an impact on the outcome in round three.

Payments in round one and two, seem to have almost the same affect on the payments in round three. However the payments of the previous rounds have an indirect influence on

the payments of the third round because the investment decisions are dependent on the payments.

Conclusion
The experiment shows an easy way to test how theoretical assumptions in a lecture. The results represent pretty much the theoretical hypothesis, that people will tend to behave as free riders in a environment of private supply of public goods. The detailed analysis of the results showed that students are learning quickly, and free riders students are increasing. In the end about a third of the players acted as free riders. Obvious differences did not occurre because of gender and the quality of marks. Economic students were slightly outperforming BA students in the third round. However, the differences are very small. In the analysis with regressions we could see that previous group investment decisions have an influence on later decisions. The same applies for payments but this was intuitive. For further ways of discussing the results with students we refer to Holt & Laury and their paper about classroom experiments.

Literature

 * Burlando, Roberto & Guala Francesco (2005): Heterogeneous Agents in Public Good Experiments. Experimental Economics. Vol. 8 pp. 35- 54.
 * Burlando, Roberto & Hey John D. (1997): Do Anglo-Saxons free-ride more? Journal of Public Economics. Vol. 64 pp. 41 – 60.
 * Holt, Charles A. & Laury Susan K. (1997): Classroom Games: Voluntary Provision of a Public Good. The Journal of Economic Perspectives. Vol. 11 pp. 209 – 215.
 * Leuthold, Jane H (1993): A Free Rider Experiment for the Large Class. The Journal of Economic Education. Vol 24. pp. 353 –


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Instructional design/Cognitive behaviors/Invariant Tasks: Principles for Learning

Back to Topic:Instructional Design > Cognitive behaviors > Invariant Tasks > Define >  Learn >  Teach >  Tactics >  Try It >  Example

Source: Invariant Tasks by Charles M. Reigeluth. Used by Permission.

Overview: Before you can figure out how to teach an invariant task, it is helpful to know how invariant tasks are learned. Different learning theories provide different perspectives on how they are learned. In this section, we provide a description from the perspective of behaviorist theory, cognitive / information processing theory, cognitive / schema theory, and constructivist theory. We then provide an integrated view of principles for learning invariant tasks.

Behaviorist Learning Theory
There are several kinds of behaviorist learning theories. You may be familiar with "conditioned response theory" developed by Pavlov, whereby a response that already occurs in the presence of one stimulus can be "conditioned" to occur following a different stimulus. This learning theory is very important for emotional learning, but has little relevance to most learning of invariant tasks.

Far more relevant is "reinforcement theory," first developed by E. L. Thorndike (1913). and further developed by B.F. Skinner and others. In reinforcement theory, an invariant task is viewed as a "response" and is learned when it becomes "associated" with an appropriate stimulus. For example, "3.14" is a response that should become associated with "Pi". This learning process occurs whenever "reinforcement" follows the response. For example, each time a learner responds with "3.14", a reinforcer such as "Right!" or "Good!" or even just a smile with a nod will increase the probability of the learner responding the same way in the future. With sufficient repetition of these stimulus-response-reinforcement events, the response will come to occur automatically in the presence of the stimulus.

Cognitive / Information Processing Theory
There are at least two major kinds of cognitive theory relevant to learning invariant tasks: information-processing theory and schema theory. According to the information-processing model of learning (see Figure 1 below), there is a series of stages by which new information is learned (Gagné, 1985). Information is received by receptors (such as the eyes and ears), from which it is passed to the sensory register where all of it is held, but for only a few hundredths of a second. At this point, selective perception acts as a filter which causes some aspects of the information to be ignored and others to be attended to. For example, the ears (receptors) receive the sounds comprising "Pi equals 3.14," along with various other background sounds, and all those sounds are passed on to the sensory register in the brain. Then through the selective perception process, some of the information (hopefully the "Pi equals 3.14 part) is attended to."

Figure: The Information-Processing Model of Learning

That information which is attended to is transformed and passed on to short-term memory, which can only contain a few items of information at a time (usually identified as 7+2 items, depending on their complexity). For example, if "Pi equals 3.14" is attended to, it is then passed on to short-term memory, where it might be said to "echo" for a few seconds, and the echoing can be prolonged through rehearsal." Items can persist in short-term memory for up to about 20 seconds without rehearsal, but with constant rehearsal they can be retained indefinitely.

Finally, the information may be passed to long-term memory. This process is called encoding. For example, if appropriate encoding processes are exercised to link the "Pi equals 3.14" with prior knowledge, then the information is passed on to long-term memory." It is likely that different types of knowledge are encoded in different ways, which is why they require different methods of instruction. It is typically only this stage which we call "learning", for information which is not passed on to long-term memory is lost (at least, it is not retrievable). It is necessary to turn to other theories, such as schema theory, for descriptions of how the encoding process may occur.

Cognitive / Schema Theory
The other major kind of cognitive theory is schema theory. It proposes that, when new knowledge is encoded, it is organized into schemas, which are networks of related pieces of knowledge. For example, an invariant task can be encoded as a new schema, complete with such contextual factors as conditions for its use, in which case it will be at least loosely related to other schemata, or more typically it can be assimilated into an existing schema. But more importantly for instructional purposes, specific elements of the invariant task can often be learned--or more accurately, retrieved--more easily by relating them to certain carefully selected prior knowledge, especially meaningful knowledge. For example, it is easier to remember the colors of the rainbow and their order (red, orange, yellow, green, blue, indigo, violet) by associating them with the name, "Roy G. Biv."

Constructivist Theory
In contrast to the objectivist views of learning from both the behaviorist and cognitive information processing theories presented above, constructivists do not subscribe to the notion that knowledge exists independent of the learner. Instead, constructivist theory is founded on the premise that knowledge is both individually constructed and socially coconstructed by learners as they interpret their experiences (Jonassen, 1990). Unlike the theories presented above which focus on how information is encoded into long term memory, constructivists focus on the way that knowledge is constructed by the learner in working memory (Mayer, 1999).

This difference in perspective on learning impacts how learning is supported. Given the constructivist emphasis on the learner’s experience, there is a strong focus on “learning in context”. Therefore, as described by Driscoll (2005, p. 393), constructivist conditions for learning typically include:
 * Embedding learning in complex, realistic and relevant environments
 * Providing for social negotiation
 * Supporting multiple perspectives and the use of multiple modes of representation
 * Encouraging ownership in learning
 * Nurturing self awareness of the knowledge construction process

An Integrated View
There are two major degrees of memorization: recognition and recall. In recognition for a list, the name of the list and an item from the list are both presented to the learner, who indicates whether or not the item belongs to the list: "Which of the following were Presidents of the United States: Abraham Lincoln, Fred Washington, . . . ?" For an ordered list, two or more items from the list are presented or performed, and you indicate whether or not they are in the right order. In recall for a list, the name of the list is presented, and you have to retrieve the items from your own memory: "List ten Presidents of the United States below" or "Change the oil in your car."

Does association learning occur the same way? An association, in its simplest form, has two elements which must be paired together (associated with each other): a stimulus, which is presented to the learner, and a response (either mental or physical), which is provided by the learner. A state with its capital, a person with her name, a painting with its artist, a symbol with its name, and the letters of the alphabet with the finger movement necessary to type each on a standard keyboard are all cases in point. In its more complex forms, an association can have many elements which are all to be associated with each other, such as a person, a place, a date, and (the name of) an event. In this case, you usually have one stimulus and multiple responses. For example, "the discovery of America" might be associated with "Christopher Columbus," "1492," "Queen Isabel of Spain," and "the Nina, Pinta, and Santa Maria."

In recognition for an association, the stimulus and a response are both presented, and you indicate whether or not they are a correct match, or you match up the correct ones. "Was the Declaration of Independence signed in 1770?" is such an item. In recall for an association, the stimulus is presented, and you have to retrieve the response from your own memory. "When was the Declaration of Independence signed?" is a case in point. In spite of these differences, association learning is similar to list learning in that it is a rote (nonmeaningful) form of learning which is committed to memory primarily by repetition. It is also acquired gradually over time with practice, and it can be learned to the point of recognition or to the point of recall. Learning a rote procedure may require learning two things: when to do each action, and how to do each action. But in many cases, the learners may already know how to do each action, such as an experienced computer user learning how to use a particular web browser to search the Internet. That learner just needs to learn what actions to take when, not how to take them.

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Instructional design/Cognitive behaviors/Invariant Tasks: Principles for Teaching

Back to Topic:Instructional Design > Cognitive behaviors > Invariant Tasks > Define >  Learn >  Teach >  Tactics >  Try It >  Example

Source: Invariant Tasks by Charles M. Reigeluth. Used by Permission.

Overview: In the next two sections of this lesson, we address tactics to teach invariant tasks. In this section, we review the tactics associated with the Drill and Practice Model of Instruction. In the next section, we consider how to incorporate Drill and Practice tactics into a game based format. Please continue this lesson by viewing the short video presentation below and by reviewing the key Drill and Practice tactics, including a closer look at mnemonics, flash cards and feedback.

Video Presentation: Teaching Invariant Tasks
Please view the short video presentation linked here which highlights the key tactics associated with the Drill and Practice Model of Instruction.

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Teaching Invariant Tasks: The Drill and Practice Model of Instruction
As highlighted within the video, the following instructional tactics facilitate memorization. These tactics collectively are referred to as the "Drill and Practice Model of Instruction."

 * Select subject-matter content and decide what to teach based on need
 * Routine tactics include:
 * Presentation: Present the subject matter and give directions on the focus area
 * Practice: Allow time to review the material and actively practice
 * Feedback: Provide informational and motivation feedback (see below)
 * Enrichment tactics for difficult content include:
 * Chunking: Break content into smaller "chunks"
 * Repetition: Repeat the practice steps
 * Mnemonic: Incorporate memory aids (see below)
 * Prompting: Prompt learner to respond
 * Motivational tactics should build learner:
 * Confidence
 * Satisfaction
 * Review material

A Closer Look at Mnemonics
As noted above, mnemonics are memory aids which add meaning. The following highlights ways to incorporate mnemonics as a memory aid:

 * By tying items together using first letter mnemonics to:

 * A. Make a word or acronym, for example:

 * K-CAASE" to remember Bloom's types of learning:
 * Knowledge, Comprehension, Application, Analysis, Synthesis, Evaluation.

 * "ROY G. BIV" to remember the order of the colors in the rainbow:
 * Red, Orange, Yellow, Green, Blue, Indigo, Violet.

 * B. Make a phrase or sentence, for example:

 * "My Very Earnest Mother Just Served Us Nine Pickles" to remember the order of the planets from the sun:
 * Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto.

 * By associating with something you know by using:

 * Ideas or "tricks", for example:

 * To remember that Augusta is the capital of Maine, think of how everyone likes to go to Maine for vacations in August.

 * Visuals or images, for example:

 * To remember the mnemonic, K-CAASE, think of a case that is so full of K's that it is stretched, hence the AA instead of just A.

 * To remember "My Very Earnest Mother . . . ", provide a picture of a mother earnestly serving nine kids one pickle each.

 * By adding a pattern:
 * A song mnemonic, such as the the alphabet song.
 * A rhyme mnemonic, such as: "I before e, except after c, or when it says "aye", as in neighbor or rein."

Additional Examples: Additional mnemonics examples can be found at:
 * www.memory-key.com
 * www.fun-with-words.com
 * www.netnaut.com

Flash Cards
To facilitate practice, try flash cards. Here are some examples of tools to create flash cards:
 * Memorizable.com - wiki-based flash cards
 * jMemborize.org - open-source software to create flash cards

Providing Feedback
As shown in the video, both informational and motivational feedback play an important role in teaching invariant tasks. Consider these principles when providing feedback:

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text:
Invariant Tasks: Tactics for Teaching

Back to Topic:Instructional Design > Cognitive behaviors > Invariant Tasks > Define >  Learn >  Teach >  Tactics >  Try It >  Example

Source: Invariant Tasks by Charles M. Reigeluth. Used by Permission.

Overview: As described previously, the Drill and Practice Model of Instruction is often used to teach invariant tasks, such as to facilitate memorization of facts. These instructional tactics can be further enhanced by incorporating them into game based instruction. Within this section of the lesson, a video demonstration of tactics to teach invariant tasks using a game based format is presented.

Video Presentation: Tactics for Teaching - A Game Example
Please view the short video presentation linked here which demonstrates how invariant tasks can be taught within a game based scenario. Note that the basic format of the game builds upon the Generic Board Game (GBG) format as presented in Framegames By Thiagi by Sivasailam "Thiagi" Thiagarajan - see also The Thiagi Group web site for more information on Framegames.

When watching the video, note how the routine Drill and Practice tactics of presentation, practice and feedback are present within the game. In addition, repetition, review and feedback (both informational and motivational) are built into both the play of the game, as well as the debrief session.

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title: Invariant Tasks: Tactics for Teaching