Nobuyuki Hanaki
email: nobuyuki.hanaki@univ-amu.fr

Nicolas Jacquemet
email: nicolas.jacquemet@univ-lorraine.fr

Stéphane Luchini
email: stephane.luchini@univ-amu.fr

Adam Zylbersztejn
email: zylbersztejn@gmail.com.

Juergen Bracht

Colin Camerer

Guillaume Fréchette

Asen Ivanov

Frédéric Koessler

Rosemarie Nagel

Ariel Rubinstein

Jason F Shogren

Jean-Marc Tallon

Antoine Terracol

Marie-Claire Villeval

Jacquemet Hanaki

Cognitive Ability and the Effect of Strategic Uncertainty

Keywords: Strategic Uncertainty, Robot, Bounded Rationality, Experiment JEL Classification: C92, D83

How is one's cognitive ability related to the way one responds to strategic uncertainty? We address this question by conducting a set of experiments in simple 2 × 2 dominance solvable coordination games. Our experiments involve two main treatments: one in which two human subjects interact, and another in which one human subject interacts with a computer program whose behavior is known. By making the behavior of the computer perfectly predictable, the latter treatment eliminates strategic uncertainty. We find that subjects with higher cognitive abilities are more sensitive to strategic uncertainty than those with lower cognitive abilities.

Introduction

Coordination games provide a useful game-theoretical paradigm for analyzing a wide range of economic phenomena, such as macroeconomic fluctuations [START_REF] Cooper | Coordinating Coordination Failures in Keynesian Models[END_REF], bank runs and speculative currency attacks on financial markets [START_REF] Morris | Global Games: Theory and Applications[END_REF][START_REF] Heinemann | Understanding Financial Crises : The Contribution of Experimental Economics[END_REF], and commercial production processes [START_REF] Brandts | Legitimacy, Communication and Leadership in the Turnaround Game[END_REF]. Because of the multiplicity and the Pareto-rankability of the Nash equilibria in these games, and because decisions are usually made in a state of strategic uncertainty regarding others' behavior, the resulting outcomes can be driven away from the Pareto-Nash equilibrium -a phenomenon known as coordination failure.

Coordination failure has been shown to be a persistent pattern in numerous lab implementations (Camerer, 2003, Ch.7). The present paper contributes to a large body of experimental studies exploring this welfare-reducing phenomenon. A vast part of this literature is based on the core idea that coordination failures arise from strategic uncertainty, and various institutional designs are put forth as a remedy against it: introducing repeated encounters, varying the stability and the size of groups, providing information feedback, allowing for observation of others' past behavior, or introducing pre-play communication between players (see also [START_REF] Devetag | When and why? A critical survey on coordination failure in the laboratory[END_REF], for an extensive survey of this literature.) However, although these mechanisms are usually found to improve efficient coordination, they fall short of completely solving the problem of coordination failure.

In this paper, we take a further step to deepen our understanding of the nature of coordination failure. Our experimental results confirm that strategic uncertainty is an important determinant of the efficiency of strategic decision-making. Even more importantly, our experiment shows that individual cognitive abilities have a strong link with the way strategic uncertainty influences the decisions of subjects in our experimental coordination games.

Our investigation involves a classic 2 × 2 coordination game, based on [START_REF] Selten | Reexamination of the perfectness concept for equilibrium points in extensive games[END_REF] and [START_REF] Rosenthal | Games of perfect information, predatory pricing and the chain-store paradox[END_REF], and presented in Table 1. With L < S < H, m < h, and s < h, the game is onestep dominance solvable: the elimination of Player B's weakly dominated strategy l immediately leads to the Pareto-Nash equilibrium (R, r). Moreover, from the standard theory perspective, (R, r) is a natural candidate for a focal point, since it is also risk-dominant. 1 Notwithstanding these predictions, various studies have found a frequent failure to achieve the efficient equilibrium (see, e.g., [START_REF] Beard | Do People Rely on the Self-Interested Maximization of Others? An Experimental Test[END_REF][START_REF] Beard | Reliant behavior in the United States and Japan[END_REF][START_REF] Goeree | Ten Little Treasures of Game Theory and Ten Intuitive Contradictions[END_REF][START_REF] Cooper | Evidence on the equivalence of the strategic and extensive form representation of games[END_REF][START_REF] Jacquemet | What drives failure to maximize payoffs in the lab? A test of the inequality aversion hypothesis[END_REF] both in sequential and simultaneous implementations of this game. Depending on the exact experimental setup, between 20% and 84% of observed outcomes are not Pareto efficient. While the literature has long focused on the strategic uncertainty faced by Player A as the source of coordination failures 1 Another Nash equilibrium, (L, l), involves a weakly dominant strategy l by Player B. The existence of a clear-cut theoretical benchmark distinguishes this game from another well-known 2x2 coordination game, the stag hunt, in which each Nash equilibrium is supported by a certain solution concept -either payoff-dominance or risk-dominance. games to demonstrate that some subjects do not pay attention to the payoffs of their opponent, and thus do not realize that the opponent has a dominant strategy. Thus, some Player As in our coordination game may choose L without taking Player Bs' behavior into consideration at allwhich precludes any meaningful role of strategic uncertainty on the decision-making of the former. Therefore, the first aim of this paper is to understand the extent to which deviations from strategy R by Player As is due to strategic uncertainty, which constitutes an important step towards designing more efficient mechanisms aimed at eliminating coordination failure. To address this issue we conduct a set of experiments based on four variations of a dominance solvable coordination game shown in Table 1, in which human subjects (acting as Player As) interact with Player Bs represented by either (a) other human subjects, or (b) a computer program. Computerized Player Bs are programmed to always choose r, and this fact is clearly explained to the subjects. Therefore, subjects acting as Player As interacting with computers do not face any strategic uncertainty, which provides an empirical benchmark for assessing the effect of strategic uncertainty on Player As' behavior in human-human interactions.

In this sense, our experiment is related to a recent and growing body of experimental studies that seek to separate and evaluate the behavioral effect of strategic uncertainty in collective decision-making. For example, in an alternating bargaining game, [START_REF] Johnson | Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining[END_REF] investigated the effects of two potential causes for failure in backward induction: confusion or other-regarding social preferences. They found evidence that confusion was an important cause of deviations from the equilibrium outcome. [START_REF] Houser | Revisiting Kindness and Confusion in Public Goods Experiments[END_REF] and [START_REF] Ferraro | The Source and Significance of Confusion in Public Goods Experiments[END_REF] do the same in public good contribution experiments, and estimate that confusion explained up to around one half of contribution levels. [START_REF] Fehr | Does Money Illusion Matter?[END_REF] focused on the strategic aspects of "nominal illusion". They considered four-player repeated price setting games, and introduced a negative nominal shock in the middle of the experiment. They found that roughly half of non-immediate adjustment to the new equilibrium after the shock was due to individual bounded rationality (or confusion) and the other half was due to strategic uncertainty.

Finally, [START_REF] Akiyama | It is not just confusion! Strategic uncertainty in an experimental asset market[END_REF] investigated the magnitude of the effect of strategic uncertainty in explaining the observed deviation of price forecasts from the fundamental values in an experimental asset market à la [START_REF] Smith | Bubbles, Crashes. and Endogenous Expectations in Experimental Spot Asset Markets[END_REF]. They found significant effects of both confusion and strategic uncertainty. 2 Our second objective is to shed new light on the relationship between cognitive ability and strategic thinking. In particular, we investigate whether the failure to seek efficiency by choosing R is more widespread among Player As with low cognitive abilities than for those with high cognitive abilities. We address this question by conducting a cognitive ability test in several experimental sessions (involving both human-human and human-robot interactions), and correlate the efficiency of observed behavior and subjects' test scores, while controlling for the presence of strategic uncertainty.

From this perspective, our study contributes to recent literature that investigates the relationship between subjects' cognitive abilities and their degree of strategic sophistication. For example, Brañas-Garza, García-Muñoz, and Hernán (2012) reported that subjects with higher scores on the Cognitive Reflection Test (CRT, Frederick, 2005) choose, on average, numbers closer to the Nash equilibrium in the beauty contest games. In the same vein, [START_REF] Akiyama | It is not just confusion! Strategic uncertainty in an experimental asset market[END_REF] reported that the magnitude of the effect of strategic uncertainty is positively correlated with subjects' scores on the CRT test, while the effect of confusion is negatively correlated with the score. [START_REF] Burks | Cognitive skills affect economic preferences, strategic behavior, and job attachment[END_REF] reported that subjects (trainee truckers) with higher scores in Raven's progressive matrix test 3 are more patient and more willing to take calculated risks. In addition, they report that subjects with higher Raven's test scores more accurately predict others' behavior in a sequential prisoners' dilemma game, and better adapt their behavior to others' behavior. [START_REF] Carpenter | Cognitive ability and strategic sophistication[END_REF] showed that subjects with higher scores in Raven's test more frequently win in "Race to 5, 10, or 15" games 4 and guessed others' choices better in a 20-player beauty contest game. Finally, [START_REF] Gill | Cognitive abilities and learning to play equilibrium: A level-k analysis[END_REF] also reported that subjects with higher scores in Raven's test not only choose numbers closer to the equilibrium in a repeated 3-player beauty contest game, but also respond to the average score of other subjects in the group by choosing number close to the equilibrium when facing with others with higher scores 2 Other studies, somewhat less related to ours, used robots that do not follow equilibrium strategies as a way to control for subjects' beliefs about the behavior of their opponents. For instance, [START_REF] Ivanov | Can relaxation of beliefs rationalize the winner's curse? An experimental study[END_REF] used robots to replicate the observed behaviors of subjects in the past, and [START_REF] Embrey | Bargaining and Reputation: An Experiments on Bargaining in the Presence of Behavioral Types[END_REF] and [START_REF] Costa-Gomes | Cognition and Behavior in Two-Person Guessing Games: An Experimental Study[END_REF] used robots to make some players follow the predetermined distribution of boundedly rational behaviors. 3 Raven's test is widely used to measure "fluid intelligence", that is "the capacity to think logically, analyse and solve novel problems, independent of background knowledge" (Mullainathan and Shafir, 2013, p.48). 4 The "Race to 5 (or 10 or 15)" game is a two player sequential move game in which two players, moving alternatively, can put either 1, 2 or 3 stones in a common hat which is empty at the beginning. The player who puts the 5th (or 10th or 15th, respectively) stone in the hat wins. The first mover has a clear advantage in this game, and one can derive the winning strategy by a backward induction. The difficulty of deriving the winning strategy increases with the number of target stones.

than when facing with others with lower scores. To sum up, these empirical studies suggest that people with high cognitive abilities respond more aptly to strategic conditions they face than those with low cognitive abilities. The present study extends this investigation to a new and important economic environment -the coordination game.

As will be seen, we find that Player As' failure to choose R can be only partially explained by uncertainty about their partners' intentions: in many cases, the former act in this manner even when interacting with a computer program that is known to always act reliably by choosing r. We also report that Player As with high cognitive abilities (measured in terms of Raven's test scores) tend to be more sensitive to strategic uncertainty than those with low cognitive abilities.

Experimental design

We consider four payoff matrices based on the simultaneous-move coordination game shown in Table 1. Our main manipulation lies in varying the nature of Player B, who may be represented either by a human subject (Human treatment) or a pre-programmed computer (Robot treatment). All games and treatments are implemented using a between-subject design -only one version of the game is played in each experimental session. In all the sessions, the one-shot game is repeated ten times with participants' roles remaining fixed, pairs being rematched in each round using a perfect stranger, round-robin procedure5 and take-home earnings corresponding to a single round randomly drawn at the end of each experimental session. At the end of each round, subjects are only informed of their own payoffs.

Treatments and hypotheses

The four experimental game matrices are presented in Table 2. Two of them have already been experimentally studied in the literature. Baseline Game 1 (shown on the top left panel of Table 2) was used as the baseline treatment in [START_REF] Beard | Do People Rely on the Self-Interested Maximization of Others? An Experimental Test[END_REF]; [START_REF] Beard | Reliant behavior in the United States and Japan[END_REF]; Jacquemet andZylbersztejn (2013, 2014). Egalitarian Game 2 (shown on the bottom right panel of Table 2) was one of the additional matrices introduced by [START_REF] Jacquemet | What drives failure to maximize payoffs in the lab? A test of the inequality aversion hypothesis[END_REF] in an attempt to assess the effect of the relative payoff structure on subjects' behavior. The latter study reports a strong divergence between both players' behavior in these two games: weak reliability from Player Bs (80.7% of decisions r) coupled with weak reliance from Player As (49% of decisions R) in BG1, and nearly universal reliability from Player Bs (94.3% of r) coupled with strong (yet imperfect) reliance from Player As (74% of R) in EG2.6 Importantly, Jacquemet and Zylbersztejn (2014) provide systematic evidence that these outcomes cannot be explained by inequality aversion.

The payoff structures of BG1 and EG2 differ in terms of both players' monetary incentives to seek efficiency. In BG1, Player As may improve their situation only slightly when moving from L to (R, r) (from 9.75 to 10, a difference of .25), while a failed attempt to rely on Player Bs, resulting in (R, l), is very costly (yielding only 3 to Player As). In EG2, these two cases become more balanced -the gain for moving from L to (R, r) increases (from 8.5 to 10, a difference of 1.5), and the cost of relying on the other player in vain becomes less severe, with (R, l) now giving 6.5 to Player As. Analogous variations occur for Player Bs. The efficiency premium (conditional on Player As' reliance) is quite low in BG1 (from 4.75 to 5, a difference of 0.25) and drastically rises in EG2 (from 8.5 to 10, a difference of 1.5). Altogether, EG2 provides much more salient monetary incentives to act efficiently to both players. 7 In order to account for subjects' responses to the changes in their own as well as their partners' monetary incentives, we introduce two intermediate payoff matrices: Baseline Game 2 (BG2) and Egalitarian Game 1 (EG1) shown respectively in the top-right and bottom-left corners of Table 2. Each of the two games differs in only one dimension -that is, either Player As' payoffs or Player Bs' payoffs -as compared to BG1 and EG2: BG2

7 Some studies have also documented the effect of the saliency of monetary incentives in coordination games.

See, for example, [START_REF] Battalio | Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games[END_REF] for symmetric 2 × 2 games, and [START_REF] Goeree | Ten Little Treasures of Game Theory and Ten Intuitive Contradictions[END_REF]; Devetag and Ortmann (2010) for n-player minimum and median effort games.

(EG1) has Player A's payoffs taken from EG2 (BG1) and Player B's payoffs taken from BG1 (EG2). Thus, the four games enable us to test the following hypotheses for the Human condition:

Hypothesis 1 In the human treatment, the variations in the monetary incentives affect players' behavior as follows:

(a) Player As react to the variations in their own monetary incentives to seek efficiency: the proportion of decisions R is higher in BG2 than in BG1, and in EG2 than in EG1;

(b) Player Bs react to the variations in their own monetary incentives to act efficiently: the proportion of decisions r is higher in EG1 than in BG1, and in EG2 than in BG2;

(c) Player As react to the variations in Player Bs' monetary incentives to act efficiently: the proportion of decisions R is higher in EG1 than in BG1, and in EG2 than in BG2.

The strategic uncertainty that Player As face cannot be directly observed or measured by the experimenter. Therefore, assessing its behavioral effect requires a benchmark in which the actual degree of strategic uncertainty can be controlled for. To that end, each of the four games is implemented under two different conditions: Human and Robot. In the Human treatment, two human subjects interact in ways described above. In the Robot treatment, a human subject acting as Player A interacts with a computerized Player B who is pre-programmed to always choose r. Subjects in the Robot treatment are clearly informed they are interacting with a preprogrammed computer: "the computer chooses r at each round, without exception" (bold in the original instruction sheet). This is the only difference in the rules and procedures between Human and Robot treatments.As a result, subjects in the Robot treatment do not face any strategic uncertainty. This leads us to the following hypothesis:

Hypothesis 2 The Robot treatment neutralizes strategic uncertainty Player As face. As a result, the proportion of actions R in a given game is higher in the Robot treatments than in the Human treatments.

While not choosing R in the Human treatment may not necessarily arise from strategic uncertainty, the same behavior in the Robot treatment must be due to reasons other than strategic uncertainty. Thus, comparing Player As' decisions between Human and Robot treatments enables us to capture the behavioral effect of strategic uncertainty.

Once the behavioral results are established, we then investigate the relationship between subjects' cognitive abilities and their sensitivity to the changes in the degree of strategic uncertainty. We measure each participants cognitive ability by implementing a standard psychological test developed by John C. Raven (see [START_REF] Raven | General Introduction and Overview: The Raven Progressive Matrices Tests: Their Theoretical Basis and Measurement Model[END_REF], for an overview). Subjects are asked to solve Raven's test at the end of all experimental sessions involving the BG2 and EG1 games, under both Robot and Human treatments. Based on existing experimental results (discussed in the opening section), we formulate the following hypothesis:

Hypothesis 3 Subjects with high cognitive abilities are more sensitive to changes in the degree of strategic uncertainty than those with low cognitive abilities.

Experimental procedures

Upon arrival, participants are randomly assigned to their computers and asked to fill in a short personal questionnaire containing basic questions about their age, gender, education, etc. The pre-distributed written set of instructions is then read aloud. Player As are informed that they will play an unrevealed number of rounds of the same game, each round with a different partner, and that their own role will not change during the experiment. Before starting, subjects are asked to answer a quiz assessing their understanding of the game they are about to play. Once the quiz and any questions from participants are answered, the experiment begins.

The experiment generates observations under eight experimental conditions, varying according to the payoff structure (BG1, BG2, EG1 or EG2) and Player A's partner (human subject in the Human treatment or computer in the Robot treatment). All conditions are implemented separately, using a between-subject design: each subject plays only one of the four games, and interacts either with other subjects or with a computer.

In addition, all sessions involving BG2 and EG1 include computerized post-experiment tasks. An additional 5 euros is paid to each subject for completing this part. Immediately after the end of the experimental game, participants are provided with a brief round-by-round summary of their decisions and outcomes, and are asked to provide any relevant comments and indicate the things that might have affected their decisions during the experiment in a blank space on their computer screens. They are also asked to solve a part of the advanced version of Raven's test -composed of 16 items to be completed within 10 minutes.

For each payoff matrix, we ran three Human treatment sessions (involving 20 subjects per session: 10 Player As interacting with 10 Player Bs), and two Robot treatment sessions (involving 20 Player As per session interacting with automated Player Bs). The data for the BG1 and EG2 Human treatments come from [START_REF] Jacquemet | What drives failure to maximize payoffs in the lab? A test of the inequality aversion hypothesis[END_REF], while all the other sessions were carried out in October 2012 and February and March 2014. All sessions took place at the Laboratoire d'Economie Experimentale de Paris (LEEP) at University Paris 1 Panthéon-Sorbonne. Of the 398 participants (190 males), 323 were students with various fields of specialization. 8 The majority of subjects (57%) had already taken part in economic experiments run at LEEP. Participants' average age was 24.05. Subjects were recruited via an on-line registration system based on Orsee [START_REF] Greiner | An Online Recruitment System for Economic Experiments[END_REF] and the experiment was computerized through software developed under Regate [START_REF] Zeiliger | A presentation of Regate, Internet based Software for Experimental Economics[END_REF] and z-Tree [START_REF] Fischbacher | z-Tree: Zurich toolbox for ready-made economic experiments[END_REF]. Sessions lasted about 45-60 minutes, with .

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Results

Figure 1 provides descriptive statistics regarding the behavior of Player As in all our experimental treatments. The share of Player As who chose R in each round is displayed separately for each payoff matrix, and the two curves provide a comparison between the Human treatment and the Robot treatment. Before moving to a detailed analysis of the treatment effects, three main observations can be made. First, our Human treatment replicates the results seen in the existing literature: a high proportion of Player As decide to play L, even after several rounds of the game. Second, between game comparisons of behavior in the Human treatments show this pattern is barely influenced by the strategic context: while Player As react to changes in incentives they face (BG2 vs BG1, and EG2 vs EG1), they appear rather insensitive to changes in incentives faced by Player Bs (EG1 vs BG1, and EG2 vs BG2). Finally, while the share of decisions R in the Robot treatment always weakly dominates the one in the Human treatment, the absence of strategic uncertainty in this context does not remove all decisions L.

In the remainder of this section, the main question we seek to answer is whether and to what extent strategic uncertainty drives the observed decisions to play L. In the Human treatment, two factors explain the decisions of Player As: the behavior of Player Bs in the experiment and how Player As adjust to this behavior. The variations in payoffs between games allows these two factors to be measured separately. We then move to an analysis of the Robot treatments, in which strategic uncertainty is removed by design. .

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Results from the Human treatment

As summarized in Hypothesis 1, the variations in payoffs between games should induce variations in the decisions of both players, hence resulting in a variation in the actual strategic uncertainty faced by Player As. Figure 2 provides an overview of individual behavior in the Human treatment. Aggregate results suggest that both players react to the variations in their own payoff scheme. Holding Player Bs' payoffs constant, Player As are more likely to seek efficiency as their monetary incentives to do so become more salient: the frequency of R increases from 49% in BG1 to 73% in BG2 (p = .001), and from 45% in EG1 to 74% in EG2 (p = .005). 9 Analogously, Player Bs become 9 We test the difference in proportion of a given outcome between two experimental conditions by carrying out a two-sided bootstrap proportion test that accounts for within-subject correlation -i.e. the fact that the same individual takes 10 decisions. The procedure consists of bootstrapping subjects and their corresponding decisions over all ten rounds instead of bootstrapping decisions as independent observations (see, e.g., Jacquemet, Joule, Luchini, and Shogren, 2013, for a detailed description of the procedure). In Round 1, data are independent and thus allow us to analyze behavior with a standard bootstrap proportion test. Frequencies in Round 1 are 23.3% in BG1 and 50.0% in BG2 (p = .027), and 30.0% in EG1 and 50.0% in EG2 (p = .091).

EG2

more efficient the higher the cost of acting otherwise: the frequency of r increases from 81% in BG1 to 92% in EG1 (p = .026) and from 81% in BG2 to 94% in EG2 (p = .012). However, despite Player Bs' responsiveness to their personal monetary incentives, Player As remain insensitive to this factor: the differences between BG1 and EG1 and between BG2 and EG2 are small and not statistically significant (p = .694 and p = .898, respectively). 10These three observations are supported by the individual-level data summarized in Figure 3. The left-hand side provides the Empirical Distribution Function (EDF) of Player As' frequency of decisions R, i.e. the number of decisions R taken throughout the ten rounds of the game. Statistical tests indicate first order stochastic dominance of the distributions between BG2 and BG1 (p = .007) and between EG2 and EG1 (p = .021).11 This confirms that Player As' behavior depends on the saliency of their own monetary incentives. Figure 3.(b) presents the EDFs of Player Bs' individual frequencies of decisions r. These individual-level data stand in line with the aggregate outcomes, showing that Player Bs do react to their personal costs of inefficient behavior: the EDF from EG1 first order stochastically dominates the EDF from BG1 (p = .039), and the EDF from EG2 first order stochastically dominates the EDF from BG2 (p = .002). This amounts to a significant change in the actual strategic uncertainty Player A faces. Figure 3.(a) also shows that there are no significant differences between EG1 and BG1 (p = .783) or between EG2 and BG2 (p = .914); Player As do not seem to react to the changes in the saliency of Player Bs' monetary incentives.

Result 1 In the presence of strategic uncertainty, the saliency of monetary incentives affects players' behavior as follows:

(a) The proportion of decisions R is higher in BG2 than in BG1, and in EG2 than in EG1:

Player As become more likely to act efficiently the more salient their monetary incentives;

(b) The proportion of decisions r is higher in EG1 than in BG1, and in EG2 than in BG2: Player Bs become more likely to act efficiently the more salient their monetary incentives;

(c) The proportion of decisions R is not significantly different in EG1 than in BG1, nor in EG2 than in BG2: Player As ignore the saliency of Player Bs' monetary incentives.

The effect of strategic uncertainty: comparing Human and Robot treatments

In the Robot treatment, Player Bs' decisions are generated by computers always playing r, hence eliminating the strategic uncertainty faced by Player As. The change in behavior from Player As hence identifies the effect of strategic uncertainty in the Human treatment. In Figure 1 we presented aggregate statistics on the behavior of Player As. Figure 4 provides individual data for all four games and both treatments. Each curve provides the EDF of the number of decisions R taken by each individual in the Human treatment and in the Robot treatment. In the aggregate, in three games out of four we find a statistically significant increase in the proportion of decisions R when Player As interact with computerized Player Bs rather than other human subjects: from 49.0% to 77.0% in BG1, from 44.7% to 69.0% in EG1 and from 77.0% to 86.6% in EG2. In BG2, however, we only observe a weak increase -from 72.5% to 77.3%.12 . These results are true all along the distribution of the number of decisions R. The EDF in the Robot treatment first order stochastically dominates the EDF in the Human treatment for BG1 (p < .001), BG2 (p = .004) and EG1 (p = .011); this pattern is not statistically significant for EG2 (p = .134). The most noticeable difference between the two distributions is the proportion of Player As who invariably choose R when facing a computer rather than another subject: 50.0% against 10.0% in BG1, 65.5% against 30.0% in BG2, 37.5% against 10.0% in EG1 and 57.9% against 40.0% in EG2. This increase is significant at a 1% threshold for games BG1, BG2 and EG1 (p = .001, p = .004 and p = .010 respectively) and barely insignificant in EG2 (p = .111). .

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♯
Result 2 Strategic uncertainty only partially explains Player As' failure to seek efficiency in the coordination game. Player As do not consistently select the Pareto-Nash strategy R even when interacting with a computer who is known to always act efficiently by choosing r.

Cognitive ability and strategic uncertainty

The crucial question raised by the Human-Robot comparison is why do Player As continue acting inefficiently in the absence of strategic uncertainty? We investigate this question based on the cognitive abilities of Player As. Cognitive ability is measured by Raven's test, performed after the game only in BG2 and EG1, in both Human and Robot treatments. It corresponds to the number of correct answers to the set of 16 questions.

The main outcome of interest is the change in the correlation of cognitive ability and actual decisions by treatment. The internal validity of the comparison depends on the randomization between treatments with regards to cognitive abilities. A multiple-treatment comparison using .

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. round Kruskal-Wallis test with Bonferroni correction does not reject the null hypothesis that Raven's test scores in the four experimental conditions come from the same population (with p = .275). 13This result confirms that subjects are properly randomized regarding their cognitive abilities. Table 3 reports the individual correlations between the score in Raven's test and decisions in the game, measured by the number of choices R (between 0 and 10) made throughout the 10 rounds of the game. We find a positive and significant correlation between these two variables in the Robot treatments which suggests that subjects with a higher cognitive ability are more likely to play R. However, this correlation disappears in Human treatments. To gain further insights on the transition between the Robot and Human treatments, we categorize individuals in our experimental sample according to their score on the Raven's test. Player As are divided into three groups, which correspond to the three tertiles of the overall score distribution, (i.e. considering all Player As from all four experimental conditions, hence 140 subjects.) Subjects in the low ability group have a Raven's test score below 7, those with a Raven's test score of 7 to 10 are in the medium ability group and those with a score above 10 are in the high ability group.

Figure 5 presents the proportion of decisions R across rounds by cognitive ability group.14 The aggregate dynamics are very similar across cognitive ability groups, with an increase in the frequency of decisions R in the first rounds and a stabilization afterwards. This result holds regardless of whether decisions are taken with computers or humans acting as Player Bs. However, interacting with computers instead of humans induces an initial upward shift in the ratio of R that persists over time in the medium and the high ability groups, whereas no such shift occurs in the low ability group. The mean increase in proportion of decisions R in Round 1 induced by .

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Robots

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Robots playing with a computer rather than a human is 22.4% (p = .057) for the medium ability group and 38.3% for the high ability group (p = .003). The mean difference between these proportions is still present in Round 10, but to a lesser extent: 15.9% (p = .074) for the medium ability group and 11.5% (p = .022) for the high ability group. In the low ability group, we find a small and insignificant upward shift in the proportion of decisions R in Round 1 (12.6%, p = .203), while the proportions of decisions R are almost equally likely in Round 10 (the difference being -5.5%, p = .618) in Robot and Human treatments.

Figure 6 provides the EDFs of the number of decisions R made by each subject across ten rounds for each cognitive ability group in Human and Robot treatments. Three results emerge. First, the EDFs in the Humans treatment are not statistically different across cognitive ability groups. 15 Second, this is not the case in the Robot treatment: the EDF for the low cognitive ability group is first order stochastically dominated by the EDF for the medium and high cognitive ability groups (p = .003 and p = .001, respectively). Finally, we observe no such relationship for the medium and high ability groups: the EDFs are not significantly different (p = .318). The main reason for these results is that the subjects in the low ability group do not respond to the absence of strategic uncertainty in Robot treatments by increasing the frequency of decisions R (p = .415), whereas subjects in the medium and high ability groups do so (the tests are based on comparisons between treatments for each cognitive ability group, the p-values for both are p = .001.)

Such behavior is in line with Hypothesis 3, i.e. Player As with higher cognitive abilities are more sensitive to the change in the degree of strategic uncertainty between Human and Robot 15 To ensure a sufficient sample size in each ability group, we pooled the outcomes from both games in each treatment. The tests are performed using two-sided bootstrap K-S tests. The p-values of the two-by-two comparisons are: p = .288 for the low ability group vs. the medium ability group, p = .599 for the low vs. the high and p = .695 for the medium vs. the high.

treatments. To provide a formal test of the hypothesis, we first denote R the mean number of R decisions across 10 rounds by treatment (Robot vs. Human) and type (low cognitive ability vs. high cognitive ability). The test of Hypothesis 3 is then defined as follows: Empirical results indicate that our hypothesis is likely to be verified with R(Robot, high) = 8.8, R(Human, high) = 5.8, R(Robot, low) = 5.4, and R(Human, low) = 5.0, which is consistent with the hypothesis. We statistically tested the result by putting all the terms of Equation ( 1) to the left-hand side, so that the test reduces to a comparison test of multiple means with coefficients (1; -1; -1; 1). 16 The test rejects the null hypothesis when the low cognitive ability group is compared to the high cognitive ability group (p = .051), as well as when it is compared to the medium and high cognitive ability groups pooled together (p = .056). These results allow us to state our last result:

Result 3 Player As with high cognitive abilities are more sensitive to the changes in strategic uncertainty than those with low cognitive ability.

Conclusion

Coordination failure is a widely documented phenomenon, with possibly dramatic economic consequences. While most experimental investigations try to identify the possible sources of strategic uncertainty underlying such failures, very few explore the effect of strategic uncertainty per se. In addition, little is known about whether and how behavior under strategic uncertainty is related to individual cognitive abilities.

We used four variations of a classic 2 × 2 dominance solvable coordination game to explore the link between coordination failure, strategic uncertainty and cognitive abilities. To isolate the behavioral effect of strategic uncertainty, we compare the decisions made when facing other human subjects (Human treatment) to those made against computer programs whose perfectly efficient behavior is common knowledge (Robot treatment). We find that the occurrence of coordination failure cannot be entirely explained by strategic uncertainty. First, a non-negligible share of our subjects failed to act efficiently even in the Robot treatment. Second, behavioral response to strategic uncertainty is related to individual cognitive abilities. Subjects with higher cognitive abilities (as measured by their scores on Raven's test) systematically adapt their decisions to the varying degree of strategic uncertainty (i.e. between the Human and Robot treatment), while those with lower cognitive abilities fail to do so.

The relationship between cognitive abilities and the sensitivity to strategic uncertainty is a challenge for institutions aimed at fostering efficient coordination by reducing strategic uncertainty. These mechanisms -such as the widely studied affect of communication between participantsusually involve focusing agents' actions on the desirable equilibrium. However, the presence of players with a low strategic focus -such as the Raven's test low-scorers in our experiment -may undermine the effect and lower the economic value of such institutions. As noted by [START_REF] Ellingsen | When does communication improve coordination?[END_REF] in the context of a theoretical analysis of communication and coordination in a levelk setup, "there is a need for evidence that systematically distinguishes the effects of preferences, belief, and rationality" (p.1714). We believe that our experimental design and collected data on the cognitive underpinnings of behavior under strategic uncertainty and the resulting coordination failure is an important step in this direction.

Figure 1 :

 1 Figure 1: Proportion of decisions R across rounds and treatments

Figure 2 :

 2 Figure 2: Share of the decisions R (r) for Player As (B) in the Human treatments, across rounds

Figure 3 :

 3 Figure 3: EDF of the total number of decisions R and r decisions by game

Figure 4 :

 4 Figure 4: EDF of the individual number of decisions R by treatment

Figure 5 :

 5 Figure 5: Proportion of decisions R across rounds and treatments by ability group

Figure 6 :

 6 Figure 6: EDF of the total number of decision R by treatment and cognitive ability group

  R(Robot, high) -R(Human, high) = R(Robot, low) -R(Human, low) H 1 : R(Robot, high) -R(Human, high) > R(Robot, low) -R(Human, low) (1)

Table 1 :

 1 A simple two-person two-action dominance solvable coordination game

		Player B
		l	r
	Player A	L (S ; s) R (L ; m) (H ; h) (S ; s)
	in these experiments, recent evidence provides different clues for explaining this behavior. For
	example, Polonio, Di Guida, and Coricelli (2014) use eye-tracking data gathered from simple 2×2

Table 2 :

 2 The experimental games

		B			B
		l	r		l	r
	A	L (9.75 ; 3.00) ( 9.75 ; 3.00) R (3.00 ; 4.75) (10.00 ; 5.00)	A	L (8.50 ; 3.00) ( 8.50 ; 3.00) R (6.50 ; 4.75) (10.00 ; 5.00)
		Baseline 1			Baseline 2
		B			B
		l	r		l	r
	A	L (9.75 ; 8.50) ( 9.75 ; 8.50) R (3.00 ; 8.50) (10.00 ; 10.00)	A	L (8.50; 8.50) ( 8.50 ; 8.50) R (6.50 ; 8.50) (10.00 ; 10.00)
		Egalitarian 1			Egalitarian 2

Table 3 :

 3 Spearman's rank correlation of decisions R and Raven's test score

	of R decisions

We avoid the end-game effect by providing no information about the exact number of repetitions.

In the present study, we focus on the determinants on Player As' behavior, considering Player Bs' solely as a source of strategic uncertainty.[START_REF] Jacquemet | Learning, words and actions: experimental evidence on coordination-improving information[END_REF] offer a systematic analysis of the patterns of Player Bs' decisions in this game.

In one EG2 Robot treatment session, we had 18 subjects instead of 20, so for the Robot treatment there were 40 subjects for BG1, BG2 and EG1, and 38 subjects for EG2. For the Human treatment sessions, we had 60 subjects (half of whom are Player As) for each of the four games.

The analogous frequencies in Round 1 for Player Bs are 80.0% in BG1 and 83.3% in EG1 (p = .731), and 76.7% in BG2 and 86.7% in EG2 (p = .232); for Player As, they are: 23.3% in BG1 and 30.0% in EG1 (p = .583), and 50.0% in BG2 and 50.0% in EG2 (p = .889).

Our first order stochastic dominance test is based on a bootstrap version of the univariate Kolmogorov-Smirnov (KS) test. The advantage of this test as compared to the standard KS test is it allows for ties (see, e.g.,[START_REF] Abadie | Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Model[END_REF][START_REF] Sekhon | Multivariate and Propensity Score Matching Software with Automated Balance Optimization[END_REF].

These shifts are significant according to bootstrap proportion tests at the 1% threshold in BG1 (p = .001) and in EG1 (p = .005), at the 5% threshold in EG2 (p = .033) and are not statistically significant in BG2 (p = .305)

The same test applied at the session-level (10 sessions) instead of the experimental-condition-level yields a p-value of .694.

The data from BG2 and EG1 are pooled to focus on the overall effect of removing strategic uncertainty and guarantee sufficient sample sizes in each category.

Given the group sizes, the bootstrap test is based on re-sampling subjects and the number of times they choose decision R. To account for asymmetry in the empirical distribution, we computed an equal-tail bootstrap p-value. See[START_REF] Davidson | Bootstrap methods in econometrics[END_REF] for further details on this procedure.

* This project is partly financed by JSPS-ANR bilateral research grant "BECOA" (ANR-11-FRJA-0002).


Pauline Chaste

Gudrun Nygren

Henrik Anckarsäter

Maria Råstam

Mary Coleman

Marion Leboyer

Christopher Gillberg

Dr Catalina Betancur
email: catalina.betancur@creteil.inserm.fr

Mutation screening of the ARX gene in patients with autism

Keywords: X chromosome, mental retardation, epilepsy

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Mutations in the X-linked gene Aristaless related homeobox (ARX) have recently been shown to cause mental retardation, either isolated or associated with a broad spectrum of neurological disorders. The first ARX mutations were found in families with mental retardation and various forms of epilepsy, including West syndrome (infantile spasms, hypsarrhythmia, and mental retardation), myoclonic epilepsy, or Partington syndrome (dystonic movements of the hands, mental retardation, and seizures) (Stromme et al., 2002b). Subsequently, ARX mutations have been reported in familial and sporadic cases of nonsyndromic mental retardation [START_REF] Bienvenu | ARX, a novel Prd-class-homeobox gene highly expressed in the telencephalon, is mutated in X-linked mental retardation[END_REF], X-linked lissencephaly with abnormal genitalia [START_REF] Kitamura | Mutation of ARX causes abnormal development of forebrain and testes in mice and X-linked lissencephaly with abnormal genitalia in humans[END_REF], agenesis of the corpus callosum, hydranencephaly, ataxia, and different types of epilepsy (for review see [START_REF] Suri | The phenotypic spectrum of ARX mutations[END_REF]. Furthermore, the reevaluation of two families with an ARX mutation originally diagnosed with X-linked mental retardation (Stromme et al., 2002b) showed that one patient had autism and three had autistic features [START_REF] Turner | Variable expression of mental retardation, autism, seizures, and dystonic hand movements in two families with an identical ARX gene mutation[END_REF]. This striking phenotypic variability is partly explained by the type of mutation, with duplications and missense mutations resulting in mental retardation alone or with epilepsy or autism, whereas loss-of-function mutations result in more severe phenotypes with brain malformations and abnormal genitalia [START_REF] Suri | The phenotypic spectrum of ARX mutations[END_REF]. The most frequently reported mutation is a 24-bp duplication in exon 2, c.428-451dup(24 bp), which results in the expansion of a polyalanine tract and accounts for about 30% of all described mutations. Based on the results of the first mutation screening of ARX in individuals with mental retardation [START_REF] Bienvenu | ARX, a novel Prd-class-homeobox gene highly expressed in the telencephalon, is mutated in X-linked mental retardation[END_REF], it was suggested that ARX mutations could be as common as fragile X syndrome among the mentally retarded population [START_REF] Sherr | The ARX story (epilepsy, mental retardation, autism, and cerebral malformations): one gene leads to many phenotypes[END_REF]. More recent studies, however, have shown that ARX mutations are not as frequent as initially suspected [START_REF] Gronskov | Screening of the ARX gene in 682 retarded males[END_REF]. The human ARX gene maps to chromosome Xp22.13 and is composed of five coding exons. It encodes a transcription factor expressed predominantly in the fetal and adult brain (Stromme et al., 2002b), thought to regulate essential processes during brain development, including neuronal proliferation, migration and differentiation [START_REF] Kitamura | Mutation of ARX causes abnormal development of forebrain and testes in mice and X-linked lissencephaly with abnormal genitalia in humans[END_REF][START_REF] Friocourt | The role of ARX in cortical development[END_REF].

Autism is a behaviorally defined neurodevelopmental syndrome with a strong heritable component and marked genetic heterogeneity [START_REF] Veenstra-Vanderweele | Autism as a paradigmatic complex genetic disorder[END_REF]. Monogenic disorders (e.g., fragile X syndrome, tuberous sclerosis complex, neurofibromatosis, various rare metabolic disorders) and chromosomal abnormalities are identified in about 10% of patients, but the underlying cause remains unknown in the majority of patients [START_REF] Gillberg | The Biology of the Autistic Syndromes[END_REF]. The search for genetic variants conferring liability to autism using linkage and association analyses has failed to identify any definite genes [START_REF] Veenstra-Vanderweele | Autism as a paradigmatic complex genetic disorder[END_REF]. The prevalence of autism is approximately four times higher in males than in females. The higher prevalence of males together with the description of cases with chromosomal aberrations involving the X chromosome [START_REF] Vorstman | Identification of novel autism candidate regions through analysis of reported cytogenetic abnormalities associated with autism[END_REF], suggest the implication of X-linked genes in autism. Mutations in several X-linked genes have been identified in individuals with autism spectrum disorders. The most frequently reported genetic disorder in autism is the fragile X syndrome, involving CGG expansions in the FMR1 gene, found in about 2% of patients Hal author manuscript inserm-00109595, version 1 with autism [START_REF] Wassink | Chromosomal abnormalities in a clinic sample of individuals with autistic disorder[END_REF]. Other mutations of X-linked genes described in a few cases with autism spectrum disorders include MECP2 [START_REF] Carney | Identification of MeCP2 mutations in a series of females with autistic disorder[END_REF][START_REF] Zappella | Study of MECP2 gene in Rett syndrome variants and autistic girls[END_REF], neuroligins NLGN3 and NLGN4X [START_REF] Jamain | Mutations of the X-linked genes encoding neuroligins NLGN3 and NLGN4 are associated with autism[END_REF], DMD [START_REF] Wu | Association of Duchenne muscular dystrophy with autism spectrum disorder[END_REF], CDKL5 [START_REF] Evans | Early onset seizures and Rett-like features associated with mutations in CDKL5[END_REF], and the creatine transporter SLC6A8 [START_REF] Salomons | X-linked creatine transporter defect: an overview[END_REF]. Together, these findings strongly suggest that other genes on the X chromosome are also potential candidates for autism. In particular, the ARX gene is a compelling candidate. Indeed, approximately 75% of subjects with autism also have mental retardation, and about 30% have epilepsy. The discovery of ARX mutations in patients with mental retardation, often associated with epilepsy and sometimes with autism [START_REF] Nawara | The ARX mutations: a frequent cause of X-linked mental retardation[END_REF]Turner et al., 2002), suggests that ARX could be involved in other cases of autism. Thus, the aim of this study was to assess the frequency of ARX mutations in autism. We screened the ARX gene in 226 males with autism spectrum disorders and mental retardation; 42 of the patients had epilepsy.

MATERIALS AND METHODS

Patients

A total of 226 males with an autism spectrum disorder and mental retardation were included in the study. They were recruited by the Paris Autism Research International Sibpair (PARIS) study at specialized clinical centers in seven countries (France, Sweden, Norway, Italy, Belgium, Austria, and the United States). There were 77 subjects from families with two or more affected siblings (45 with males only and 32 brother/sister pairs) and 149 sporadic cases. None of the familial cases was ascertained from known X-linked pedigrees with mental retardation or neurological disorders.

Diagnoses were based on clinical evaluation by experienced clinicians, DSM-IV criteria, and the Autism Diagnostic Interview-Revised (ADI-R) [START_REF] Lord | Autism Diagnostic Interview-Revised: a revised version of a diagnostic interview for caregivers of individuals with possible pervasive developmental disorders[END_REF]. Among the patients studied, 218 had autism and 8 had pervasive developmental disorder not otherwise specified. Laboratory tests to ruleout medical causes of autism included standard karyotyping, fragile X testing, and metabolic screening; brain imaging and EEG were performed when possible. Patients diagnosed with medical disorders such as fragile X syndrome or chromosomal abnormalities were excluded from the study.

Forty-two patients had epilepsy and 6 had an abnormal EEG but no seizures. There were 198 individuals of Caucasian origin, 12 Black, 2 Asian and 14 of mixed ethnicity. The local Research Ethics Boards reviewed and approved the study. Informed consent was obtained from all families participating in the study.

ARX mutation analyses

Genomic DNA was prepared from blood or lymphoblastoid cell lines. The complete ARX coding sequence including the exon-intron boundaries was amplified by PCR. Exon 2 was amplified in two overlapping fragments. Primer sequences were kindly provided by Prof Jozef Gécz (Stromme et al., 2002b) or reported previously [START_REF] Kato | Mutations of ARX are associated with striking pleiotropy and consistent genotype-phenotype correlation[END_REF]. The amplicons were screened for mutations by direct sequencing using the ABI BigDye Terminator sequencing kit (Applied Biosystems, Foster City, CA, USA) and an ABI 3100 sequencer (Applied Biosystems).

Hal author manuscript inserm-00109595, version 1

RESULTS

Genomic DNA from 226 patients with autism spectrum disorders was screened for intragenic ARX mutations by sequencing analysis. No pathogenic mutations were identified in any sample. We identified one synonymous variant in exon 4, c.1347C>T (p.G449G), in 10 individuals. This variant has been described previously as a polymorphism [START_REF] Gronskov | Screening of the ARX gene in 682 retarded males[END_REF][START_REF] Kato | Mutations of ARX are associated with striking pleiotropy and consistent genotype-phenotype correlation[END_REF].

DISCUSSION

Our results indicate that coding mutations in the ARX gene are not associated with autism in our family sample. Since our analysis was limited to the coding sequence ARX, we cannot exclude that mutations in the promoter and other regulatory sequences may disrupt the activity of the ARX gene in some individuals with autism. Similarly, we cannot exclude the presence of duplications or deletions of ARX in our patients, as we did not perform quantitative analyses. Furthermore, the absence of coding changes does not preclude epigenetic abnormalities that might affect gene expression.

Autism was described in 4 subjects among 50 mentally retarded males in 9 X-linked families with ARX mutations (Stromme et al., 2002a;[START_REF] Turner | Variable expression of mental retardation, autism, seizures, and dystonic hand movements in two families with an identical ARX gene mutation[END_REF]. They belonged to two families carrying the duplication c.428-451 dup(24 bp), which represents the most frequent mutation of the ARX gene found in mental retardation and epilepsy. Interestingly, the same mutation in other family members manifested as isolated mental retardation or was associated with dystonia, infantile spasms, generalized tonic-clonic seizures or ataxia, underlining the intrafamilial phenotypic variability associated with ARX mutations (Stromme et al., 2002a). Similarly, Nawara et al. [START_REF] Nawara | The ARX mutations: a frequent cause of X-linked mental retardation[END_REF] reported 5 families with 19 affected patients with X-linked mental retardation carrying the 24-bp duplication; in one of the families, 2 of 4 affected males had autism.

The precise prevalence of ARX mutations in mental retardation is at present unknown but is likely to be low. The first study to explore ARX in mental retardation found mutations in 7 of 9 extended families with mental retardation linked to Xp22.1, 2 of 148 families with two affected brothers and 1 of 40 sporadic cases, suggesting that ARX mutations were a common cause of mental retardation [START_REF] Bienvenu | ARX, a novel Prd-class-homeobox gene highly expressed in the telencephalon, is mutated in X-linked mental retardation[END_REF]. The most recent estimates indicate that mutations in the ARX gene account for 9.5% of families with X-linked mental retardation but are less frequent in families with two affected brothers (2.2%) [START_REF] Poirier | Screening of ARX in mental retardation families: consequences for the strategy of molecular diagnosis[END_REF]. By contrast, the yield of ARX mutation analysis in sporadic males with mental retardation is extremely low. A recent Danish study screened exon 2 for two recurrent expansions of polyalanine tracts in 682 males with mental retardation, revealing only one putative mutation [START_REF] Gronskov | Screening of the ARX gene in 682 retarded males[END_REF]. Our negative findings after systematic sequence analysis of ARX in a large set of patients with autism and mental retardation, including 45 families with 2 or more affected brothers, 32 brother-sister pairs and 149 sporadic cases, are compatible with those reported for mental retardation.

In conclusion, the results of the present study indicate mutations of the ARX gene are a very rare cause of autism, as previously shown for other X-linked genes, such as MECP2 [START_REF] Carney | Identification of MeCP2 mutations in a series of females with autistic disorder[END_REF][START_REF] Zappella | Study of MECP2 gene in Rett syndrome variants and autistic girls[END_REF], NLGN3, and NLGN4X [START_REF] Jamain | Mutations of the X-linked genes encoding neuroligins NLGN3 and NLGN4 are associated with autism[END_REF], which have been screened in large Hal author manuscript inserm-00109595, version 1 cohorts of patients with autism. Thus, with the exception of FMR1, the number of patients found to be mutated for each X-linked gene appears to be very low. In addition, our findings suggest that routine molecular screening of ARX is not indicated in families with two siblings with autism or in sporadic patients.

ACKNOWLEDGMENTS

We are grateful to all the patients and their parents for their cooperation. We thank ML Picoche for technical assistance, the DNA and cell bank of the INSERM U679 (IFR des Neurosciences, Hôpital Pitié-Salpêtrière), and the Centre d'Investigations Cliniques, Hôpital Robert Debré, for obtaining the samples from the French families. This research was supported by Fondation Jérôme Lejeune, INSERM, Assistance Publique-Hôpitaux de Paris, Fondation pour la Recherche Médicale, Fondation France Télécom, Fondation de France, and the Swedish Medical Research Council. The participants of the Paris Autism Research International Sibpair (PARIS) Study are: France: INSERM U513, Université Paris XII, Créteil: Catalina Betancur; Department of Psychiatry, Hôpital Albert Chenevier et Henri Mondor, AP-HP, Créteil: Marion Leboyer; Service de Psychopathologie de l'Enfant et l'Adolescent, Hôpital Robert Debré, AP-HP, Paris: Pauline Chaste, Deborah Cohen, Catherine Colineaux, Nadia Chabane, Marie-Christine Mouren-Siméoni. Sweden: Department of Child and Adolescent Psychiatry, Göteborg University, Göteborg: Christopher Gillberg, Maria Råstam, Gudrun Nygren, Henrik Anckarsäter, Carina Gillberg, Ola Ståhlberg. Norway: Centre for Child and Adolescent Psychiatry, University of Oslo, Oslo: Eili Sponheim; Department of Pediatrics, Rikshospitalet, University of Oslo, Oslo: Ola H. Skjeldal. USA: Department of Pediatrics, Georgetown University School of Medicine, Washington D.C.: Mary Coleman; Children's National Medical Center, George Washington University School of Medicine, Washington, D.C.: Philip L. Pearl; New York State Institute for Basic Research in Developmental Disabilities, Staten Island, New York: Ira L. Cohen, John Tsiouris. Italy: Divisione di Neuropsichiatria Infantile, Azienda Ospedaliera Senese, Siena: Michele Zappella. Austria: Department of General Psychiatry, University Hospital, Vienna: Harald Aschauer. Belgium: Centre de Génétique Humaine, Institut de Pathologie et de Génétique, Gerpinnes, Loverval: Lionel Van Maldergem.


Kevin Carpentier
email: kevin.carpentier@hds.utc.fr

Domitile Lourdeaux
email: domitile.lourdeaux@hds.utc.fr

An Approach for Narrative Scaffolding in Open-World Simulations for Training

Keywords: virtual training, interactive storytelling, constraint satisfaction problem, structuralism, semiotic, semantic representation

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Context

This paper describes an approach for framing a sequence of events in a virtual simulation to comply with narrative constraints. We focus our studies on virtual environments for training (VET) and especially on open-world simulations. Open-world simulations offers a high freedom of action to enable situated learning. In order to mimic real work situations, such simulations are populated with autonomous characters upon which no direct control can be enforced. Such a design permits the emergence of unexpected scenarios without authoring effort. Pedagogical control is added by taking into account expert knowledge from trainers or by joining an Intelligent Tutoring System (ITS) to the VET. Trainers and ITS can monitor the simulation by dynamically prescribing relevant learning situations. Then, a scenario manager is responsible for guiding the simulation toward the prescribed situations. This architecture enables the generation of a highly personalized pedagogical scenario which is experienced by the user in the simulation. Yet, trainers are not storytelling experts and an ITS does not always consider narrative aspects. Without narrative control, pedagogical scenarios lack story continuity and tension management. Our purpose is to ensure that events taking place in the simulation, occurring autonomously or resulting from a prescription, tell an appealing story. A first difficulty lies in recognizing attractive plot lines in a sequence of event. Another difficulty is to add narrative aspects to trainer's prescriptions without prejudice to the pedagogical intent. In order to achieve this, we propose to consider the problem as a constraint satisfaction problem. The originality lies in the semantic representation of narrative constraints to allow easy authorship and deep reasoning.

To illustrate our work, we propose here a simple example of training of operators on hazardous-matter loading. A trainer prescribes a pedagogical situation where the learner would have to handle a hazardous-matter leak on a tank. Such an incident usually results from human neglect. Therefore, the prescription involves a responsible and a leaking valve. The prescription could be instantiated by picking any character and any tank in the virtual environment. However, by selecting these entities according to narrative rules, we can create continuity upon the sequence of events. A storyworld is gradually scaffolding each time a prescription is enriched with narrative content.

We named this approach "diegetization" in reference to the authoring process of building the diegesis [START_REF] Odin | De la fiction[END_REF]. The diegesis is the universe in which the story take place. In the next section of this paper, motivations for the choice of a narrative construction are presented. Then, a brief review of related works is presented. The process of diegetization and its application are described in section 3 and 4. The last section concludes this paper with discussions and perspectives.

Narrative for learning

A first argument for the use of narrative in learning context is quite pragmatic. Indeed, as narrative is a natural expressive form [START_REF] Bruner | Acts of meaning[END_REF], it can be presented through different modalities. It can be told through text or speech, shown through pictures or, as in this case, experienced through an interactive simulation. Moreover, narrative is a support for cognitive activities. Through narrative, learners are engaged in active thinking and are supported in their process of meaning construction [START_REF] Dettori | Narrative learning in technology-enhanced environments[END_REF]. This helps learners to organize knowledge and to develop cognitive abilities [START_REF] Schank | Tell me a story: Narrative and intelligence[END_REF]. Narrative can also be instrumented to build motivation. Motivation is most significant to ease learning processes in pedagogical activities [START_REF] Malone | Making learning fun: A taxonomy of intrinsic motivations for learning[END_REF] in many ways. First, a storyline can arouse learners' curiosity. By taking into account their behaviours, an interactive narrative reinforces the learners' feeling of control in the simulation. Moreover, a storyworld is where fantasy can take place: learners can identified themselves with characters depicted through the story. Finally, narrative also provides interpersonal motivation through cooperation and competition between the user and the other characters depicted in the storyline. Besides, a strong motivation comes from recognition: it happens when the learners are rewarded for their good behaviours.

As storytelling proves to be particularly efficient for learning and training, we aim to add a narrative layer upon the pedagogical prescription over the scenario. The definition of a quality criteria of a narrative is therefore fundamental to assess the quality of the content generated by the system. An engine for building narrative has to offer variability, thus same kind of situations can be told through different stories. It also has to be resilient to cope with whatever actions the autonomous characters or users may perform against the storyline. However, the production of a VET is a very time-consuming task. The addition of narrative to a VET should be easy and should require a minimal amount of authoring. The work presented in this paper try to tackle the issue of balancing quality and resilience without compromising variability and minimal handmade authoring.

Related Work

First attempts of story generation make the narrative emerges from the mechanical execution of world rules [START_REF] Klein | Automatic novel writing: A status report[END_REF][START_REF] Meehan | TALE-SPIN, an interactive program that writes stories[END_REF][START_REF] Bringsjord | Artificial intelligence and literary creativity: Inside the mind of brutus, a storytelling machine[END_REF]. [START_REF] Dehn | Story generation after TALE-SPIN[END_REF] argues that such systems, qualified as world-simulation based story generation lack the creative process of the author. She proposed an author-intent-based process: the author build a story around a sequence of events, therefore he/she is able to add/modify/remove characters, locations or plot points in order to create richer stories. [START_REF] Pérez | MEXICA: A computer model of a cognitive account of creative writing[END_REF] pushed this notion further and proposed an engine that simulates an author's behaviour in a two-phased generation process: an engagment stage to explore every possibilities and a reflection stage to ensure coherency. We think a similar approach can be adapted to our dynamic context to foster the story quality.

Recent works on story generation are usually pinned on a spectrum ranging from strong story approaches to strong autonomy approaches depending on the amount of global control [START_REF] Mateas | Towards integrating plot and character for interactive drama[END_REF]. In strong autonomy approaches [START_REF] Swartjes | Let's pretend i had a sword[END_REF], virtual characters act independently without any coordination. Yet, the story emerges from the individual decisions of the virtual characters. However, the lack of coordination between characters infringes the global quality of stories. In [START_REF] Mott | U-director: a decision-theoretic narrative planning architecture for storytelling environments[END_REF][START_REF] Young | An architecture for integrating plan-based behavior generation with interactive game environments[END_REF], a central agent controls the simulation to ensure that the unfolding of events follows a specific path. Thanks to this control, it is possible to generate stories of high quality. Yet, as virtual characters are being supervised their behaviours might seem incoherent. To tackle this issues, some works attempt to balance global control with autonomous behaviours. In [START_REF] Riedl | Dynamic experience management in virtual worlds for entertainment, education, and training[END_REF], the world is populated by semi-autonomous characters: they act freely until the Automated Story Director gives them an order. Even if the transition between the autonomous stage and the controlled stage is subtle, the switch in the personality might seem incoherent to the user. Facade [START_REF] Mateas | Façade: An experiment in building a fully-realized interactive drama[END_REF] also relies on a hybrid approach: virtual characters act autonomously to satisfy a goal proposed at a higher level by a drama manager which handle the coherency. Unfortunately, this kind of approach requires a huge amount of authoring.

Whatever approach is used, an interactive storytelling system embeds preferences about narrative aspects. Such preferences can either be explicit or implicit. Explicit preferences are specific plot points which are preferred over other because they are mandatory for the story continuity or because they induce a particular tension effect [START_REF] Porteous | Applying planning to interactive storytelling: Narrative control using state constraints[END_REF]. Implicit preferences allow a more subtle control by putting constraints on properties of the scenario. For instance, in Idtension [START_REF] Szilas | A computational model of an intelligent narrator for interactive narratives[END_REF], characters' actions are selected to maximise narrative criterion such as the cognitive load or the level of conflict.

The work presented in this paper is another attempt to balance strong story approach with emergent behaviours. The simulation in which the scenario take place is executed through a character-based approach: the VET is populated by autonomous characters upon which no control is possible. However, they were designed to reproduce human behaviours, they do not comply to narrative constraints. Therefore, global supervision is necessary to manage tension, to assure narrative continuity and to provide an appealing story.

Approach

Narrative Theory

[19] defines a narrative as the recounting of a sequence of events that have a continuant subject and constitute a whole. This definition constitutes a lower bound to what has to be achieved: the events taking place in the simulation must have a continuant subject and be holistically understandable. Since classical era, the minimal steps of a story have been canonized. Grammatical views of narrative were proposed to analyse existing texts [START_REF] Propp | Morphology of the Folktale[END_REF][START_REF] Todorov | La grammaire du récit[END_REF]. They were used more recently to generate narrative [START_REF] Peinado | Evaluation of automatic generation of basic stories[END_REF]. A purely grammatical approach is too restrictive and would hardly fit the resilience objective. Yet, [START_REF] Beck | La linguistique historique et son ouverture vers la typologie[END_REF] suggested the concept of grammaticality which rests upon three principles:

1. A narrative is better than another one if it is more compliant to a grammar than the other one. 2. Narrative structures must respect grammar ordering.

3. High-level constraints are more important than low-level constraints.

These considerations focus on the sequence of a narrative but struggle to depict the structure of one element of the sequence. Building his theory upon Greimas' actancial model [START_REF] Greimas | Sémantique structurale : recherche et méthode[END_REF][START_REF] Bremond | Logique du récit[END_REF] proposed a more abstract model consisting of the following elements:

-Functions are relevant actions in regard of the story progression-Example:

Saving the World -Roles are functions grouped together -Example: The Savior -Actants are abstract entities entitled with one or many roles -Example :

The Protagonist -Actors are concrete instances of actants -Example: Eric This structuralist approach offers a framework to describe abstract story organizations. Therefore, it can be used to model stereotypical narrative structures such as the dramatic situations listed by [START_REF] Polti | Les 36 situations dramatiques[END_REF] or [START_REF] Souriau | Les deux cent mille Situations dramatiques[END_REF].

These thoughts from various semioticians have guided the design of the diegetization process. First, we design a model, inspired by Bremond's grammar, to inform abstract narrative patterns. Graph matching algorithms recognize these narrative sequences in the unfolding of events. Then, techniques for constraint satisfaction problems are used to select and instantiate patterns fulfilling the provided pedagogical goal. A quality criteria assess the best pattern among the possibilities. This process illustrated in figure 1 is explained in following sections.

Models

The diegetization process requires to reason about two kinds of knowledge: knowledge about the world depicted by the simulation and knowledge about narrative patterns. For the sake of modularity, these two kinds of knowledge are informed in two different models. Consequently, the model of narrative patterns can be used with different models of the world which makes the approach fully domain-independent. For both models, the use of semantic representation allow for rich inferences about object capabilities and their evolution. The World model and the Diegetic model are ontologies written in Owl/rdf language. Therefore, they benefits from owl semantic inferences and can easily be queried using SparQL for graph pattern matching.

WORLD Model. The World model describes the world simulated by the virtual environment. It especially informs knowledge about the agents that populate the virtual world, the objects with which the user can interact and possible actions he/she can trigger. The World model is written by experts of the domain of application and do not consider any narrative aspects. It is fully domain-dependent.

DIEGETIC Model. The Diegetic model is directly inspired by Bremond's grammar. It describes high-level entities to enable the specification of narrative structures:

-Element described meaningful entities within a narrative context. There are two types:

• Role: a set of capabilities -Example : The Traitor • Actant: an aggregation of Role -Example : Antagonist Elements can either be impersonated by characters, concrete objects (items, locations, etc.) or abstract objects (life, love, etc.).

-Function: a relationship linking an Element to another one or to a primitive type (boolean, float, string, etc.). They can be involved in two kind of expressions:

• Constraints are nomological constraints describing the state in which an Element should be to make a narrative structure possible -Example: (?x is-a :Antagonist)(?x :has-ally ?y) • Properties are relationships checked by a narrative structure -Example:

(?x is-a :Treator)(?y is-a :Protagonist)(?x :harm ?y). :is-a,:has-ally and :harm are examples of functions. Functions are associated with :

• an intrinsic-significance (IS) value which measures the importance of the object for the subject of the relation on a zero to one scale. Example: the :has-ally function has an IS 0.7. It means that the modification or the removal of the function between ?x and ?y is quite important for ?x. • an extrinsic-significance (ES) value which describes the importance of the function in a narrative structure. Example: the :harm function has an ES value of 0.95. It means this function is fundamental for the pattern in which it is expressed to be meaningful. -Pattern is a specific set of functions between roles, it is also referred as narrative structure. -Path describes the preferable transition between two Patterns -Example :

Treason -> Remorse.

The diegetic model is fully domain-independent and is used to describe any narrative pattern. It can be filled by storytelling experts, yet, we plan to write a canonical library of narrative patterns inspired by Polti's dramatic situations [START_REF] Polti | Les 36 situations dramatiques[END_REF]. A sequence of narrative pattern written in the Diegetic representation is shown in figure 2.

Instantiation

Periodically, the pedagogical module produces a pedagogical prescription. It depicts a world state which should be encountered by the learner. Situations are formalized through rdf graphs consisting in fragments of a World model. Such fragment generally includes both conceptual descriptions such as (?anyvalve :has-state :leaking) as much as instantiated descriptions such as (:Valve01 :has-state :leaking). Graphs including abstract concepts need to be instantiated by referring to the up-to-date world state. A graph can be instantiated in various ways (figure 3).

Narrative Framing

For each instantiated situation, a possible world is created by assuming that the situation is true in the current world state. The narrative framing process searches possible world to recognize narrative patterns which are consistent with the storyline. This is a three-stage process: alignment, exploration and consistency-checking.

Alignment. The world state, which is fully domain-dependent, must be translated in terms of generic diegetical functions e.g. either properties or constraints. As both models are expressed through ontological representations, we use alignment rules to infer existing diegetical functions in the current world state. These rules are common-sense knowledge and can be written by pedagogical experts. For instance, a simple rule infers that characters involved in cooperative work (world model) are mutual allies (diegetic model).

Exploration. SparQL queries are generated from the description of the patterns in terms of functions. Each possible world, describing an alternate world state, is interrogated by these queries. The results from these queries feature all possible instantiations of the pedagogical prescription fitting into a narrative structure. Queries are generated so that their results provide a mechanism similar to late commitment [START_REF] Swartjes | Let's pretend i had a sword[END_REF]: a pattern frames a situation if it finds no contradictions. A framed situation involves the entities of the initial prescription. Beside, it also involves other entities needed to fill all the elements in the pattern. A framed situation is formalized through a graph S whose nodes are elements and whose arcs are functions. At this stage, each possibility is explored regardless of the coherence between the pattern and past events.

Coherency-checking. This stage aims to assure coherency of the whole story taking place since the beginning of the simulation. It checks the existence of a path between current situations and previous ones. Inconsistent situations are dismissed. In the case where no situations survive this stage, trade-off are performed: constraints are relaxed by deleting less-valued properties and a new cycle of exploration/consistency-checking is performed. The coherency-checking stage ensures that the narrative elements remain consistent. For instance, an ally will remain an ally throughout the plot line unless a pattern of treason make it otherwise.

Narrative Program Assessment

[24] proposed a formal description of the evolution of the entities in a story through narrative program. A narrative program is the gain or the loss of a function R between a subject S 2 and an object O when it is considered by an observer S 1 . In other words, a narrative program describes a shift in the relationship between S 2 and O as perceived by S 1 . S 1 , S 2 and O can be assimilated to diegetical elements (objects, characters, places, etc.).

We proposed to use narrative program to measure the evolution of dramatic tension during the sequence of events. The narrative program assessment computes the value of the tension generated between two simulation steps by using the intrinsic and extrinsic significance defined in section 3.2. An instrinsic value between S 1 and S 2 , noted I(S 1 , S 2 ), is the maximum of the products of the intrinsic-significance of the function in all the possible paths between S 1 and S 2 . E(R) is the extrinsic-significance of the function R. T (S 1 ) is the tension for the subject S1. Its value is the sum of all narrative programs (N P ) in which it is involved :

T (S 1 ) = (s,r,o)∈N P (S1) I(S 1 , s) * (1 + I(S1, o)) * E(r) . (1)
We propose to use the value T (U ser) where U ser is the entity representing the user in the knowledge base in order to monitor the dramatic tension he/she perceives.

Decision using a quality criteria

Each framed situation S is evaluated according to three criterion:

-O(S) ∈ [0, 1] is a measure of adequacy between opening needs and opening opportunities. The opening measures the number of narrative path that can follow the current step. In the beginning of the simulation, the opening needs are high to maximise the possibilities of diegetization. Such constraints can be relaxed when the session reaches its end. -T (S) ∈ [0, 1] is the ratio between the estimated tension of S and the expected value of tension according to a pre-defined curve. -G(S) ∈ [0, 1] is an evaluation of the grammaticality of a framed situation. It takes into account the trade-off made on the constraints during the exploration/consistency-checking cycle.

The narrative utility of S according to the current step of simulation is U (S) = O(S) + T (S) + G(S). The situation S with the highest U (S) is selected to be the world state prescription.

Results

Implementation

We implemented the diegetization approach in Java using the Jena Framework [28]. It communicates as an agent in the multi-agent system of the Humans platform [START_REF] Lanquepin | HUMANS: a HUman models based artificial eNvironments software platform[END_REF]. The Director module introduced by [START_REF] Barot | Dynamic scenario adaptation balancing control, coherence and emergence[END_REF] is used to lead seamlessly the simulation toward the world state prescriptions. At the moment, the story is only represented by mimetic means. The user experienced the story through the actions of the characters and through the different event taking place. Further research will consider possibilities to foster narrative understanding such as dialog generation and extra-diegetic indication. At the moment, a selection among the thirty-six Polti's dramatic situations [START_REF] Polti | Les 36 situations dramatiques[END_REF] have been informed as pattern in the Diegetic model.

Application

The approach have been applied on a very delimited use-case: virtual training for loading hazardous-matter in oil depot. We design a World model with the help of domain expert for this application. It includes four characters. Bob is the user's avatar. Philip is one of Bob's co-workers. Eric works in a different team. Paul is their supervisor. Philip, Eric and Paul are controlled by autonomous characters. Workers have to perform hazardous-matter loading on a tank through valves. Leaks can occur due to carelessness in the procedure.

For the sake of the demonstration we only present three steps in the simulation with two different tension curves (figure 4). The first condition involves a classical aristotelian tension arc, in which the climax, occurring at the second step has a medium tension value. In the second condition, the climax has a high tension value and is followed by a step with a medium tension value. In both conditions, a first diegetization procedure is run after the pedagogical module from the Humans platform [START_REF] Carpentier | Dynamic selection of learning situations in virtual environment[END_REF] has issued a prescription : (?someone :trigger-leak ?valve). A new diegetization procedure without specific pedagogical goal is issued after the resolution of the previous situation. Partial results In the first step, the prescription issued by the pedagogical module is instantiated for each characters. In particular these situations can be framed by S1,S2 and S3 (other possibilities were not presented in the figure). In the condition 1, S2 is preferred to S1 according to the tension adequacy criteria. S3 is dismissed in both condition because it lacks opening opportunities.

In both S1 and S2 Bob is offended by another worker. In S1, Bob is offended by someone who is his ally. The intrinsec-significance of offend and has-ally are taken into account to compute T (Bob) in the narrative program assessment. S1 is more tense than S2. It is explained by the fact that it is harder to be offended by someone you are supposed to rely on. Thanks to quality evaluation, S1 fits with the first tension curve whereas S2 fits with the second tension curve. S1 is followed by S4 and S6. The extrinsec-significance of beg is quite high. Therefore, to comply with the expected tension in condition 1, S6 is preferred over S4. In the first step, a role is given to elements of the simulation (characters in this case). It is gradually strengthened and enriched throughout the scenario to scaffold the story universe in accordance with a predefined tension curve.

Our work on pedagogical orchestration of training simulation leads us to consider using narrative as a motivational factor. Yet, the simulation taking place in an open-world, the control possibilities are quite seldom. To tackle this difficulty, we proposed the process of diegetization which relies on the recognition and on the scaffolding of narrative structure. Our propositions were implemented in the Humans platform and tested on a small use-case. Results are in agreement with the objectives. In the short term, we will apply the proposition to a real use-case in training for risk prevention. Experiments on the perception and the opinion of the generated storylines by the user will be conducted. Thanks to this study, we will be able to consider the best possibilities to foster story understanding without breaking the feeling of immersion of the user.

Fig. 1 .

 1 Fig. 1. Schematic view of the diegetization process

Fig. 3 .

 3 Fig. 3. Instantiation

Fig. 4 .

 4 Fig. 4. Curve of tension for condition 1 and 2

Fig. 5 .

 5 Fig. 5. Results of the diegetization process in condition 1 and 2

Acknowledgements

This work was made possible thanks to the funding of ANR project: NIKITA (Natural Interaction, Knowledge and Immersive systems for Training in Aeronautic).