Finite mixture analysis of beauty-contest data using generalised beta distributions

This paper introduces a mixture model based on the beta distribution, without preestablished means and variances, to analyze a large set of Beauty-Contest data obtained from diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a better t of the experimental data, and more precision to the hypothesis that a large proportion of individuals follow a common pattern of reasoning, described as iterated best reply (degenerate), than mixture models based on the normal distribution. The analysis shows that the means of the distributions across the groups of experiments are pretty stable, while the proportions of choices at dierent levels of reasoning vary across groups.Keywords: Beauty-Contest experiments, decision theory, reasoning hierarchy, finite mixture distribution, beta distribution, EM algorithm.

Billiards and Brains: Cognitive Ability and Behavior in a p-Beauty Contest

"Beauty contests" are well-studied, dominance-solvable games that generate two interesting results. First, most behavior does not conform to the unique Nash equilibrium. Second, there is considerable unexplained heterogeneity in behavior. In this work, we evaluate the relationship between beauty contest behavior and cognitive ability. We find that subjects with high cognitive ability exhibit behavior that is closer to the Nash equlibrium. We examine this finding through the prism of economic and biological theory.beauty contest; rationality; cognitive ability; Nash equlibrium

Who should be called to the lab? A comprehensive comparison of students and non-students in classic experimental games

This study compares the behavior of students and non-students in a number of classic experimental games. We find that students are more likely to behave as homo-economicus agents than non-students in games involving other-regarding preferences (Dictator Game, Trust Game and Public Good Game). These differences persist even when controlling for demographics, cognitive ability and risk preferences. In games that do not engage other-regarding preferences (Beauty-contest and Second-price Auction) there is limited evidence of differences in behaviour between subject pools. In none of the five games is there evidence of significant differences in comprehension between students and non-students. Within subject analyses indicate that students are highly consistent in their other-regarding preferences while non-student subjects are inconsistent across other-regarding games. Our findings suggest that experiments using students will provide a lower bound estimate of other-regardedness in the general population while exaggerating the stability of other-regarding preferences.lab experiments, convenience samples, other-regarding preferences, consistency

Cognitive effort in the Beauty Contest Game

This paper analyzes cognitive effort in 6 different one-shot p-beauty games. We use both Raven and Cognitive Reflection tests to identify subjects' abilities. We find that the Raven test does not provide any insight on beauty contest game playing but CRT does: subjects with higher scores on this test are more prone to play dominant strategies.Beauty Contest Game, Raven, Cognitive Reflection Test

On the absorbability of the Guessing Game Theory. A Theoretical and Experimental Analysis

Theory absorption, a notion introduced by Morgenstern and Schwödiauer (1972) and further elaborated by Güth and Kliemt (2004), discusses the problem whether a theory can survive its own acceptance. Whereas this holds for strategic equilibria according to the assumptions on which they are based, the problem if theories are absorbable by at most boundedly rational decision makers is hardly discussed. Based on guessing game experiments we discuss the requirements of equilibrium theory absorption and test experimentally the effects of informing none, some or all players about how to derive equilibrium predictions.theory absorption; guessing game; p-beauty contest; individual behaviour; elimination of dominated strategies

Teaching Nash Equilibrium and Strategy Dominance: A Classroom Experiment on the Beauty Contest

The aim of this investigation is to display how the use of classroom experiments may be a good pedagogical tool to teach the Nash equilibrium (NE) concept. The basic game for our purposes is a repeated version of the Beauty Contest Game (BCG), a simple guessing game whose repetition lets students react to other players’ choices and to converge iteratively to the equilibrium solution. We performed this experiment with undergraduate students without any previous knowledge about game theory. After four rounds, we observed in all groups a clear decreasing tendency in the average chosen number. So, our findings prove that, by playing a repeated BCG, students quickly learn how to reach the NE solution.Classroom Experiments, Beauty Contest Game, Teaching, Nash Equilibrium.

Hierarchical Reasoning versus Iterated Reasoning in p-Beauty Contest Guessing Games

This paper analyzes strategic choice in p-beauty contests. We first show that it is not generally a best reply to guess the expected target value (accounting for the own weight) even in games with n>2 players and that iterated best response sequences are not unique even after perfect/cautious refinement. This implies that standard formulations of ``level-k'' models are neither exactly nor uniquely rationalizable by belief systems based on iterated best response. Second, exact modeling of iterated reasoning weakens the fit considerably and reveals that equilibrium types dominate the populations. We also show that ``levels of reasoning'' cannot be measured regardless of the underlying model. Third, we consider a ``nested logit'' model where players choose their level. It dispenses with belief systems between players and is rationalized by a random utility model. Besides being internally consistent, nested logit equilibrium fits better than three variants of the level-k model in standard data sets.logit equilibrium, hierarchical response, level-k, beauty contest

A cognitive hierarchy theory of one-shot games: Some preliminary results

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modelling principles in noncooperative game theory. This paper relaxes mutual consistency to predict how players are likely to behave in in one-shot games before they can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f (k). Zero-step players randomize. Players using k (≥ 1) steps best respond given partially rational expectations about what players doing 0 through k - 1 steps actually choose. A simple axiom which expresses the intuition that steps of thinking are increasingly constrained by working memory, implies that f (k) has a Poisson distribution (characterized by a mean number of thinking steps τ ). The CH model converges to dominance-solvable equilibria when τ is large, predicts monotonic entry in binary entry games for τ < 1:25, and predicts effects of group size which are not predicted by Nash equilibrium. Best-fitting values of τ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable p-beauty contests. The CH model also has economic value because subjects would have raised their earnings substantially if they had best-responded to model forecasts instead of making the choices they did