Predicting one Shot Play in 2x2 Games Using Beliefs Based on Minimax Regret

We present a simple procedure that selects the strategies most likely to be played by inexperienced agents who interact in one shot 2x2 matching pennies games. As a first step we axiomatically describe players’ beliefs. We find the minimax regret criterion to be the simplest functional form that satisfies all the axioms. Then we hypothesize players act as if they were best responding to the belief their opponent plays accordino to minimax regret. When compared with existing experimental evidences about one shot matching pennies games, the procedure correctly indicates the choices of around 80% of the players. Applications to other classes of games are also explored.Predictions, Minimax regret, Beliefs, Matching pennies, Experiments

Approximate Well-supported Nash Equilibria below Two-thirds

In an epsilon-Nash equilibrium, a player can gain at most epsilon by changing his behaviour. Recent work has addressed the question of how best to compute epsilon-Nash equilibria, and for what values of epsilon a polynomial-time algorithm exists. An epsilon-well-supported Nash equilibrium (epsilon-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most epsilon less than the best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee

Ten Little Treasures of Game Theory and Ten Intuitive Contradictions

This paper reports laboratory data for a series of two-person games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment for which behavior conforms quite nicely to the predictions of the Nash equilibrium or relevant refinement. In each case we change a key payoff parameter in a manner that does not alter the equilibrium predictions, but this theoretically neutral payoff change has a major (often dramatic) effect on observed behavior. These contradictions are generally consistent with simple economic intuition and with a model of iterated noisy introspection for one-shot games.Nash equilibrium, noncooperative games, experiments, bounded rationality, introspection

Stated versus inferred beliefs: A methodological inquiry and experimental test

If asking subjects their beliefs during repeated game play changes the way those subjects play, using those stated beliefs to evaluate and compare theories of strategic behavior is problematic. We experimentally verify that belief elicitation can alter paths of play in a repeated asymmetric matching pennies game. In this setting, belief elicitation improves the goodness of fit of structural models of belief learning, and the prior beliefs implied by such structural models are both stronger and more realistic when beliefs are elicited than when they are not. These effects are, however, confined to the player type who sees a strong asymmetry between payoff possibilities for her two strategies in the game. We also find that “inferred beliefs” (beliefs estimated from past observed actions of opponents) can be better predictors of observed actions than the “stated beliefs” resulting from belief elicitation.beliefs; stated beliefs; belief elicitation; inferred beliefs; estimated beliefs; belief updating; repeated games; experimental methods

Are the Treasures of Game Theory Ambiguous?

Goeree & Holt (2001) observe that, for some parameter values, Nash equilibrium provides good predictions for actual behaviour in experiments. For other payoff parameters, however, actual behaviour deviates consistently from that predicted by Nash equilibria. They attribute the robust deviations from Nash equilibrium to actual players’ considering not only marginal gains and losses but also total pay-offs. In this paper, we show that optimistic and pessimistic attitudes towards strategic ambiguity may induce such behaviour.

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