Thinking about Attention in Games: Backward and Forward Induction

Behavioral economics improves economic analysis by using psychological regularity to suggest limits on rationality and self-interest (e.g. Camerer and Loewenstein 2003). Expressing these regularities in formal terms permits productive theorizing, suggests new experiments, can contribute to psychology, and can be used to shape economic policies which make normal people better off

On the Rule of Chance Moves and Information in Two-Person Games

The value of information has been the subject of many studies in a strategic context.The central question in these studies is how valuable the information hidden in the chance moves of a game is for one or more of the players.Generally speaking, only the extra possibilities that are beneficial for the players have been considered so far.In this note we study the value of information for a special class of two-person games.For these games we also investigate how badly the players can do, both with and without knowing the result of the chance move. In this way one can determine to what extent the players are restricted in their possibilities by the fact that some information is hidden in the chance moves of the games.This allows for a comparison of the influence of the chance move to the control that the players have over the game result.information;games;control

On values of repeated games with signals

We study the existence of different notions of value in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in general. Then we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We also prove two other positive results without assumptions on the signaling structure: the existence of the $\sup$ value in any game and the existence of the uniform value in recursive games with nonnegative payoffs.Comment: Published at http://dx.doi.org/10.1214/14-AAP1095 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Solving Large Extensive-Form Games with Strategy Constraints

Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zero-sum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many situations, however, we would like to constrain the set of possible strategies. For example, constraints are a natural way to model limited resources, risk mitigation, safety, consistency with past observations of behavior, or other secondary objectives for an agent. In small games, optimal strategies under linear constraints can be found by solving a linear program; however, state-of-the-art algorithms for solving large games cannot handle general constraints. In this work we introduce a generalized form of Counterfactual Regret Minimization that provably finds optimal strategies under any feasible set of convex constraints. We demonstrate the effectiveness of our algorithm for finding strategies that mitigate risk in security games, and for opponent modeling in poker games when given only partial observations of private information.Comment: Appeared in AAAI 201

Adaptive social learning

This paper investigates the learning foundations of economic models of social learning. We pursue the prevalent idea in economics that rational play is the outcome of a dynamic process of adaptation. Our learning approach offers us the possibility to clarify when and why the prevalent rational (equilibrium) view of social learning is likely to capture observed regularities in the field. In particular it enables us to address the issue of individual and interactive knowledge. We argue that knowledge about the private belief distribution is unlikely to be shared in most social learning contexts. Absent this mutual knowledge, we show that the long-run outcome of the adaptive process favors non-Bayesian rational play.social Learning ; informational herding ; adaptation ; analogies ; non-Bayesian updating

When is the individually rational payoff in a repeated game equal to the minmax payoff?

We study the relationship between a player’s (stage game) minmax payoff and the individually rational payoff in repeated games with imperfect monitoring. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely repeated game ‘nearly’ satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.