Economists use the word rational in a narrow way. To an economist, a rational actor is someone who makes decisions that maximize her (or his) preferences subject to constraints imposed by the environment. So, this actor knows her preferences and knows how to go about optimizing. It is a powerful approach, but it probably is only distantly related to what you mean when you think of yourself as r...

In future battlefields and other emerging multiagent applications, agents must communicate in an inherently hostile environment in which an adversary has strong incentives to disrupt or intercept communication. Intelligent agents must balance network performance with possible harm suffered from the adversary’s attacks, given that the adversary is actively and rationally balancing his own costs ...

The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be inexact or uncertain, which requires that the model of matrix games has the ability to represent and deal with imprecise payoffs. To meet suc...

We consider a zero-sum stopping game (Dynkin’s game) with a threshold probability criterion in discrete time stochastic processes. We first obtain fundamental characterization of value function of the game and optimal stopping times for both players as the result of the classical Dynkin’s game, but the value function of the game and the optimal stopping time for each player depend upon a thresh...

We apply existing, and develop new, zero-sum game techniques for designing polynomial-time algorithms to compute additive approximate Nash equilibria in bimatrix games. In particular, we give a polynomial-time algorithm that given an arbitrary bimatrix game as an input, outputs either an additive 1 3 -Nash equilibrium or an additive 1 2 -well-supported Nash equilibrium; and we give a polynomial...

We present a simple primal-dual algorithm for computing approximate Nash equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold’em poker). Our algorithm only performs basic iterations (i.e matvec multiplications, clipping, etc., and no calls to external first-order oracles, no matrix inversions, etc.) and is applicable to a broad class...

Zero-sum stochastic games provide a formalism to study competitive sequential interactions between two agents with diametrically opposing goals and evolving state. A solution to such games with discrete state was presented by Littman (Littman, 1994). The continuous state version of this game remains unsolved. In many instances continuous state solutions require nonlinear optimisation, a problem...

Laboratory subjects repeatedly played one of two variations of a simple two-person zero-sum game of ‘‘hide and seek’’. Three puzzling departures from the prescriptions of equilibrium theory are found in the data: an asymmetry related to the player’s role in the game; an asymmetry across the game variations; and positive serial correlation in subjects’ play. Possible explanations for these depar...

We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some second order Hamilton-Jacobi equation. Key-words : stochastic differential game, asymmetric information, viscosity solution. A.M.S. classification : 49N70, 49L...