A coupling game is a new model for partly cooperative and partly non-cooperative games. This paper describes benefits that result when coupling rational cooperation, under some situations, is increased. We prove that if a coupling game is strictly rational and partly cooperative, the higher the coupling factors, the larger the social payoff, which is the sum of the payoffs of all players. Other...

The slow-coloring game is played by Lister and Painter on a graph G. On each round, Lister marks a nonempty subsetM of the remaining vertices, scoring |M | points. Painter then deletes a subset of M that is independent in G. The game ends when all vertices are deleted. Painter’s goal is to minimize the total score; Lister seeks to maximize it. The score that each player can guarantee doing no w...

We study a zero sum differential game under strong assumptions of convexity — the cost is convex for one player, and concave for the other. An explicit necessary and sufficient condition for a saddle point of the game is given in terms of convex analysis subgradients of the conjugate of the cost function. A generalized Hamiltonian equation is shown to describe saddle trajectories of the game.

This paper examines the convergence of payoffs and strategies in Erev and Roth’s model of reinforcement learning.When all players use this rule it eliminates iteratively dominated strategies and in two-person constant-sum games average payoffs converge to the value of the game. Strategies converge in constant-sum games with unique equilibria if they are pure or if they are mixed and the game is...

Subjective games of incomplete information are formulated where some of the key assumptions of Bayesian games of incomplete information are relaxed. The issues arising because of the new formulation are studied in the context of a class of nonzero-sum, two-person games, where each player has a different model of the game. The static game is investigated in this note. It is shown that the proper...

The Nash equilibria of a two-person, non-zero-sum game are the solutions of a certain linear complementarity problem (LCP). In order to use this for solving a game in extensive form, the game must first be converted to a strategic description such as the normal form. The classical normal form, however, is often exponentially large in the size of the game tree. If the game has perfect recall, a ...

We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sum-rate optimal point on the boundary of the multipleaccess channel capacity region is the unique Nash Equilibrium of the corresponding water-fil...

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...