Two important metrics for measuring the quality of routing paths are the maximum edge con-gestion C and maximum path length D. Here, we study bicriteria in routing games where eachplayer i selfishly selects a path that simultaneously minimizes its maximum edge congestion Ciand path length Di. We study the stability and price of anarchy of two bicriteria games:• Max games, where ...

We examine a solution concept, called the “value,” for n-person strategic games. In applications, the value provides an a-priori assessment of the monetary worth of a player’s position in a strategic game, comprising not only the player’s contribution to the total payoff but also the player’s ability to inflict losses on other players. A salient feature is that the value takes account of the co...

We examine a solution concept, called the “value,” for n-person strategic games. In applications, the value provides an a-priori assessment of the monetary worth of a player’s position in a strategic game, comprising not only the player’s contribution to the total payoff but also the player’s ability to inflict losses on other players. A salient feature is that the value takes account of the co...

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...

An infinite two-player zero-sum game with a Borel winning set, in which the opponent’s actions are monitored eventually but not necessarily immediately after they are played, admits a value. The proof relies on a representation of the game as a stochastic game with perfect information, in which Nature operates as a delegate for the players and performs the randomizations for them.

We show that even when the information structure is independent of the state of nature, the value of the n-stage zero-sum game with incomplete information is not necessarily monotonic with respect to the length of the game. More precisely, we give an example of such an n-stage game in which v~>v~<v~.

In this paper we study the nonzero-sum Dynkin game in continuous time, which is a two-player noncooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.

Coalgebraic games have been recently introduced as a generalization of Conway games and other notions of games arising in different contexts. Using coalgebraic methods, games can be viewed as elements of a final coalgebra for a suitable functor, and operations on games can be analyzed in terms of (generalized) coiteration schemata. Coalgebraic games are sequential in nature, i.e. at each step e...

In this document we provide a couple of exercises that help understand the basic concepts of game theory, including pure and mixed strategies, zero sum and non-zero sum games, and saddle-point and Nash solutions. The definition for concepts and the ideas for these exercises were taken in part from [1, 2]. Before we start, let us introduce some notation. We are going to assume that we have only ...