A Complete Solver for Constraint Games

Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the classical representation of a $n$-players game is given by a $n$-dimensional matrix of exponential size for each player. In this paper we use the framework of Constraint Games in which CSP are used to represent utilities. Constraint Programming --including global constraints-- allows to easily give a compact and elegant model to many useful games. Constraint Games come in two flavors: Constraint Satisfaction Games and Constraint Optimization Games, the first one using satisfaction to define boolean utilities. In addition to multimatrix games, it is also possible to model more complex games where hard constraints forbid certain situations. In this paper we study complete search techniques and show that our solver using the compact representation of Constraint Games is faster than the classical game solver Gambit by one to two orders of magnitude.Comment: 17 page

Computing equilibria using interval constraints

Abstract. Finding Nash equilibria is a hard computational problem which is central to game theory and whose applications range from decision-making to the analysis of multi-agent systems. Despite considerable recent interest and significant recent improvements, the problem remains essentially open in the case of n-person games. We investigate the use of interval-based constraint solving techniques to compute equilibria. We report on experiments made using several encodings of randomlygenerated games into continuous CSP, and draw conclusions regarding both the scalability of interval methods for game-theoretic applications and the impact of the symbolic representation of polynomials and of the choice of the propagation technique on the speed of resolution. 1 Introduction an