A Complete Solver for Constraint Games
This provides a more efficient solution for researchers and practitioners in game theory and AI who need to analyze complex games with compact representations.
The paper tackles the problem of compactly representing multi-agent games with conflicting objectives by using Constraint Programming to model utilities, and shows that their solver is 10 to 100 times faster than the classical solver Gambit.
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.