  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.
