In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to so...

We show that in zero-sum polymatrix games, a multiplayer generalization of two-person zerosum games, Nash equilibria can be found efficiently with linear programming. We also show that the set of coarse correlated equilibria collapses to the set of Nash equilibria. In contrast, other important properties of two-person zero-sum games are not preserved: Nash equilibrium payoffs need not be unique...

We consider graphical games in which edges are zero-sum games between the endpoints/players; the payoff of a player is the sum of the payoffs from each incident edge. We give a simple reduction of such games to two-person zero-sum games; as a corollary, a mixed Nash equilibrium can be computed efficiently by solving a linear program and rounding off the results. The same is true when the games ...

Algorithms for pruning game trees generally rely on a game being zero-sum, in the case of alpha-beta pruning, or constant-sum, in the case of multi-player pruning algorithms such as speculative pruning. While existing algorithms can prune non-zero-sum games, pruning is much less effective than in constant-sum games. We introduce the idea of leaf-value tables, which store an enumeration of the p...

We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal complements which we call anti-potential games and anti-zero-sum games, respectively. Perhaps surprisingly, every anti-potential game comes either from the ...

This paper deals with perturbed matrix games. The main result is that the sets of solutions of perturbed games converge to subsets of solutions of appropriate lexicographic games. We consider applications of these results to dynamic games. In particular, we consider applications to repeated games with weighted discounted criteria and to finite-horizon stochastic games with perturbed transition ...

We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M(i, j) = C(i, j). We complement the known EXP-hardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum game to within an add...