Nash Equilibria in Games over Graphs Equipped with a Communication Mechanism

We study pure Nash equilibria in infinite-duration games on graphs, with partial visibility of actions but communication (based on a graph) among the players. We show that a simple communication mechanism consisting in reporting the deviator when seeing it and propagating this information is sufficient for characterizing Nash equilibria. We propose an epistemic game construction, which conveniently records important information about the knowledge of the players. With this abstraction, we are able to characterize Nash equilibria which follow the simple communication pattern via winning strategies. We finally discuss the size of the construction, which would allow efficient algorithmic solutions to compute Nash equilibria in the original game

Computer aided synthesis: a game theoretic approach

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 solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Games on graphs with a public signal monitoring

We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic game abstraction, which conveniently allows to represent the knowledge of the players about these deviations, and give a characterization of Nash equilibria in terms of winning strategies in the abstraction. We then use the abstraction to develop algorithms for some payoff functions.Comment: 28 page

Robust equilibria in mean-payoff games

We study the problem of finding robust equilibria in multiplayer concurrent games with mean payoff objectives. A (k, t)-robust equilibrium is a strategy profile such that no coalition of size k can improve the payoff of one its member by deviating, and no coalition of size t can decrease the payoff of other players. While deciding whether there exists such equilibria is undecidable in general, we suggest algorithms for two meaningful restrictions on the complexity of strategies. The first restriction concerns memory. We show that we can reduce the problem of the existence of a memoryless robust equilibrium to a formula in the (existential) theory of reals. The second restriction concerns randomisation. We suggest a general transformation from multiplayer games to two-player games such that pure equilibria in the first game correspond to winning strategies in the second one. Thanks to this transformation, we show that the existence of robust equilibria can be decided in polynomial space, and that the decision problem is PSPACE-complete