Potential games are games with potential functions. Technically, the potential function defines a refinement concept. We provide justification for this refinement concept using the notion of robustness of equilibria. A Nash equilibrium of a complete information game is said to be robust if every incomplete information game where payoffs are almost always given by the complete information game h...

To find the possible equilibrium states of forest ecosystems one are suggested to use the theory of differential games. At within the 4-tier model of mosaic forest communities it established the existence of the Nash equilibrium states in such ecosystems. Key–Words: Forest ecosystem, the equilibrium of the ecosystem, differential game, Nash equilibrium October 30, 2016

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(logm+log n) pure strategies. This result induces an N log logN algorithm for computing an approximate Nash equilibrium in games where the number of actions is polynomial in the number of players (m = poly(n)), where N =...

In this paper we reconsider the concept of Berge equilibrium. In a recent work, [Colman, A. M., Körner, T., Musy, O. and Tazdaït, T. [2011] Mutual support in games: Some properties of Berge equilibria, Journal of Mathematical Psychology 55, 166–175]. proposed a correspondence for two-player games between Berge and Nash equilibria by permutation of the utility functions. We define here more gene...

We survey a research line recently initiated by Mavronicolas et al. [14, 15, 16], concerning a strategic game on a graph G(V,E) with two confronting classes of randomized players: ν attackers who choose vertices and wish to minimize the probability of being caught by the defender, who chooses edges and gains the expected number of attackers it catches. So, the defender captures system rationali...

(2) NASH EQUILIBRIUM Nash Equilibrium is a solution of a game or a condition in a game involving two or more players, in which no player has anything to gain by changing only his own strategy unilaterally, i.e. no player can benefit by changing his strategy while the other players keep their strategies unchanged. The set of strategy choices and the corresponding payoffs (benefits or rewards) co...

In this paper we study boolean game with prioritized norms. Norms distinguish illegal strategies from legal strategies. Notions like legal strategy and legal Nash equilibrium are introduced. Our formal model is a combination of (weighted) boolean game and so called (prioritized) input/output logic. After formally presenting the model, we use examples to show that non-optimal Nash equilibrium ca...

In 1950, John Nash contributed a remarkable one-page PNAS article that defined and characterized a notion of equilibrium for n- person games. This notion, now called the "Nash equilibrium," has been widely applied and adapted in economics and other behavioral sciences. Indeed, game theory, with the Nash equilibrium as its centerpiece, is becoming the most prominent unifying theory of social sci...

Kalai and Lehrer (93a, b) have shown that if players' beliefs about the future evolution of play is absolutely continuous with respect to play induced by optimal strategies then Bayesian updating eventually leads to Nash equilibrium. In this paper, we present the ̄rst set of necessary and su±cient conditions that ensure that Bayesian updating eventually leads to Nash equilibrium. More important...