We consider the generalized Nash equilibrium problem which, in contrast to the standard Nash equilibrium problem, allows joint constraints of all players involved in the game. Using a regularized Nikaido-Isoda-function, we then present three optimization problems related to the generalized Nash equilibrium problem. The first optimization problem is a complete reformulation of the generalized Na...

In many types of games, mixed Nash equilibria is not a satisfying solution concept, as mixed actions are hard to interpret. However, pure Nash equilibria, which are more natural, may not exist in many games. In this paper we explore a class of graphical games, where each player has a set of possible decisions to make, and the decisions have bounded interaction with one another. In our class of ...

This paper presents a Nash equilibrium model where the underlying objective functions involve uncertainty and nonsmoothness. The well-known sample average approximation method is applied to solve the problem and the first order equilibrium conditions are characterized in terms of Clarke generalized gradients. Under some moderate conditions, it is shown that with probability one, a statistical e...

Consider the N -person non-cooperative game in which each player’s cost function and the opponents’ strategies are uncertain. For such an incomplete information game, the new solution concept called a robust Nash equilibrium has attracted much attention over the past several years. The robust Nash equilibrium results from each player’s decision-making based on the robust optimization policy. In...

In his dissertation of 1950, Nash based his concept of solution to a game on the principles that “a rational prediction should be unique, that the players should be able to deduce and make use of it.” In this paper, we address the issue of when such definitive solutions are possible. We assume player rationality at least as strong as Aumann’s rationality. By formalizing Nash’s reasoning, we sho...

We investigate behavior in two unprofitable games—where Maxmin strategies do not form a Nash equilibrium yet guarantee the same payoff as Nash equilibrium strategies—that vary in the riskiness of the Nash strategy. We find that arguments for the implausibility of Nash equilibrium are confirmed by our experiments; however, claims that this will lead to Maxmin play are not. Neither solution conce...

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...

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. ...

We study a spatial model of party formation in which the set of agendas is the unit circle. We characterize the sets of pure-strategy Nash equilibria under the plurality and proportional rules. In both rules, multiple configurations of parties are possible in Nash equilibrium. We refine our predictions using a new notion called “defection-proof” Nash equilibrium. Under the plurality rule, only ...