In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an ε-approximate Nash equilibrium with near-optimal value in a two-player game is as hard as finding a hidden clique of size O(logn) in the random graph G(n,1/2). This raises the question of whether a similar intractability holds for approximate Nash equilibrium without side constraints such as high value. We give ...

In game theory, “refinement” refers to the selection of a subset of equilibria, typically on the grounds that the selected equilibria are more plausible than other equilibria. These notes are a brief, largely informal, survey of some of the most heavily used refinements. Throughout, “equilibria” means Nash equilibria (NE), unless I state otherwise explicitly. And throughout, I assume that the g...

Pareto-optimal Nash equilibrium is a refinement of the Nash equilibrium. An evolutionary method is described in order to detect this equilibrium. Generative relations induces a non-domination concept which is essentially in the detection method. Numerical experiments with games having multiple Nash equilibria are presented. The evolutionary method detects correctly the Pareto-optimal Nash equil...

We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler’s [Journal of Mathematical Economics, 18 (1989), 141–153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generali...

This paper defines “negotiation-proof Nash equilibrium”, a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested players may choose to coordinate, nonbindingly and voluntarily, their choice of strategies and make a joint objection, and it takes the perfect fore...

In this paper, we investigate a distributed Nash equilibrium seeking problem for a timevarying multi-agent network consisting of two subnetworks. We propose a subgradientbased distributed algorithm to seek a Nash equilibrium of a zero-sum game, where the two subnetworks share the same sum objective function. We show that the proposed distributed algorithm with homogenous stepsize can achieve a ...

Nash [13] introduced the concept of Nash equilibria in non-cooperative games and proved that any game possesses at least one such equilibrium. A well-known algorithm for computing a Nash equilibrium of a 2-player game is the Lemke-Howson algorithm [11], however it has exponential worst-case running time in the number of available pure strategies [15]. Recently, Daskalakis et al [4] showed that ...

Among the most fundamental problems in Al-gorithmic Game Theory are those concerning the Nash equilibria of a strategic game: states where no player could unilaterally deviate to improve her utility. Such algorithmic problems, including their decision, search and approximation variants , have been studied extensively in the last few years. The fundamental theorem of Nash [4,5] that Nash equilib...

in this paper, we prove some coupled coincidence point theorems for mappings with the mixedmonotone property and obtain the uniqueness of this coincidence point. then we providing useful examples in nash equilibrium.

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...