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 this article, two-person zero-sum games are investigated in the fuzzy environment. Several models constructed by Maeda in the symmetrical fuzzy environment are extended to the models in the asymmetric fuzzy environment. The existence of equilibrium strategies for these extended models is proposed in the asymmetric fuzzy environment. However, in some cases, Nash equilibrium strategies may not...

We extend the classical transportation problem from linear optimization and introduce several competing forwarders. This results in a noncooperative game which is commonly known as generalized Nash equilibrium problem. We show the existence of Nash equilibria and present numerical methods for their efficient computation. Furthermore, we discuss several equilibrium selection concepts that are ap...

We study learning in finitely repeated 2× 2 normal form games, when players have incomplete information about their opponents’ payoffs. In a laboratory experiment we investigate whether players (a) learn the game they are playing, (b) learn to predict the behavior of their opponent, and (c) learn to play according to a Nash equilibrium of the repeated game. Our results show that the success in ...

Using lattice-theoretical methods, we analyze the existence and order structure of Nash equilibria of non-cooperative games where payoffs satisfy certain monotonicity properties (which are directly related to strategic complementarities) but need not be quasiconcave. In games with strategic complementarities the equilibrium set is always non-empty and has an order structure which ranges from th...

We assume that the players’ cost functions are not necessarily dependent on the actions of all players. This is due to better mimicking the standard social media rules. A communication graph is defined for the game through which players are able to share their information with only their neighbors. We assume that the communication neighbors necessarily affect the players’ cost functions while t...

Nash equilibrium analysis has become the de facto standard for judging the solution quality achieved in systemscomposed of selfish users. This mindset is so pervasive in computer science that even the few papers devoted todirectly analyzing outcomes of dynamic processes in repeated games (e.g., best-response or no-regret learningdynamics) have focused on showing that the perform...

Garing et al [3] is the first paper in which Bayesian Nash equilibrium is treated. They analysis Bayesian extension of routing game specified by the type-space model of Harsanyi [4] as information structure, and they collected several results: (1) the existence and computability of pure Nash equilibrium, (2) the property of the set of fully mixes Bayesian Nash equilibria and (3) the upper bound...

In this paper we show that some decision problems regarding the computation of Nash equilibria are to be considered particularly hard. Most decision problems regarding Nash equilibria have been shown to be NP-complete. While some NP-complete problems can find an alternative to tractability with the tools of Parameterized Complexity Theory, it is also the case that some classes of problems do no...

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...