A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadra...

<p style='text-indent:20px;'>We study a nonzero-sum risk-sensitive stochastic differential game for controlled reflecting diffusion processes in the nonnegative orthant. We treat two cost evaluation criteria, namely, discounted and ergodic cost. Under certain assumptions, we establish existence of Nash equilibria. Also, completely characterize equilibrium criterion space stationary Markov...

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...

A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temporal objectives are constrained by a convection-diffusion-reaction equation ruling spread aquifer, and velocity flow solves an elliptic partial equation. The existence Nash equilibrium proved using fixed point strategy. uniqueness result for also under some additional assumptions. Some num...

Our goal in this paper is to merge several central ideas in economic theory: strategic behavior (incentive compatibility), differential (or incomplete) information, and the Arrow-Debreu model of general equilibrium. By strategic behavior we refer to the literature which models economic institutions as games in strategic form and uses Nash equilibrium as the solution concept. This literature, mo...

We provide a single reduction that demonstrates that in normal-form games: 1) it is NP-complete to determine whether Nash equilibria with certain natural properties exist (these results are similar to those obtained by Gilboa and Zemel [17]), 2) more significantly, the problems of maximizing certain properties of a Nash equilibrium are inapproximable (unless P = NP), and 3) it is #P-hard to cou...

We consider risk-sensitive generalizations of Nash and correlated equilibria in noncooperative games. We prove that, except for a class of degenerate games, unless a two-player game has a pure Nash equilibrium, it does not have a risksensitive Nash equilibrium. We also show that every game has a risk-sensitive correlated equilibrium. The striking contrast between these existence results is due ...

Game Theory (Von Neumann & Morgenstern, 1944) is a branch of applied mathematics and economics that studies situations (games) where self-interested interacting players act for maximizing their returns; therefore, the return of each player depends on his behaviour and on the behaviours of the other players. Game Theory, which plays an important role in the social and political sciences, has rec...

ABayesian game is a game of incomplete information in which the rules of the game are not fully known to all players. We consider the Bayesian game of Battle of Sexes that has several Bayesian Nash equilibria and investigate its outcome when the underlying probability set is obtained from generalized Einstein–Podolsky–Rosen experiments. We find that this probability set, which may become non-fa...

In computer networks and social networks, the betweenness centrality of a node measures the amount of information passing through the node when all pairs are conducting shortest path exchanges. In this paper, we introduce a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness in the network. To reflect real world...