Related papers: A three-person deterministic graphical game withou…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of…
We consider a multi-player non-zero-sum turn-based game (abbreviated as multi-player game) on a finite directed graph. A secure equilibrium (SE) is a strategy profile in which no player has the incentive to deviate from the strategy because…
We show that an N-person non-cooperative semi-Markov game under limiting ratio average pay-off has a pure semi-stationary Nash equilibrium. In an earlier paper, the zero-sum two person case has been dealt with. The proof follows by reducing…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…
We investigate the complexity of bounding the uncertainty of graphical games, and we provide new insight into the intrinsic difficulty of computing Nash equilibria. In particular, we show that, if one adds very simple and natural additional…
We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…
This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The…
We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…
We consider a large population dynamic game in discrete time where players are characterized by time-evolving types. It is a natural assumption that the players' actions cannot anticipate future values of their types. Such games go under…
Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…
The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular,…
We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a $N$-player setting and break down…
We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focusses on a strategic dynamic…
We present an example of symmetric ergodic $N$-players differential games, played in memory strategies on the position of the players, for which the limit set, as $N\to +\infty$, of Nash equilibrium payoffs is large, although the game has a…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…