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We study a static game played by a finite number of agents, in which agents are assigned independent and identically distributed random types and each agent minimizes its objective function by choosing from a set of admissible actions that depends on its type. The game is anonymous in the sense that the objective function of each agent depends on the actions of other agents only through the empirical distribution of their type-action pairs. We study the asymptotic behavior of Nash equilibria, as the number of agents tends to infinity, first by deriving laws of large numbers characterizes almost sure limit points of Nash equilibria in terms of so-called Cournot-Nash equilibria of an associated nonatomic game. Our main results are large deviation principles that characterize the probability of rare Nash equilibria and associated conditional limit theorems describing the behavior of equilibria conditioned on a rare event. The results cover situations when neither the finite-player game nor the associated nonatomic game has a unique equilibrium. In addition, we study the asymptotic behavior of the price of anarchy, complementing existing worst-case bounds with new probabilistic bounds in the context of congestion games, which are used to model traffic routing in networks.
We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a two-player
In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the correlations that inf
This paper shows the existence of $mathcal{O}(frac{1}{n^gamma})$-Nash equilibria in $n$-player noncooperative aggregative games where the players cost functions depend only on their own action and the average of all the players actions, and is lower
We consider normal-form games with $n$ players and two strategies for each player, where the payoffs are i.i.d. random variables with some distribution $F$ and we consider issues related to the pure equilibria in the game as the number of players div
In this paper we consider non zero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of Ergodic BSDEs, and prove the existence of a Nash equi