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We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…
In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established…
This work addresses the issue of the convergence of an $N$-player game towards a limit model involving a continuum of players, as the number of agents $N$ goes to infinity. More precisely, we investigate the convergence of Nash equilibria…
We consider the problem of optimal charging of plug-in electric vehicles (PEVs). We treat this problem as a multi-agent game, where vehicles/agents are heterogeneous since they are subject to possibly different constraints. Under the…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this problem requires exponential time, several…
We study the typical structure of games in terms of their connectivity properties. A game is said to be `connected' if it has a pure Nash equilibrium and the property that there is a best-response path from every action profile which is not…
We consider non-cooperative unsplittable congestion games where players share resources, and each player's strategy is pure and consists of a subset of the resources on which it applies a fixed weight. Such games represent unsplittable…
A growing body of literature in networked systems research relies on game theory and mechanism design to model and address the potential lack of cooperation between self-interested users. Most game-theoretic models applied to system…
For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…
We propose and analyze a broad family of games played by resource-constrained players, which are characterized by the following central features: 1) each user has a multi-dimensional action space, subject to a single sum resource…
We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other…
We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As…
In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. Interference games represent the fundamental resource allocation conflict between users of the radio spectrum. In…
We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study…
We introduce a stochastic learning process called the dampened gradient approximation process. While learning models have almost exclusively focused on finite games, in this paper we design a learning process for games with continuous…
A central question in routing games has been to establish conditions for the uniqueness of the equilibrium, either in terms of network topology or in terms of costs. This question is well understood in two classes of routing games. The…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
Several works have recently suggested to model the problem of coordinating the charging needs of a fleet of electric vehicles as a game, and have proposed distributed algorithms to coordinate the vehicles towards a Nash equilibrium of such…
We study the computational complexity of Nash equilibria in concurrent games with limit-average objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a…