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Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…

In this paper we introduce the discontinuous universal feedback for the problem of Nash equilibrium in two person non-zero sum differential game. We assume that there exist functions satisfying some conditions analogous to the infinitesimal…

In recent and past works, convexity is usually assumed on each individual part of the action functional in order to demonstrate the existence and uniqueness of a Nash equilibrium on some interval [0, T] (this meant that each hessian was…

We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random…

We consider a symmetric two-player contest, in which the choice set of effort is constrained. We apply a fundamental property of the payoff function to show that, under standard assumptions, there exists a unique Nash equilibrium in pure…

In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal follow the regularized leader (FTRL) family of algorithms, and we consider…

In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…

An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and…

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a…

We consider a nonzero-sum N-player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carath\'eodory functions and the transitions of the system are assumed to have a…

We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the…

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…

In this paper we investigate a system of coupled inequalities consisting of a variational-hemivariational inequality and a quasi-hemivariational inequality on Banach spaces. The approach is topological, and a wide variety of existence…

In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length…

In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…

We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…

Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…

We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…

In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…

We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…