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This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash…
In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled…
We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite games with a unique…
We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden…
This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented many-player games defined by an interaction graph between the players. In a recent breakthrough, Rubinstein showed…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the…
We consider graphical $n$-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce probabilistic distributions in all non-terminal positions. The…
We introduce natural strategic games on graphs, which capture the idea of coordination in a local setting. We study the existence of equilibria that are resilient to coalitional deviations of unbounded and bounded size (i.e., strong…
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 games of strategic substitutes and strategic complements on networks. We introduce two different evolutionary dynamics in order to refine their multiplicity of equilibria, and we analyse the system through a mean field approach.…
If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…
We investigate the degree of discontinuity of several solution concepts from non-cooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria are dealt with. Formally,…
Algorithms and models based on game theory have nowadays become prominent techniques for the design of digital controllers for critical systems. Indeed, such techniques enable automatic synthesis: given a model of the environment and a…
This paper studies the existence of pure Nash equilibria in resource graph games, which are a general class of strategic games used to succinctly represent the players' private costs. There is a finite set of resources and the strategy set…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the…
Playing a symmetric bi-matrix game is usually physically implemented by sharing pairs of 'objects' between two players. A new setting is proposed that explicitly shows effects of quantum correlations between the pairs on the structure of…
Contrary to the customary view that the celebrated Nash-equilibrium theorem in Game Theory is paradigmatic for non-cooperative games, it is shown that, in fact, it is essentially based on a particularly strong cooperation assumption.…
We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…