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Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…
The finitely repeated Prisoners' Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained…
In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem,…
We consider a network composed of two interfering point-to-point links where the two transmitters can exploit one common relay node to improve their individual transmission rate. Communications are assumed to be multi-band and transmitters…
This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
We introduce a class of Bayesian bidding games for which we prove that the set of pure Nash equilibria is a (non-empty) sublattice and we give a sufficient condition for uniqueness that is often verified in the context of markets with…
In this paper we consider strong Nash equilibria, in mixed strategies, for finite games. Any strong Nash equilibrium outcome is Pareto efficient for each coalition. First, we analyze the two--player setting. Our main result, in its simplest…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
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…
We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our…
We revisit in this paper the relation between evolution of species and the mathematical tool of evolutionary games, which has been used to model and predict it. We indicate known shortcoming of this model that restricts the capacity of…
In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To…
We analyze the distributed power allocation problem in parallel multiple access channels (MAC) by studying an associated non-cooperative game which admits an exact potential. Even though games of this type have been the subject of…
We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out…
Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…
This paper discusses a special type of multi-user communication scenario, in which users' utilities are linearly impacted by their competitors' actions. First, we explicitly characterize the Nash equilibrium and Pareto boundary of the…
We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…