Related papers: Query Complexity of Approximate Nash Equilibria

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…

This paper studies the limits of empirical means of open-loop Nash equilibria of linear-quadratic stochastic differential games as the number of players goes to infinity, when the corresponding mean field game is of potential type and may…

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play…

Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…

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…

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…

Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash…

In many cases the Nash equilibria are not predictive of the experimental players' behaviour. For some games of Game Theory it is proposed here a method to estimate the probabilities with which the different options will be actually chosen…

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…

Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We…

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…

This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…

We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…

There has been substantial progress on finding game-theoretic equilibria. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, and other fine-grained quantities have…

Contemporary applications of machine learning in two-team e-sports and the superior expressivity of multi-agent generative adversarial networks raise important and overlooked theoretical questions regarding optimization in two-team games.…

In this work, we provide a structural characterization of the possible Nash equilibria in the well-studied class of security games with additive utility. Our analysis yields a classification of possible equilibria into seven types and we…

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for…

We consider a 3-player game in the normal form, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage players make their choices knowing only the average payoffs from…

Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…

We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic…