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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…

The Colonel Blotto Problem proposed by Borel in 1921 has served as a widely applicable model of budget-constrained simultaneous winner-take-all competitions in the social sciences. Applications include elections, advertising, R&D and more.…

Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions,…

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model…

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 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…

This paper develops a distributed Nash Equilibrium seeking algorithm for heterogeneous multi-robot systems. The algorithm utilises distributed optimisation and output control to achieve the Nash equilibrium by leveraging information shared…

We study the problem of solving matrix games of the form $\min_{\mathbf{p}\in\Delta}\max_{\mathbf{w}\in\mathcal{W}}\mathbf{p}^{\top}A\mathbf{w}$, where $A$ is a matrix and $\Delta$ is the probability simplex. This problem encapsulates…

We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…

This paper addresses the distributed Nash Equilibrium seeking problem for aggregative games, where legitimate players' decisions are affected by potential malicious players. To describe players' behavior, we introduce a novel heterogeneous…

This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding…

We initiate the study of how to perturb the reward in a zero-sum Markov game with two players to induce a desirable Nash equilibrium, namely arbitrating. Such a problem admits a bi-level optimization formulation. The lower level requires…

Cut games are among the most fundamental strategic games in algorithmic game theory. It is well-known that computing an exact pure Nash equilibrium in these games is PLS-hard, so research has focused on computing approximate equilibria. We…

This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of…

We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…

This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal…

Nash equilibrium (NE) is a central concept in game theory. Here we prove formally a published theorem on existence of an NE in two proof assistants, Coq and Isabelle: starting from a game with finitely many outcomes, one may derive a game…

The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…

This paper resolves the open question of designing near-optimal algorithms for learning imperfect-information extensive-form games from bandit feedback. We present the first line of algorithms that require only…

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…