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We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was…
This paper investigates the convergence time of log-linear learning to an $\epsilon$-efficient Nash equilibrium in potential games, where an efficient Nash equilibrium is defined as the maximizer of the potential function. Previous…
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…
We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
Decoding how rational agents should behave in shared systems remains a critical challenge within theoretical computer science, artificial intelligence and economics studies. Central to this challenge is the task of computing the solution…
Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
Adversarial team games model multiplayer strategic interactions in which a team of identically-interested players is competing against an adversarial player in a zero-sum game. Such games capture many well-studied settings in game theory,…
We introduce Cut-and-Play, a practically-efficient algorithm for computing Nash equilibria in simultaneous non-cooperative games where players decide via nonconvex and possibly unbounded optimization problems with separable payoff…
We study $n$-agent Bayesian Games with $m$-dimensional vector types and linear payoffs, also called Linear Multidimensional Bayesian Games. This class of games is equivalent with $n$-agent, $m$-game Uniform Multigames. We distinguish…
We prove that finding an epsilon-Nash equilibrium in a succinctly representable game with many players is PPAD-hard for constant epsilon. Our proof uses succinct games, i.e. games whose payoff function is represented by a circuit. Our…
In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…
Equilibrium solution concepts of normal-form games, such as Nash equilibria, correlated equilibria, and coarse correlated equilibria, describe the joint strategy profiles from which no player has incentive to unilaterally deviate. They are…
The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a…
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…
Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak…
The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of…
We consider an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the computation of Nash equilibria in such games as…
In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established…