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In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed…

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an…

We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE…

In many real-world settings agents engage in strategic interactions with multiple opposing agents who can employ a wide variety of strategies. The standard approach for designing agents for such settings is to compute or approximate a…

This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…

A growing number of machine learning architectures, such as Generative Adversarial Networks, rely on the design of games which implement a desired functionality via a Nash equilibrium. In practice these games have an implicit complexity…

Many emerging applications - such as adversarial training, AI alignment, and robust optimization - can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While…

The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set of linear constraints together with integer…

This paper contributes a new class of games called spacetime games with perfect information. In spacetime games, the agents make decisions at various positions in Minkowski spacetime. Spacetime games can be seen as the least common…

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…

The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash equilibrium (NE) of a rank-$0$, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for…

Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…

We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for…

Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…

This is a short introduction to the subject of strategic games. We focus on the concepts of best response, Nash equilibrium, strict and weak dominance, and mixed strategies, and study the relation between these concepts in the context of…

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning…

We study the memory requirements of Nash equilibria in turn-based multiplayer games on possibly infinite graphs with reachability, safety, shortest-path, B\"uchi and co-B\"uchi objectives. We present constructions for finite-memory Nash…

In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…

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…