Related papers: Perturbing Best Responses in Zero-Sum Games

This paper studies a variant of two-player zero-sum matrix games, where, at each timestep, the row player selects row $i$, the column player selects column $j$, and the row player receives a noisy reward with expected value $A_{i,j}$, along…

This paper examines the convergence behaviour of simultaneous best-response dynamics in random potential games. We provide a theoretical result showing that, for two-player games with sufficiently many actions, the dynamics converge quickly…

Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…

This article considers a two-player strategic game for network routing under link disruptions. Player 1 (defender) routes flow through a network to maximize her value of effective flow while facing transportation costs. Player 2 (attacker)…

The fundamental laws of quantum world upsets the logical foundation of classic physics. They are completely counter-intuitive with many bizarre behaviors. However, this paper shows that they may make sense from the perspective of a general…

Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for…

Bargaining games, where agents attempt to agree on how to split utility, are an important class of games used to study economic behavior, which motivates a study of online learning algorithms in these games. In this work, we tackle when…

We consider a scheduling game on parallel related machines, in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to…

This paper proposes new, end-to-end deep reinforcement learning algorithms for learning two-player zero-sum Markov games. Different from prior efforts on training agents to beat a fixed set of opponents, our objective is to find the Nash…

We study the problem of computing an $\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \in \mathbb{R}^{m \times n}$, when the players' strategies are constrained to lie in simple sets. We…

This paper proposes Mutation-Driven Multiplicative Weights Update (M2WU) for learning an equilibrium in two-player zero-sum normal-form games and proves that it exhibits the last-iterate convergence property in both full and noisy feedback…

In this paper, an aggregate game approach is proposed for the modeling and analysis of energy consumption control in smart grid. Since the electricity user's cost function depends on the aggregate load, which is unknown to the end users, an…

The Policy-Space Response Oracles (PSRO) framework scales equilibrium computation to large zero-sum games by iteratively expanding a restricted strategy set using deep reinforcement learning (DRL). A central challenge is to construct, under…

We study the performance of approximate Nash equilibria for linear congestion games. We consider how much the price of anarchy worsens and how much the price of stability improves as a function of the approximation factor $\epsilon$. We…

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…

Counterfactual Regret Minimization and variants (e.g. Public Chance Sampling CFR and Pure CFR) have been known as the best approaches for creating approximate Nash equilibrium solutions for imperfect information games such as poker. This…

In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…

In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. Interference games represent the fundamental resource allocation conflict between users of the radio spectrum. In…

We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players…

Decentralised optimisation tasks are important components of multi-agent systems. These tasks can be interpreted as n-player potential games: therefore game-theoretic learning algorithms can be used to solve decentralised optimisation…