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The Nash equilibrium is an important benchmark for behaviour in systems of strategic autonomous agents. Polymatrix games are a succinct and expressive representation of multiplayer games that model pairwise interactions between players. The…

Computer Science and Game Theory · Computer Science 2016-03-17 Argyrios Deligkas , John Fearnley , Tobenna Peter Igwe , Rahul Savani

We consider a class of N-player stochastic games of multi-dimensional singular control, in which each player faces a minimization problem of monotone-follower type with submodular costs. We call these games "monotone-follower games". In a…

Optimization and Control · Mathematics 2019-02-05 Jodi Dianetti , Giorgio Ferrari

We study natural improvement dynamics in weighted congestion games with polynomial latencies of maximum degree $d\geq 1$. We focus on two problems regarding the existence and efficiency of approximate pure Nash equilibria, with a reasonable…

Computer Science and Game Theory · Computer Science 2020-11-09 Ioannis Caragiannis , Angelo Fanelli

We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…

Computer Science and Game Theory · Computer Science 2011-11-14 Ioannis Caragiannis , Angelo Fanelli , Nick Gravin , Alexander Skopalik

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…

Computer Science and Game Theory · Computer Science 2026-04-13 Alexandros Hollender , Gilbert Maystre , Sai Ganesh Nagarajan

The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…

Computer Science and Game Theory · Computer Science 2023-08-22 Sam Ganzfried

We study the problem of computing approximate Nash equilibria of bimatrix games, in a setting where players initially know their own payoffs but not the payoffs of the other player. In order for a solution of reasonable quality to be found,…

Computer Science and Game Theory · Computer Science 2013-02-18 Paul Goldberg , Arnoud Pastink

We study the deterministic and randomized query complexity of finding approximate equilibria in bimatrix games. We show that the deterministic query complexity of finding an $\epsilon$-Nash equilibrium when $\epsilon < \frac{1}{2}$ is…

Computer Science and Game Theory · Computer Science 2014-02-13 John Fearnley , Rahul Savani

We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…

Computer Science and Game Theory · Computer Science 2026-02-18 Rafael Frongillo , Melody Hsu , Mary Monroe , Anish Thilagar

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…

Optimization and Control · Mathematics 2026-01-08 Ishani Karmarkar , Liam O'Carroll , Aaron Sidford

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…

Computer Science and Game Theory · Computer Science 2013-07-19 Yakov Babichenko , Ron Peretz

This paper studies the last-iterate convergence properties of the exponential weights algorithm with constant learning rates. We consider a repeated interaction in discrete time, where each player uses an exponential weights algorithm…

Artificial Intelligence · Computer Science 2024-07-10 Maurizio d'Andrea , Fabien Gensbittel , Jérôme Renault

The current state-of-the-art methods for showing inapproximability in PPAD arise from the $\varepsilon$-Generalized-Circuit ($\varepsilon$-GCircuit) problem. Rubinstein (2018) showed that there exists a small unknown constant $\varepsilon$…

Computational Complexity · Computer Science 2024-09-13 Argyrios Deligkas , John Fearnley , Alexandros Hollender , Themistoklis Melissourgos

We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…

Computer Science and Game Theory · Computer Science 2017-11-28 Matthias Feldotto , Martin Gairing , Grammateia Kotsialou , Alexander Skopalik

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…

Computer Science and Game Theory · Computer Science 2013-08-01 Leslie Ann Goldberg , Paul W. Goldberg , Piotr Krysta , Carmine Ventre

We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$-group regularized logistic regression recovers a game, whose Nash…

Machine Learning · Computer Science 2019-01-30 Asish Ghoshal , Jean Honorio

We revisit the complexity of deciding, given a {\it bimatrix game,} whether it has a {\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\mathcal{NP}}$-hard~\cite{GZ89}. We show that…

Computational Complexity · Computer Science 2019-07-25 Vittorio Bilò , Marios Mavronicolas

In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon in expectation by unilateral deviation. An epsilon well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with…

Computer Science and Game Theory · Computer Science 2014-03-24 Yogesh Anbalagan , Sergey Norin , Rahul Savani , Adrian Vetta

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…

Computational Complexity · Computer Science 2008-02-21 Mihalis Yannakakis

In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an $\eps$-approximate Nash equilibrium with near-optimal value in a two-player game is as hard as finding a hidden clique of size $O(\log n)$ in the random…

Computational Complexity · Computer Science 2011-04-20 Per Austrin , Mark Braverman , Eden Chlamtac