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We propose a new version of the tug-of-war game and a corresponding dynamic programming principle related to the $p$-Laplacian with $1<p<2$. For this version, the asymptotic H\"older continuity of solutions can be directly derived from…

Analysis of PDEs · Mathematics 2022-12-22 Ángel Arroyo , Mikko Parviainen

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…

Computer Science and Game Theory · Computer Science 2020-05-25 Thodoris Lykouris , Vasilis Syrgkanis , Eva Tardos

Thompson sampling has been shown to be an effective policy across a variety of online learning tasks. Many works have analyzed the finite time performance of Thompson sampling, and proved that it achieves a sub-linear regret under a broad…

Machine Learning · Computer Science 2020-11-10 Cem Kalkanli , Ayfer Ozgur

A commonly used heuristic in RL is experience replay (e.g.~\citet{lin1993reinforcement, mnih2015human}), in which a learner stores and re-uses past trajectories as if they were sampled online. In this work, we initiate a rigorous study of…

Machine Learning · Computer Science 2021-12-09 Liran Szlak , Ohad Shamir

We analyze the convergence properties of the two-timescale fictitious play combining the classical fictitious play with the Q-learning for two-player zero-sum stochastic games with player-dependent learning rates. We show its almost sure…

Optimization and Control · Mathematics 2022-04-05 Muhammed O. Sayin , K. Alperen Cetiner

Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum…

Optimization and Control · Mathematics 2016-03-16 Bruno Ziliotto

Lanchester's model of combat has certain deficiencies in its standard form arising from the neglect of the influence of random fluctuations. Several approaches to rectify this have been proposed and various results are scattered throughout…

Physics and Society · Physics 2019-05-09 Michael J. Kearney , Richard J. Martin

Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on…

Computer Science and Game Theory · Computer Science 2015-07-14 Dominik Peters , Edith Elkind

Monte Carlo Tree Search (MCTS) has recently been successfully used to create strategies for playing imperfect-information games. Despite its popularity, there are no theoretic results that guarantee its convergence to a well-defined…

Computer Science and Game Theory · Computer Science 2015-09-02 Vojtěch Kovařík , Viliam Lisý

We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes…

Computer Science and Game Theory · Computer Science 2017-03-23 Juba Ziani , Venkat Chandrasekaran , Katrina Ligett

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…

Logic · Mathematics 2012-04-25 Paulo Oliva , Thomas Powell

We study the problem of guaranteeing low regret in repeated games against an opponent with unknown membership in one of several classes. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to…

Computer Science and Game Theory · Computer Science 2022-07-05 Anthony DiGiovanni , Ambuj Tewari

In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to…

Optimization and Control · Mathematics 2025-11-19 Ruimeng Hu , Jihao Long , Haosheng Zhou

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Probability · Mathematics 2022-03-24 Mathieu Laurière , Ludovic Tangpi

We consider the Deduction Theorem used in the literature of game theory to run a purported proof by contradiction. In the context of game theory, it is stated that if we have a proof of $\phi \vdash \varphi$, then we also have a proof of…

Artificial Intelligence · Computer Science 2021-08-31 Holger I. Meinhardt

Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to…

Logic in Computer Science · Computer Science 2019-07-10 Chenyi Zhang , Jun Pang

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

Optimization and Control · Mathematics 2023-08-22 Pierre Lavigne , Laurent Pfeiffer

We study the asymptotic macroscopic properties of the mixed majority-minority game, modeling a population in which two types of heterogeneous adaptive agents, namely ``fundamentalists'' driven by differentiation and ``trend-followers''…

Statistical Mechanics · Physics 2009-11-10 A. De Martino , I. Giardina , G. Mosetti

Stochastic differential games have been used extensively to model agents' competitions in Finance, for instance, in P2P lending platforms from the Fintech industry, the banking system for systemic risk, and insurance markets. The recently…

Optimization and Control · Mathematics 2021-03-23 Jiequn Han , Ruimeng Hu , Jihao Long

In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…

Optimization and Control · Mathematics 2021-12-02 Bruno Ziliotto