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Related papers: A Stopping Game on Zero-Sum Sequences

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We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

Optimization and Control · Mathematics 2020-07-09 Géraldine Bouveret , Roxana Dumitrescu , Peter Tankov

The paper is concerned with a zero-sum differential game in the case where a payoff is determined by the exit time, that is, the first time when the system leaves the game domain. Additionally, we assume that a part of domain's boundary is…

Optimization and Control · Mathematics 2024-05-02 Ekaterina Kolpakova

We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…

Number Theory · Mathematics 2026-03-31 Ivan Bortnovskyi , Michael Lucas , Steven J. Miller , Iana Vranesko , Ren Watson , Cameron White

An algorithm based on backward induction is devised in order to compute the optimal sequence of games to be played in Parrondo games. The algorithm can be used to find the optimal sequence for any finite number of turns or in the steady…

Physics and Society · Physics 2014-09-24 L. Dinis

We study the convergence time of the best response dynamics in player-specific singleton congestion games. It is well known that this dynamics can cycle, although from every state a short sequence of best responses to a Nash equilibrium…

Computer Science and Game Theory · Computer Science 2008-12-18 Heiner Ackermann , Heiko Roeglin

Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…

Optimization and Control · Mathematics 2019-05-17 Jérôme Renault

We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and…

Optimization and Control · Mathematics 2013-11-15 Guillaume Vigeral

We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time…

Mathematical Finance · Quantitative Finance 2026-03-31 Tiziano De Angelis , Caio César Graciani Rodrigues , Peter Tankov

We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino.…

Optimization and Control · Mathematics 2017-02-23 Rida Laraki , Jérôme Renault

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…

Machine Learning · Computer Science 2013-02-12 H. Brendan McMahan

We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such…

Optimization and Control · Mathematics 2012-08-03 Marianne Akian , Jean Cochet-Terrasson , Sylvie Detournay , Stéphane Gaubert

We study the existence of different notions of value in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in…

Optimization and Control · Mathematics 2016-01-08 Hugo Gimbert , Jérôme Renault , Sylvain Sorin , Xavier Venel , Wiesław Zielonka

We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two…

Computer Science and Game Theory · Computer Science 2011-01-17 Nicole Immorlica , Adam Tauman Kalai , Brendan Lucier , Ankur Moitra , Andrew Postlewaite , Moshe Tennenholtz

Direct reciprocity is a mechanism for sustaining mutual cooperation in repeated social dilemma games, where a player would keep cooperation to avoid being retaliated by a co-player in the future. So-called zero-determinant (ZD) strategies…

Populations and Evolution · Quantitative Biology 2017-11-27 Genki Ichinose , Naoki Masuda

A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is…

Quantum Physics · Physics 2011-06-22 Salman Beigi

We prove that every two-player nonzero-sum stopping game in discrete time admits an \epsilon-equilibrium in randomized strategies for every \epsilon >0. We use a stochastic variation of Ramsey's theorem, which enables us to reduce the…

Probability · Mathematics 2007-05-23 Eran Shmaya , Eilon Solan

Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no chance devices. Also the games have the finite descent property…

Combinatorics · Mathematics 2018-10-09 Melissa Huggan , Richard J. Nowakowski , Paul Ottaway

We show that an N-person non-cooperative semi-Markov game under limiting ratio average pay-off has a pure semi-stationary Nash equilibrium. In an earlier paper, the zero-sum two person case has been dealt with. The proof follows by reducing…

Computer Science and Game Theory · Computer Science 2024-02-27 K. G. Bakshi , S. Sinha

We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…

Logic in Computer Science · Computer Science 2016-03-18 Stéphane Le Roux , Arno Pauly

We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we…

Combinatorics · Mathematics 2014-11-21 C. L. Jansen , M. Scheepers , S. L. Simon , E. Tatum