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Related papers: On zero-sum game formulation of non zero-sum game

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Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…

Computer Science and Game Theory · Computer Science 2008-12-18 Joseph Y. Halpern

Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…

Computer Science and Game Theory · Computer Science 2017-07-11 Florian Brandl

We introduce and study a two-player zero-sum game between a probabilist and Nature defined by a convex function $f$, a finite collection $\mathcal{B}$ of Markov generators (or its convex hull), and a target distribution $\pi$. The…

Probability · Mathematics 2025-09-11 Michael C. H. Choi , Geoffrey Wolfer

We consider zero-sum repeated games in which the players are restricted to strategies that require only a limited amount of randomness. Let $v_n$ be the max-min value of the $n$ stage game; previous works have characterized…

Computer Science and Game Theory · Computer Science 2019-02-12 Mehrdad Valizadeh , Amin Gohari

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

Quantum Physics · Physics 2009-10-31 David A. Meyer

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…

Computer Science and Game Theory · Computer Science 2007-07-17 Leandro C. Rego , Joseph Y. Halpern

The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…

Quantum Physics · Physics 2007-05-23 R. Vilela Mendes

We provide an in-depth study of Nash equilibria in multi-objective normal form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a utility-based approach, we assume that each player's utility can be modelled with a…

Computer Science and Game Theory · Computer Science 2022-07-19 Willem Röpke , Diederik M. Roijers , Ann Nowé , Roxana Rădulescu

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

Many real-world domains contain multiple agents behaving strategically with probabilistic transitions and uncertain (potentially infinite) duration. Such settings can be modeled as stochastic games. While algorithms have been developed for…

Computer Science and Game Theory · Computer Science 2020-06-25 Sam Ganzfried , Conner Laughlin , Charles Morefield

In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…

Optimization and Control · Mathematics 2025-05-20 Santiago J. Leudo , Ricardo G. Sanfelice

This paper introduces a class of games, called unit-sphere games, where strategies are real vectors with unit 2-norms (or, on a unit-sphere). As a result, they can no longer be interpreted as probability distributions over actions, but…

Computer Science and Game Theory · Computer Science 2015-09-21 Pingzhong Tang , Hanrui Zhang

We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a…

Optimization and Control · Mathematics 2021-09-28 François Dufour , Tomás Prieto-Rumeau

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 consider the design of a fair sensor schedule for a number of sensors monitoring different linear time-invariant processes. The largest average remote estimation error among all processes is to be minimized. We first consider a general…

Systems and Control · Computer Science 2025-04-03 Shuang Wu , Xiaoqiang Ren , Yiguang Hong , Ling Shi

The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we…

Quantum Physics · Physics 2017-12-13 Faisal Shah Khan , Travis S. Humble

This work considers two-player zero-sum semi-Markov games with incomplete information on one side and perfect observation. At the beginning, the system selects a game type according to a given probability distribution and informs to Player…

Optimization and Control · Mathematics 2021-07-16 Fang Chen , Xianping Guo , Zhong-Wei Liao

The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the…

Optimization and Control · Mathematics 2024-08-06 Hana Krakovská , Rudolf Hanel , Mark Broom

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…

Functional Analysis · Mathematics 2022-03-25 Ryan Hynd

The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that…

Computer Science and Game Theory · Computer Science 2022-09-16 David Grimsman , Philip N. Brown , Jason R. Marden