A note on a two-person zero-sum game stimulated by a Markov chain
A. Styszyński (1980)
Applicationes Mathematicae
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A. Styszyński (1980)
Applicationes Mathematicae
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Andrzej Nowak (2000)
Applicationes Mathematicae
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This paper is a first study of correlated equilibria in nonzero-sum semi-Markov stochastic games. We consider the expected average payoff criterion under a strong ergodicity assumption on the transition structure of the games. The main result is an extension of the correlated equilibrium theorem proven for discounted (discrete-time) Markov games in our joint paper with Raghavan. We also provide an existence result for stationary Nash equilibria in the limiting average payoff semi-Markov...
Wojciech Połowczuk (2000)
Applicationes Mathematicae
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We consider nonzero-sum semi-Markov games with a countable state space and compact metric action spaces. We assume that the payoff, mean holding time and transition probability functions are continuous on the action spaces. The main results concern the existence of Nash equilibria for nonzero-sum discounted semi-Markov games and a class of ergodic semi-Markov games with the expected average payoff criterion.
V. Aggarwal, K. P. K. Nair, R. Chandrasekaran (1980)
RAIRO - Operations Research - Recherche Opérationnelle
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Julio Clempner (2006)
International Journal of Applied Mathematics and Computer Science
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In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman's equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain,...
E. Z. Ferenstein (2006)
Banach Center Publications
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We study nonzero-sum multi-person multiple stopping games with players' priorities. The existence of Nash equilibrium is proved. Examples of multi stopping of Markov chains are considered. The game may also be presented as a special case of a stochastic game which leads to many variations of it, in which stopping is a part of players' strategies.
A. Styszyński (1980)
Applicationes Mathematicae
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David M. Ramsey, Krzysztof Szajowski (2006)
Banach Center Publications
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This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case...
Kristal K. Trejo, Julio B. Clempner, Alexander S. Poznyak (2015)
International Journal of Applied Mathematics and Computer Science
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In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations...
Łukasz Kuciński (2011)
Applicationes Mathematicae
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The problem of choosing an optimal insurance policy for an individual has recently been better understood, particularly due to the papers by Gajek and Zagrodny. In this paper we study its multi-agent version: we assume that insureds cooperate with one another to maximize their utility function. They create coalitions by bringing their risks to the pool and purchasing a common insurance contract. The resulting outcome is divided according to a certain rule called strategy. We address...
H. J. Girlich (1985)
Banach Center Publications
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Massimo Lorenzani (1981)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In questa nota presentiamo dei nuovi risultati sul problema di tempo d’arresto ottimale per processi di Markov con tempo discreto.
T. Radzik, K. Orłowski (1982)
Applicationes Mathematicae
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Jerzy Legut (1988)
Colloquium Mathematicae
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Heuer, Gerald H. (2001)
International Journal of Mathematics and Mathematical Sciences
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Tomasz Bielecki (1997)
Applicationes Mathematicae
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The purpose of this paper is to prove existence of an ε -equilib- rium point in a dynamic Nash game with Borel state space and long-run time average cost criteria for the players. The idea of the proof is first to convert the initial game with ergodic costs to an ``equivalent" game endowed with discounted costs for some appropriately chosen value of the discount factor, and then to approximate the discounted Nash game obtained in the first step with a countable state space game for which...