Displaying similar documents to “Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists”

Bi-personal stochastic transient Markov games with stopping times and total reward criterion

Martínez-Cortés Victor Manuel (2021)

Kybernetika

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The article is devoted to a class of Bi-personal (players 1 and 2), zero-sum Markov games evolving in discrete-time on Transient Markov reward chains. At each decision time the second player can stop the system by paying terminal reward to the first player. If the system is not stopped the first player selects a decision and two things will happen: The Markov chain reaches next state according to the known transition law, and the second player must pay a reward to the first player. The...

Nonzero-sum semi-Markov games with countable state spaces

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.

Some remarks on equilibria in semi-Markov games

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...

Markov stopping games with an absorbing state and total reward criterion

Rolando Cavazos-Cadena, Luis Rodríguez-Gutiérrez, Dulce María Sánchez-Guillermo (2021)

Kybernetika

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This work is concerned with discrete-time zero-sum games with Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system to continue its evolution. If the system is not halted, player I selects an action which affects the transitions and receives a running reward from player II. Assuming the existence of an absorbing state which is accessible from any other state, the performance of a pair...

Gibbs states for non-irreducible countable Markov shifts

Andrei E. Ghenciu, Mario Roy (2013)

Fundamenta Mathematicae

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We study Markov shifts over countable (finite or countably infinite) alphabets, i.e. shifts generated by incidence matrices. In particular, we derive necessary and sufficient conditions for the existence of a Gibbs state for a certain class of infinite Markov shifts. We further establish a characterization of the existence, uniqueness and ergodicity of invariant Gibbs states for this class of shifts. Our results generalize the well-known results for finitely irreducible Markov shifts. ...

Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games

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...

Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games

César U. S. Solis, Julio B. Clempner, Alexander S. Poznyak (2019)

Kybernetika

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This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves...

On infinite horizon multi-person stopping games with priorities

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.

Denumerable Markov stopping games with risk-sensitive total reward criterion

Manuel A. Torres-Gomar, Rolando Cavazos-Cadena, Hugo Cruz-Suárez (2024)

Kybernetika

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This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity...

Markov partitions for fibre expanding systems

Manfred Denker, Hajo Holzmann (2008)

Colloquium Mathematicae

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Fibre expanding systems have been introduced by Denker and Gordin. Here we show the existence of a finite partition for such systems which is fibrewise a Markov partition. Such partitions have direct applications to the Abramov-Rokhlin formula for relative entropy and certain polynomial endomorphisms of ℂ².