Displaying similar documents to “Modeling shortest path games with Petri nets: a Lyapunov based theory”

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...

Risk-sensitive Markov stopping games with an absorbing state

Jaicer López-Rivero, Rolando Cavazos-Cadena, Hugo Cruz-Suárez (2022)

Kybernetika

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This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility...

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...

Convergence method, properties and computational complexity for Lyapunov games

Julio B. Clempner, Alexander S. Poznyak (2011)

International Journal of Applied Mathematics and Computer Science

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We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-like function monotonically decreases and converges to a single Lyapunov equilibrium point identified...

Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players

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...

Correlated equilibria in competitive staff selection problem

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...

Equilibria in a class of games and topological results implying their existence.

R.S. Simon, S. Spiez, H. Torunczyk (2008)

RACSAM

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We survey results related to the problem of the existence of equilibria in some classes of infinitely repeated two-person games of incomplete information on one side, first considered by Aumann, Maschler and Stearns. We generalize this setting to a broader one of principal-agent problems. We also discuss topological results needed, presenting them dually (using cohomology in place of homology) and more systematically than in our earlier papers.

The Give and Take game: Analysis of a resource sharing game

Pedro Mariano, Luís Correia (2015)

International Journal of Applied Mathematics and Computer Science

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We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to Give and Take is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a...

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...