Displaying similar documents to “Some remarks on equilibria in semi-Markov games”

Markov stopping games with an absorbing state and total reward criterion

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

Kybernetika

Similarity:

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...

Denumerable Markov stopping games with risk-sensitive total reward criterion

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

Kybernetika

Similarity:

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...

Risk-sensitive Markov stopping games with an absorbing state

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

Kybernetika

Similarity:

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...

On approximations of nonzero-sum uniformly continuous ergodic stochastic games

Andrzej Nowak (1999)

Applicationes Mathematicae

Similarity:

We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].

Correlated equilibria in competitive staff selection problem

David M. Ramsey, Krzysztof Szajowski (2006)

Banach Center Publications

Similarity:

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...

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

Similarity:

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

Similarity:

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.

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

Tomasz Bielecki (1997)

Applicationes Mathematicae

Similarity:

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...

Nonzero-sum semi-Markov games with countable state spaces

Wojciech Połowczuk (2000)

Applicationes Mathematicae

Similarity:

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.

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

Martínez-Cortés Victor Manuel (2021)

Kybernetika

Similarity:

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...

Modeling shortest path games with Petri nets: a Lyapunov based theory

Julio Clempner (2006)

International Journal of Applied Mathematics and Computer Science

Similarity:

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,...

Parrondo's paradox.

Berresford, Geoffrey C., Rockett, Andrew M. (2003)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Equilibria in constrained concave bimatrix games

Wojciech Połowczuk, Tadeusz Radzik (2013)

Applicationes Mathematicae

Similarity:

We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete...

Delegation equilibrium payoffs in integer-splitting games

Sylvain Sorin, Cheng Wan (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Similarity:

This work studies a new strategic game called delegation game. A delegation game is associated to a basic game with a finite number of players where each player has a finite integer weight and her strategy consists in dividing it into several integer parts and assigning each part to one subset of finitely many facilities. In the associated delegation game, a player divides her weight into several integer parts, commits each part to an independent delegate and collects the sum of their...