Displaying similar documents to “On approximations of nonzero-sum uniformly continuous ergodic stochastic games”

Weak infinitesimal operators and stochastic differential games.

Ramón Ardanuy, A. Alcalá (1992)

Stochastica

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This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u,u)dt + sigma(xi,t,u,u)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.

Existence of Nash equilibria in two-person stochastic games of resource extraction

P. Szajowski (2006)

Banach Center Publications

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This paper deals with two-person stochastic games of resource extraction under both the discounted and the mean payoff criterion. Under some concavity and additivity assumptions concerning the payoff and the transition probability function a stationary Nash equilibrium is shown to exist. The proof is based on Schauder-Tychonoff's fixed point theorem, applied to a suitable payoff vector space.

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...

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...

A note on 'Big Match'

Jean-Michel Coulomb (2010)

ESAIM: Probability and Statistics

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We present a very simple proof of the existence of the value for 'Big Match' first shown by Blackwell and Ferguson (1968).

Differential games of partial information forward-backward doubly SDE and applications

Eddie C. M. Hui, Hua Xiao (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games...

Parrondo's paradox.

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

International Journal of Mathematics and Mathematical Sciences

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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.

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

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,...