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Displaying similar documents to “Interplay of simple stochastic games as models for the economy”

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.

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...

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).

Nash equilibrium payoffs for stochastic differential games with reflection

Qian Lin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.

On approximations of nonzero-sum uniformly continuous ergodic stochastic games

Andrzej Nowak (1999)

Applicationes Mathematicae

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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].

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.

Equilibrium transitions in finite populations of players

J. Miękisz (2006)

Banach Center Publications

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We discuss stochastic dynamics of finite populations of individuals playing symmetric games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of two-player games with two symmetric Nash equilibria, when the number of players increases, the population undergoes multiple transitions between its equilibria.

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,...

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.

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...

Stochastic stability in spatial games

Jacek Miękisz (2008)

Banach Center Publications

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We compare two concepts of stochastic stability in spatial games. The classical approach to stochastic stability, introduced by Foster and Young [8], involves single configurations in the zero-noise limit. Ensemble stability discussed in [17] refers to ensembles of configurations in the limit of an infinite number of players. The above two limits may not commute. We will discuss reasons of such behaviour. We review some results concerning the effect of the number of players and the noise...

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...