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Displaying similar documents to “Existence of Nash equilibria in two-person stochastic games of resource extraction”

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...

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].

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.

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.

Deterministic Markov Nash equilibria for potential discrete-time stochastic games

Alejandra Fonseca-Morales (2022)

Kybernetika

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In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games...

Interplay of simple stochastic games as models for the economy

Garibaldi, Ubaldo, Radivojević, Tijana, Scalas, Enrico

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Using the interplay among three simple exchange games, one may give a satisfactory representation of a conservative economic system where total wealth and number of agents do not change in time. With these games it is possible to investigate the emergence of statistical equilibrium in a simple pure-exchange environment. The exchange dynamics is composed of three mechanisms: a decentralized interaction, which mimics the pair-wise exchange of wealth between two economic agents, a failure...

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...

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.

Z -equilibria in many-player stochastic differential games

Svatoslav Gaidov (1993)

Archivum Mathematicum

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In this paper N -person nonzero-sum games are considered. The dynamics is described by Ito stochastic differential equations. The cost-functions are conditional expectations of functionals of Bolza type with respect to the initial situation. The notion of Z -equilibrium is introduced in many-player stochastic differential games. Some properties of Z -equilibria are analyzed. Sufficient conditions are established guaranteeing the Z -equilibrium for the strategies of the players. In a particular...

Stochastic differential games involving impulse controls

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

A two armed bandit type problem revisited

Gilles Pagès (2010)

ESAIM: Probability and Statistics

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In Benaïm and Ben Arous (2003) is solved a multi-armed bandit problem arising in the theory of learning in games. We propose a short and elementary proof of this result based on a variant of the Kronecker lemma.