Set-theoretic inequalities in stochastic noncooperative games with coalition.
Simple equilibria in finite games with convexity properties
This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can...
Simultaneous nondeterministic games. I
Simultaneous nondeterministic games. II
Simultaneous nondeterministic games. III
Solution set in a special case of generalized Nash equilibrium games
A special class of generalized Nash equilibrium problems is studied. Both variational and quasi-variational inequalities are used to derive some results concerning the structure of the sets of equilibria. These results are applied to the Cournot oligopoly problem.
Some remarks on equilibria in semi-Markov games
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 games with...
Split of an Optimization Variable in Game Theory
In the present paper, a general multiobjective optimization problem is stated as a Nash game. In the nonrestrictive case of two objectives, we address the problem of the splitting of the design variable between the two players. The so-called territory splitting problem is solved by means of an allocative approach. We propose two algorithms in order to find fair allocation tables
Stochastic stability in spatial games
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 level on...
Sur l’équilibre fort selon Berge
Dans cet article nous étudions les propriétés essentielles de l’équilibre fort selon Berge (EFSB) pour les jeux à personnes, ensuite nous prouvons son existence en utilisant l’inégalité de Ky Fan et donnons un procédé adéquat pour sa recherche pratique.
Sur l'équilibre fort selon Berge
In this paper we study the main properties of the strong Berge equilibrium, then we prove a theorem of its existence based on the Ky Fan inequality and finally, we provide an algorithm for its determination.
Sur une certaine alternative non-linéaire en analyse convexe