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Simple equilibria in finite games with convexity properties

Tadeusz Radzik, Piotr Więcek (2015)

Applicationes Mathematicae

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...

Some applications of the point-open subbase game

D. Guerrero Sánchez, Vladimir Vladimirovich Tkachuk (2017)

Commentationes Mathematicae Universitatis Carolinae

Given a subbase 𝒮 of a space X , the game P O ( 𝒮 , X ) is defined for two players P and O who respectively pick, at the n -th move, a point x n X and a set U n 𝒮 such that x n U n . The game stops after the moves { x n , U n : n ø } have been made and the player P wins if n ø U n = X ; otherwise O is the winner. Since P O ( 𝒮 , X ) is an evident modification of the well-known point-open game P O ( X ) , the primary line of research is to describe the relationship between P O ( X ) and P O ( 𝒮 , X ) for a given subbase 𝒮 . It turns out that, for any subbase 𝒮 , the player P has a winning strategy...

Some remarks on equilibria in semi-Markov games

Andrzej Nowak (2000)

Applicationes Mathematicae

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...

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