Displaying similar documents to “On the structure of Nash equilibrium sets in partially convex games.”

Simple equilibria in finite games with convexity properties

Tadeusz Radzik, Piotr Więcek (2015)

Applicationes Mathematicae

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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...

Convex interval games.

Gök, S.Z.Alparslan, Branzei, R., Tijs, S. (2009)

Journal of Applied Mathematics and Decision Sciences

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On two-point Nash equilibria in bimatrix games with convexity properties

Wojciech Połowczuk (2006)

Applicationes Mathematicae

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This paper considers bimatrix games with matrices having concavity properties. The games described by such payoff matrices well approximate two-person non-zero-sum games on the unit square, with payoff functions F₁(x,y) concave in x for each y, and/or F₂(x,y) concave in y for each x. For these games it is shown that there are Nash equilibria in players' strategies with supports consisting of at most two points. Also a simple search procedure for such Nash equilibria is given. ...

The equal split-off set for cooperative games

Rodica Branzei, Dinko Dimitrov, Stef Tijs (2006)

Banach Center Publications

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In this paper the equal split-off set is introduced as a new solution concept for cooperative games. This solution is based on egalitarian considerations and it turns out that for superadditive games the equal split-off set is a subset of the equal division core. Moreover, the proposed solution is single valued on the class of convex games and it coincides with the Dutta-Ray constrained egalitarian solution.

A new geometric approach to bimatrix games.

Gloria Fiestras-Janeiro, Ignacio García Jurado (1991)

Qüestiió

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In this paper we study some properties concerning the equilibrium point of a bimatrix game and describe a geometric method to obtain all the equilibria of a bimatrix game when one of the players has at most three pure strategies.

Equilibria in constrained concave bimatrix games

Wojciech Połowczuk, Tadeusz Radzik (2013)

Applicationes Mathematicae

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We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete...

Delegation equilibrium payoffs in integer-splitting games

Sylvain Sorin, Cheng Wan (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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This work studies a new strategic game called delegation game. A delegation game is associated to a basic game with a finite number of players where each player has a finite integer weight and her strategy consists in dividing it into several integer parts and assigning each part to one subset of finitely many facilities. In the associated delegation game, a player divides her weight into several integer parts, commits each part to an independent delegate and collects the sum of their...

Interval valued bimatrix games

Milan Hladík (2010)

Kybernetika

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Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities....

On noncooperative nonlinear differential games

Tomáš Roubíček (1999)

Kybernetika

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Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable...