Displaying similar documents to “Convex interval games.”

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...

The equal split-off set for cooperative games

Rodica Branzei, Dinko Dimitrov, Stef Tijs (2006)

Banach Center Publications


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.

Dynamic one-pile blocking Nim.

Flammenkamp, Achim, Holshouser, Arthur, Reiter, Harold (2003)

The Electronic Journal of Combinatorics [electronic only]


A new geometric approach to bimatrix games.

Gloria Fiestras-Janeiro, Ignacio García Jurado (1991)



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.

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

Wojciech Połowczuk (2006)

Applicationes Mathematicae


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. ...

Some values for constant-sum and bilateral cooperative games

Andrzej Młodak (2007)

Applicationes Mathematicae


We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of...