Publications
Preprint · arXiv · October 25, 2016
A three-person chess-like game without Nash equilibria.
Endre Boros, Vladimir Gurvich, Martin Milanič, Vladimir Oudalov, Jernej Vičič
Abstract
We give an example of a three person chess-like game that has no Nash equilibrium in pure stationary strategies. The game has seven positions, four outcomes (a unique cycle and three terminal positions), and its normal form is of size 2 x 2 x 4 only. Thus, our example strengthens significantly the one obtained in 2014 by Gurvich and Oudalov, which has four players, five terminals, and 2 x 4 x 6 x 8 normal form. Due to its small size, we can strengthen our new example further, by showing that it has no Nash equilibrium not only in pure but also in independently mixed strategies, for both Markov and a priori realizations.
Game Theory and ApplicationsGame Theory and Voting SystemsEvolutionary Game Theory and CooperationNash equilibriumthree-player gamesmixed strategies
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