A three-person chess-like game without Nash equilibria.
Year: 2016
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2543145484