Patent Nash equilibria in symmetric strictly competitive games

This work refines the notion of Nash equilibrium in the case of symmetric strictly competitive games. We define a (complete and typically intransitive) binary relation allowing to identify the so-called latent actions, for which there exists a maximal tree whose nodes are all preferred to the considered action. We prove the existence of patent Nash equilibria (obtained after iterated elimination of latent actions) and then describe the configurations that may arise when the two players have four (or less) actions available. (C) 2021 Elsevier B.V. All rights reserved.