Iimura, T. & Watanabe, T. Int J Game Theory (2016) 45: 719. doi:10.1007/s00182-015-0481-y
We consider the finite version of the weakly unilaterally competitive game (Kats and Thisse, in Int J Game Theory 21:291–299, 1992) and show that this game possesses a pure strategy Nash equilibrium if it is symmetric and quasiconcave (or single-peaked). The first implication of this result is that unilaterally competitive or two-person weakly unilaterally competitive finite games are solvable in the sense of Nash, in pure strategies. We also characterize the set of equilibria of these finite games. The second implication is that there exists a finite population evolutionarily stable pure strategy equilibrium in a finite game, if it is symmetric, quasiconcave, and weakly unilaterally competitive.
Weakly unilaterally competitive game Finite game Symmetric game Quasiconcave game Existence of a pure strategy equilibrium Solvable game