Simultaneous and Sequential Choice in a Symmetric Two‐Player Game with Canyon‐Shaped Payoffs

Abstract

This paper investigates a symmetric two-player game with canyon-shaped payoffs, in which a player’s payoff function is smooth and concave above and below the diagonal, but not differentiable on the diagonal. We demonstrate that there exists a first-mover advantage when the two players move sequentially and a player’s preference to the opponent’s choice is monotonic and identical between a higher strategy player and a lower strategy player. We also show that our symmetric two-player game may yield the first-mover advantage outcome in an endogenous timing game with observable delay.