The three-player lowest unique number game

This paper characterizes the unique symmetric mixed-strategy Nash equilibrium in the three-player version Lowest Unique Number Game. In this game, each player chooses a positive integer simultaneously and the player with the lowest unique number wins. The equilibrium mixing is shown to have full support and it is characterized by a constant hazard rate which is around . 46 . • Three-player Unique Number Game. • Analytical characterization of symmetric equilibrium. • Equivalence to dynamic exit games.