Problem
Each player chooses a number from 1, 2, . . . , n and writes it down; then the players compare the two numbers. If the numbers differ by one, the player with the higher number wins $1 from the other player. If the players' choices differ by two or more, the player with the higher number pays $2 to the other player. In the event of a tie, no money changes hands. Use domination to show that the strategy set of this game can be reduced. Is there a pure Nash equilibrium. Determine mixed Nash equilibrium in this game.