This game has a unique pure-strategy Nash equilibrium: both players choosing 0 (highlighted in light red). Any other strategy can be improved by a player switching their number to one less than that of the other player. In the adjacent table, if the game begins at the green square, it is in player 1's interest to move to the purple square and it is in player 2's interest to move to the blue square. Although it would not fit the definition of a competition game, if the game is modified so that the two players win the named amount if they both choose the same number, and otherwise win nothing, then there are 4 Nash equilibria: (0,0), (1,1), (2,2), and (3,3).
This game has a unique pure-strategy Nash equilibrium both players choosing 0 (highlighted in light red) Any other strategy can be improved by a player switching their number to one less than that of the other player In the adjacent table if the game begins at the green square it is in player 1's interest to move to the purple square and it is in player 2's interest to move to the blue square Although it would not fit the definition of a competition game if the game is modified so that the two players win the named amount if they both choose the same number and otherwise win nothing then there are 4 Nash equilibria (00) (11) (22) and (33)