Question

1. Two individuals are bargaining over the distribution of $100 in which payoffs must be in increments of $5. Each player must submit a one-time bid. If the sum of the bids is less than or equal to$100, each player gets the amount of the bid and the game ends. If the sum of the bids is greater than $100, the game ends and the players get nothing.

1. Does this game have a Nash equilibrium?
2. What is the most likely equilibrium strategy profile for this game?

Answer 1

(a) The game has multiple nash equilibria. Any combination of bids (a, b) where a is the bid of player 1 and b is the bid of player 2, is a Nash equilibrium strategy if a+b = 100. For example, (0,100), (5,95), (50,50), (75,25), (100,0) are all Nash equilibrium as no player can gain by deviating from the bid.

(b) The most likely equilibrium outcome is indeed when both the players bid 50 each. By bidding more they risk the total amount of bid going above 100 as they should not expect the other person to bid reasonably lower. If the player bids 50, he will be at least as well off as the other player and this strategy will be the most likely equilibrium startegy of the game.