Question

Consider the following bargaining situation and concentrate on pure strategies. Suppose that 1 piece of gold (perfectly divisible) is to be divided by two individuals. The bargaining mechanism is given by: Agents announce the amount they want to get simultaneously. If the sum of those ends up strictly higher than 1, the gold goes to charity, so that agents get 0 payoff each. Otherwise, a settlement is reached and in this case the payoffs are given as follows: Player 1 loves player 2 as much as herself so that in this situation her payoff is given by the minimum amount obtained by either one of the players whenever there is a settlement. On the other hand, player 2 competes with player 1 and her utility is given by the amount of gold she gets more than player 1 whenever there is a settlement.

1. Formulate this situation as a normal form game.

2. Find the pure strategy best responses of both of these two agents. (Either define the set in exact mathematical terms, or use a very carefully drawn, properly labeled andclean graph depicting them with the x axis representing the other player’s actions.!)

Answer 1

Situation of the normal game:

1) Payoff 0 : if the sum of those ends up strictly higher than 1, the gold goes to charity.

2) Payoff more than 1:

2.a) Player1 loves player 2: minimum amount is obtained by any of them.

2.b) Player 2 competes with player 1: Payoff of player 2 is more than the payoff obtained by player 1.

Pure strategy best responses of both of these agents will be: (2.b) situation.