Question

In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $17. If both players choose strategy B, each earns a payoff of $27. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $62 and player 2 earns $11. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $11 and player 2 earns $62. Suppose this game is infinitely repeated. What is the maximum interest rate that can sustain collusion? Round all calculations to 2 decimals. If 10% input .10

Answer 1

The matrix is shown below

	Player 2
Player 1		A	B
	A	(17, 17)	(62, 11)
	B	(11, 62)	(27, 27)

Nash equilibrium is (A, A) but is not pareto optimum. If collusion is done, optimum strategy is (B, B).

Assume that both the players follow the grim trigger strategy. This implies punsihment is given forever once any of the player deviates. Hence there are two outcome possible for this subgame: (B, B) in for all periods including the current one or (A, A) in all periods as the punishment is given forever.

For the first case, a player’s payoff is 27 for infinite period.

If he deviates in first period he will be able to secure 62 in that period but will receive only 17 for each period forever. Hence the payoff is 62 + 17? + 17?² + ... = 62(1??) + 17? . The player has no incentive to deviate if the payoff from not deviating exceed the payoff from deviating:

27 ? 62(1??) + 17?

27 ? 62? 62? + 17?

27 ? 62 – 45?

? ? 35/45 OR 0.78.

Maximum interest rate that can sustain collusion is 0.78