Question

10.Using the same payoff matrix as in question 9, suppose this game is infinitely repeated and that the interest rate is sufficiently “low.” Identify trigger strategies that permit players 1 and 2 to earn equilibrium payoffs of 140 and 180, respectively, in each period.

Short answer

The trigger strategy of the Player 1 will be choosing option A.

The trigger strategy of Player 2 will be to choose option C .

Step-by-step solution

What is trigger strategy?

The trigger strategy is a strategy that a player will adopt if the rival player decides to violate the agreement and not cooperate and seek to achieve a greater benefit at the expense of the other player's decision made in the agreement.

Using the same payoff matrix of the exercise (9) we now assume that each player's decisions will be repeated indefinitely and repeatedly in which both players collude and reach an agreement to choose the most optimal balance option, which in this case would be strategy B, D (140,180).

Finding trigger strategy of player 1 

Player 2 decides to cheat and choose option C (knowing that Player 1 will choose B) he will obtain a greater benefit (from 180 to 220).In the successive periods the trigger strategy of the Player 1 will be choosing option A and where both players will obtain - 10 .

 Finding trigger strategy of player 2

If Player 1 decides to cheat and choose option A (where it is known that Player 2 will choose D) he will get a greater benefit (from 140 to 200). The trigger strategy of Player 2 will be to choose option C. In the following periods both players will obtain -10.