The following depicts a normal-form game of price competition. Suppose that firm A deviates from a trigger strategy to support a high price. What is the present value of A's payoff from cheating?
A) 5
B) 20
C) 25
D) 35

Question

The following depicts a normal-form game of price competition.  Suppose that firm A deviates from a trigger strategy to support a high price. What is the present value of A's payoff from cheating?
A) 5 
B) 20 
C) 25 
D) 35

Quizplus · Accepted Answer

If firm A deviates from the trigger strategy and sets a high price, firm B will respond by setting a low price, and the resulting payoffs will be:
- Firm A: 20
- Firm B: 5

Since the game is infinitely repeated, we need to discount these payoffs back to the present. Using a discount factor of 0.5 (since the game is repeated every two periods), we can calculate the present value of A's payoff from cheating as follows:

PV(A's payoff) = 20 + 0.5*5 + 0.5^2*20 + 0.5^3*5 + ...
PV(A's payoff) = 20 + 2.5 + 5 + 2.5 + ...
PV(A's payoff) = 25

Therefore, A's best choice is to stick with the trigger strategy, as deviating would only lead to a lower payoff in the long run.

The Following Depicts a Normal-Form Game of Price Competition