Two states, A and B, have signed an arms-control agreement. This agreement commits them to refrain from building certain types of weapons. The agreement is supposed to hold for an indefinite length of time. However, A and B remain potential enemies who would prefer to be able to cheat and build more weapons than the other. The payoff table for A (player 1, the row player) and B (player 2, the column player) in each period after signing this agreement is below.

8.

Two states, A and B, have signed an arms-control agreement. This agreement
commits them to refrain from building certain types of weapons. The agreement is supposed to
hold for an indefinite length of time. However, A and B remain potential enemies who would
prefer to be able to cheat and build more weapons than the other. The payoff table for A (player
1, the row player) and B (player 2, the column player) in each period after signing this
agreement is below.

a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.
The rate of return is r. For what values of r would it be worth it for player A to cheat by
building additional weapons just once against TFT?

b) For what values of r would it be worth deviating from the agreement forever to build
weapons?

c) Convert both values you found in parts a and b to the equivalent discount factor d
using the formula given in lecture and section.

d) Use the answers you find to discuss the relationship between d and r: as the discount
factor is high, what happens to the rate of return? Explain why.