3. (6 points) 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.

	Refrain	Build
Refrain	0,0	-5.5
Build	5,-5	-2,-2

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

b) Convert both values you found in part (a) to the equivalent discount factor 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.

c) Assume that the states are instead using Grim Trigger (GT) strategies. How would any of the calculations in part (a) change? Why?

d) What do these calculations tell us about the sustainability of arms-control agreements? Does the punishment strategy matter?