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
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.
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