Last Updated on 28. April 2023 by Martin Schuster

Task

Suppose we have the following situation:

The game is repeated infinitely. Player B says (credibly) he plays grim trigger. A has a time preference of 0.9.

1. Is it profitable for player A to cooperate?
2. What time preference p would be necessary that A doesn’t want to cooperate anymore?

Solution

a)

Present Value with cooperation: PV_C = 8*(1/(1-0.9)) = 80

Present Value with no cooperation: PV_N = 11 + 2*(0.9/(1-0.9)) = 29

As PV_C > PV_N, cooperation is beneficial.

b)

For p < 1/3