Hi
I have been stuck on this for about 3 hours so I've come here.
I have some questions in Game Theory on Folk Theorom (http://kot.rogacz.com/Science/Studie...20Theorems.pdf)
Question 1)
Consider the infinitely repeated prisoners dilemma game under average payoffs.
Prisoners dilemma
___C__ _D
C (2,2) (0,4)
D (4,0) (1,1)
a) Can (4,0) be a payoff vector for an equilibrium strategy?
b) Can (2.25,2.25) be a payoff vector for an equilibrium strategy?
c) Can (3,3) be a payoff vector for an equilibrium strategy?
Solution.
a) No: 0 < minmax value of player 1, therefore not enforceable.
b) This can’t be determined (at least not from the folk theorem). Weights to prove feasibility would need to be (1,0,0,0), but theorem requires 0 < < 1.
c) Yes: enforceable and feasible (weights (0.5, 0, 0, 0.5).
Question 2)
Consider the following normal form game:
____B1__ B2
A1 (2,0) (0,0)
A2 (0,0) (0,2)
Give the payoff vector for an equilibrium strategy for the infinitely repeated version of this game under average payoffs. (Hint: use the folk theorem).
Solution(1,1) is a possible payoff vector.
Feasible: weights (0.625, 0, 0, 0.375)
Enforceable: minmax value is 0 for players 1 and 2.
I understand enforcement and I understand the idea of feasibility (payoffs in a vector must be possible in the game given). However, I really don't understand:
1) how to tell if a payoff is feasible?
2) Why the answer to 1)b) can't be determined
2) MOSTLY: How to calculate the feasible weights : weights (0.5, 0, 0, 0.5) in 1)c) and weights (0.625, 0, 0, 0.375) in 2
This is something to do with weighted averages of strategies but I have no idea how to calculate them.
Any help would be greatly appreciated.
Thanks,
Simon