Question

	collude	defect
collude	1128,1128	846,1269
defect	1269,846	1045,1045

if the two firms anticipate their interaction to be repeated in the future, what probability w of the game continuing is needed for a cooperative tit-for-tat strategy to be viable? (find the value of w where the present value payoff from cooperating as a monopolist is at least as great as the present value payoff from a single defection plus the Cournot profit for the rest of the game)

Answer 1

If they both collude, the payoff will be 1128 forever.

If one of them defect once, then they get a payoff of 1269 at present and then they get 1045 going forward.

For a break-even between the two, suppose the probability that the game goes forward is w.

So, we have 1128*[1+w+w^2+....]=1269+1045*[w+w^2+...]

So, we have 1128/(1-w) = 1269+1045w/(1-w)

1269(1-w)=1128-1045w

141=224w

w=141/224 = 0.62946428571

Thus, w has to be at least 141/224, so that player cooperate with each other. (Ans)