Question

Assume that if a pair of oligopolists fail to collude, their profits are equal to 1 unit each per period of unattempted collusion. Assume that if they collude, their profits are equal to 10 units each per period of successful collusion. Suppose that if one monopolist attempts collusion while the second attempts deviation, that the deviator’s profits are 15 and the attempted colluder’s profits are 0 in such a period. Assume an interest rate of r (where r is a fraction known to the participants).

i. Assume in an infinitely repeated game both players attempt to collude until one player deviates. Once this happens both players no longer attempt collusion. Find the values of r such that the above strategies constitute an equilibrium.

ii. Explain why it is still an equilibrium to not attempt collusion once a deviation was recorded. (Hint: what has changed about each players expectations?) This is important in economic theory, because it means that our theory of collusion does not depend on bluffs

Answer 1

Page Answear not collude collude 0,20 10, 10 Colinde 20, o not colinde IF game attempt to is repeated Soutel infinitely infinitely Beth Rayers Bor collude until one player deriates 10 10+ 10 57% Collusion pay off collusion (5+8) 10 & 10 (82) 5+8-5 It one player deviotes the game will get zo as a profit in that period and after that enpect a payoff of 5 unit per period from deviation t ... so on . le; 20tto (5+8) 20 + To+8)

= 20th 20+ Deviation pay off > 2048 Payoff . collusion pay off > Deviation je, 10 (8+5) > 207 (445) 10 (4+5) - (4+5) 320 = 9(r+5) >20 art 45 20 => 98 + H5>208 45208-98 1 45 > 118 8445 I Î once cheated than the collusion party get on. If they complete the payoff is I. So pay off from non collusion / competition is higher than collusion.