Question

4. (10 points) At a time when cereal maker Kellogg's demand for ready-to-eat cereal was stagnant, a spokesperson for the cereal maker Kellogg's was quoted as saying, “.....for the past several years, our individual company growth has come out of the other fellow's hide." Kellogg's has been producing cereal since 1906 and continues to implement strategies that make it a leader in the cereal industry. The payoff matrix for Kellogg and its rival to advertise or “don't advertise” is given below Kellogg's Rival Advertise Don't Advertise (0,0) Advertise (52,-4) Kellogg Don't Advertise (-4, 52) (12, 12) (a) If this were a simultaneous move one shot game, what would the Nash equilibrium outcome be? Please explain. (b) Assuming that the game is still played once, if the firms could collude, what would the collusive outcome be, assuming that they made a collusive agreement and followed the agreement. Please explain. (c) Now suppose the game is infinitely repeated. If the interest rate is 35 percent, can you do better than you could in a one-shot play of the game using a trigger strategy? Explain.

Answer 1

question (4) Kellogg's rival Advertise Don't Advertise Advertise (0,0) (52,-4) Kellogg Don't (-4,52) (12, 12) Advertise (a) Dominant strategy it is a strategy Profile That gives maximum payeys Player compared To available strategies irrespective of players are To a its all what other Choo so sing For Kellogg Because if Pay aff Advertise is a Dominant Stoategy. gives o if gival chooses Advertise which more Than 4. (when keilogy choses Don't advertise) is

52 if vival Chooses DONt advertise which is more Than 12 (when Kellogg Chooses Don't advertise) Therefore advertise is a dominant strategy for Kellogg Snimilarly for rivals we have dominant strategy This game has unique dominant Strategy wash equilibrium where Rival chooses To To advertise and will get both Kellogg and its Payas (0,0) NE: (advertise advertise) Collude will (b) if the firms are They १० fors to Don't advertise in order to get Payals (12, 12) • Because if they do not they will Collude o then which is Less Than get fagaff (0,0) collusive outcome for both Prayers.

(C) interest rate (8)= 35% = 0.35 Chooses trigger strategy is a strategy if one of wit them deviatues from their collusion aggrement and other Strategy, Then Louive after that they both will get Nash equilibrium pay caffs. factor S - Discount I ito I 1035 1+0.35 0074074 Concesive Profit for in in finitetly relerated game collusion c T = Tit 8 Tt 8 T + с 2 I T 1-8 Where с π = 12 for a payer. Colusion ㅠ (12) 46.2857 - 0.74074 deviation Profit For For infinitely repeated game deviation ㅠ 2 T + S T + S T d -T + S I-8

52 I = deviation Profit When other is forrowing collusion and other one deviate der = 0 7" - Nash equilibrium Profit deviation I d π t 8 N T I-S deviation U Since π = 0 52 + 0 =52 of Thom IS deviation Profit Profit for each Player more Than of connusion profit. So we can not do better when than from a one-shop play game using trigger Strategy