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 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) (52,-4) Advertise 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

1. Advertise is a dominant strategy for Both player. Thus (Advertise, Advertise) is a Nash  equilibrium and would be the outcome of one shot game.

b. Yes, both can be made better off if both collude but both have an incentive to cheat as they play only once. Thus ( Don’t advertise, Don’t advertise) could be the collusive outcome but both ends up with playing Advertise. And (Advertise, Advertise) would be the outcome of the above one shot game.

c. Expected payoff from Collusion=12+ 12/1.35+ 12/1.35² + ...=12/1-(1/1.35)=12(1.35)/0.35=46.2857

Expected payoff from deviation=(advertisement)=52

Thus At 35% firms will not collude and both will advertise. Thus there is no better off situation compared to one shot game.