Question

4. (10 points) At cereal a time maker when Kellogg's demand was 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 Kellog and its rival to advertise or "don't advertise is given below Kellogg's Rival Advertise Don't Advertise Advertise (0,0) (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

a) Payoff table

	A	D
A	(0*,0•)	(52*,-4)
D	(-4,52•)	(12,12)

Simultaneous one shot game

NE : (both firms advertise)

b)

if both could collude, where if both could decide, not to advertise, each is better off , & gets 12

c) r = .35, the discount Factor d = 1/(1+r)

d = 1/1.35= .7407

then if both Cooperate, present value of cooperation Payoff

Vc = 12+12d + 12d² + 12d³ + ....

= 12/(1-d)

= 46.285

if any one deviates, then cheater gets 52 this period, & punishment starts next period, where each gets 0 , the nash eqm payoff,

so present discount value PDV of cheating payoff

Vd = 52+ 0 + 0....

So

as Vc < Vd

then cooperation can't be sustained, firms can't do better