## Answers

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 + 12d ^{2} + 12d^{3} + ....*

*= 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**

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