Chapter 8 Problem 5 (1st edition)

Chapter 11 Problem 8 (2nd edition)

Kid's Corner | |||

High | Low | ||

Child's Play | High | 64 , 64 | 20 , 72 |

Low | 72 , 20 | 57 , 57 |

High payoff from cheating | (72) | |

> | cooperative payoff | (64) |

> | defect payoff | (57) |

> | low payoff from cooperating | (20) |

PV(collude) > PV(cheat)Thus, if r < 7/8, the grim trigger strategy supports collusion, and if r > 7/8, the firms have an incentive to cheat. If r=0.25, cooperation can be sustained.

==> 64 + 64/r > 72 + 57/r

==> 7/r > 8

==> 7 > 8r

==> r < 7/8

R = (1 + r - p) / pThis would need to exceed 7/8 for cheating to be worthwhile (see part d), so cooperation would still be sustained.

= (1 + 0.25 - 0.9) / 0.9

= 0.35 / 0.9

= 0.39 = 39%

If the probability of bankruptcy rises to 35%, p=0.65, and the future becomes worth less. Then, R=92%. So, if bankruptcy becomes more certain, cheating becomes worthwhile.