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%
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