Noisy Sequential Screening with Positive Selection
I study a repeated relationship between two players subject to termination. One player, the proposer, offers a transfer in each period to keep the receiver in the relationship. The receiver can accept and remain in the game until the next period, or refuse the offer and end the relationship permanently. The receiver has private information about her flow payoff from the relationship, net of transfers. Applications include repeated crisis bargaining in international relations, or surplus extraction from an agent. Unlike in Coasian bargaining, the types remaining after a stingy offer are those from whom more can be extracted, potentially leading to ratchet effects. Tirole (2016) shows that, if the receiver’s type is fully persistent, there is in fact no ratcheting after the first period. I show that, if the receiver’s payoff is affected even by small shocks from period to period, then the proposer instead makes more aggressive offers over time, leading to all receiver types quitting in the long run. The reason is that a small attempt to ratchet is only punished by exit in the unlikely case that the receiver’s type is marginal and the realized shock is unfavorable. The probability of exit can vary over time between major escalations with high risk of exit and lull periods with low risk, without ever going to zero. The solution differs depending on whether the proposer has commitment power or not, but eventual exit is inevitable in both cases.