Repeated Bargaining with Persistent Private Information

Abstract

The paper analyzes repeated contract negotiations involving the same buyer and seller where the contracts are linked because the buyer has persistent (but not fully permanent) private information. (The main application is labor contracts, where the employer has private information about the value of labor services sold by the union). The size of the surplus being divided is specified as a two-state Markov chain with transitions that are synchronized with contract negotiation dates. Equilibrium involves information cycles triggered by the success or failure of aggressive demands made by the seller. A successful demand induces the seller to again make an aggressive demand in the next negotiation, because the buyer's acceptance reveals that the current surplus is large, and because there is persistence in the Markov chain generating the surplus. Rejection of an aggressive demand, on the other hand, leads the seller to be pessimistic about the size of the surplus in the next contract, so the seller makes a "soft" offer that is sure to be accepted. Then, several contracts later, the Markov chain has made enough transitions to make the seller optimistic enough to again make an aggressive demand, and the result of this demand re-starts the information cycle. An interesting feature of this cycle is that the soft price is not constant, but declines as the cycle continues, so as to offset the buyer's option value of re-starting the cycle when the current state is bad. An explicit mapping is given for the relationship between the basic parameters and the equilibrium prices and quantities; in particular, there is a closed-form solution for the threshold belief that makes the seller indifferent between hard and soft offers.

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