Contract renewal

Consider a contract between two players, describing the payment an agent obtains from the principal, in exchange for a good or service supplied. At each point in time, either player may unilaterally demand a renegotiation of the contract, involving renegotiation costs for both players. Players’ payoffs from trade under the contract, as well as from a renegotiated contract, are stochastic, following the exponential of a L´evy process. It is argued that the optimal strategy for each player is to require a renegotiation when the contract payment relative to the outcome of a renegotiation passes a certain threshold, depending on the stochastic processes, the discount rate, and the renegotiation costs. There is strategic substitutability in the choice of thresholds, so that if one player becomes more aggressive by choosing a threshold closer to unity, the other player becomes more passive. If players may invest in order to reduce the renegotiation costs, there will be over-investment compared to the welfare maximizing levels.