Contract adjustment under uncertainty

Consider trade in continuous time between two players. The gains from trade are divided according to a contract, and at each point in time, either player may unilaterally induce a costly adjustment of the contract. Players' payoffs from trade under the contract, as well as from trade under an adjusted contract, are exogenous and stochastic. We consider players' choice of whether and when to adjust the contract payment. We show that there exists a Nash equilibrium in thresholds, where each player adjusts the contract whenever the contract payment relative to the outcome of an adjustment passes the threshold. There is strategic substitutability in the choice of thresholds, so that if one player becomes more active by choosing a threshold closer to unity, the other player becomes more passive.