Demand for contract enforcement in a barter environment

Do greater potential gains from trade enhance or erode contracting institutions? In an anonymous exchange environment traders can sign a contract, hence agreeing to interact with the assigned partner, or wait till the next match. Any contract can be endorsed (for a payment) by the enforcement agency, which then observes the interaction with a positive probability known to the traders and punishes any detected infractors. Demand for contract enforcement is the highest amount a proposer of a contract is ready to pay to the agency, in a stationary subgame perfect equilibrium. It may be strictly positive, as we show, even when contracts are broken. Surprisingly, larger potential gains from exchange may dampen the demand, but not always: the demand is boosted under agencies that oversee the interactions frequently.