Relational Supply Contracts: Voluntary Concessions in Return Policies for Continuous Quality Improvements

Not every interaction within a supply chain is specified by a formal contract vetted by lawyers. Many things are agreed to on an informal basis and it is worth exploring how these informal side agreements relate to formal contracts. This paper studies a two-firm supply chain, where repeated transactions via well-established supply chain contracts and continued quality-improvement efforts are governed by a relational contract. We are able to characterize an optimal relational contract, i.e., to develop policies for supplier and buyer that structure investments in quality and flexibility in a way that no other self-enforcing contract generates higher expected joint surplus. For this purpose, we study an infinite horizon dynamic game with Markovian dynamics modelling the stochastic influence of the firms' actions on quality. We examine both quantity-based (quantity flexibility contracts) and price-based returns mechanisms (buy backs) and show that the rough equivalence between QF and buy-back contracts in the one period newsvendor setting does not carry over to the more complex setting as regards the leeway for contract adaptation and the need for additional transfer payments.