We propose two generalizations of the Davis and Maschler (1965) reduced game property to economies with asymmetric information and apply them in the characterization of two solution concepts. One is Wilson's (1978) Coarse Core and the other is a subsolution of it which we call the Coarse+ Core.

We study contracting for a three-tier supply chain consisting of a buyer, a supplier, and a sub-supplier where disruptions of random length occur at the sub-supplier. As is common in supply chains, the buyer has a direct relationship with the supplier but not the sub-supplier; that is, the buyer...