Performance of a push supply chain under partial cross ownership with an effort-contingent demand

Supply chain under partial cross ownership (PCO) refers to the dyad in which each one holds part of its partner´s shares. In a two-echelon push supply chain under the partial cross ownership, when the demand is affected by the retailer´s effort, letting the retailer hold part of the supplier´s shares doesn´t affect the chain efficiency and both players´ profits. However, when the demand is affected by the supplier´s effort, letting the retailer hold part of the supplier´s shares does affect the chain efficiency and both players´ profits, and the supplier´s profit increases with both its own percentage of shares held by the retailer and the retailer´s share held by itself.