Optimal pricing contracts and level of information asymmetry in a supply chain

This study considers a stylized supply chain model consisting of a dominant supplier and a buyer, in which the latter possesses superior knowledge of his private cost information. The supplier's imperfect knowledge about the buyer's cost is denoted by a subjective distribution. By assuming that the distribution is uniform, we first derive the explicit expressions of the optimal equilibrium outcomes of two contract formats offered by the supplier, the simple price-only contract and sophisticated menu of contracts, respectively. Based on the optimal results, we continue to investigate how the supplier's expected profit varies with the level of information asymmetry, which is measured by the variance of the supplier's subjective distribution. Our findings indicate that the supplier's expected profits initially decrease and then increase as the supplier's knowledge of the buyer's cost becomes increasingly uncertain. That is, if the supplier could choose the level of information asymmetry, she would prefer a symmetric case (with the variance being zero) or a totally asymmetric case (with the variance being as high as possible). Numerical experiments demonstrate that our result still holds when we take into account such distributions as a truncated gamma and normal, and a fixed support of the distribution function instead of a moving support.