Price of anarchy in supply chains, congested systems and joint ventures

Abstract

This thesis studies the price of anarchy in supply chains, congested systems and joint ventures. It consists of three main parts. In the first part, we investigate the impact of imperfect competition with nonlinear demand. We focus on a distribution channel with a single supplier and multiple downstream retailers. To evaluate the performance, we consider several metrics, including market penetration, total profit, social welfare and rent extraction. We quantify the performance with tight upper and lower bounds. We show that with substitutes, while competition improves the efficiency of a decentralized supply chain, the asymmetry among the retailers deteriorates the performance. The reverse happens when retailers carry complements. We also show that efficiency of a supply chain with concave (convex) demand is higher (lower) than that with affine demand. The second part of the thesis studies the impact of congestion in an oligopoly by incorporating convex costs. Costs could be fully self-contained or have a spillover component, which depends on others' output. We show that when costs are fully self-contained, the welfare loss in an oligopoly is at most 25% of the social optimum, even in the presence of highly convex costs. With spillover cost, the performance of an oligopoly depends on the relative magnitude of spillover cost to the marginal benefit to consumers. In particular, when spillover cost outweighs the marginal benefit, the welfare loss could be arbitrarily bad. The third part of the thesis focuses on capacity planning with resource pooling in joint ventures under demand uncertainties. We distinguish heterogeneous and homogeneous resource pooling. When resources are heterogeneous, the effective capacity in a joint venture is constrained by the minimum individual contribution. We show that there exists a unique constant marginal revenue sharing scheme which induces the same outcome in a Nash equilibrium, Nash Bargaining and the system optimum. The optimal scheme rewards every participant proportionally with respect to his marginal cost. When resources are homogeneous, we show that the revenue sharing ratio should be inversely proportional to a participant's marginal cost.