Optimization and the Price of Anarchy in a Dynamic Newsboy Model
نویسندگان
چکیده
This paper examines a dynamic version of the newsboy problem in which a decision maker must maintain service capacity from several sources to attempt to meet uncertain demand for a perishable good, subject to the cost of providing sufficient capacity, and penalties for not meeting demand. A complete characterization of the optimal outcome is obtained when normalized demand is modeled as Brownian motion. The centralized optimal solution is a function of variability in demand, production variables, and the cost of insufficient capacity. A closed form expression is obtained for the unique (state dependent) market clearing prices that allows the decentralized market to sustain the centralized optimal solution. The prices are a non-smooth function of normalized demand and reserves. Consequently, prices show extreme volatility in the efficient decentralized market outcome. Standard policy designs are examined to improve the behavior of the decentralized market, including price caps and partial decentralization where the buyer owns a portion of the total service capacity. It is shown that these remedies fail: The market outcome in a partially decentralized model is shown to be inefficient even if the buyer owns a substantial portion of the service capacity. Under the presence of a price cap, a market equilibrium, efficient or not, fails to exist under very general conditions.
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