Efficiency of Scalar-Parameterized Mechanisms

• Published in: Operations research Vol. 57; no. 4; pp. 823 - 839
• Main Authors: Johari, Ramesh, Tsitsiklis, John N
• Format: Journal Article
• Language: English
• Published: Hanover, MD INFORMS 01.07.2009; Institute for Operations Research and the Management Sciences
• Subjects: Allocative efficiency; Applied sciences; bidding/auctions; Budget allocation; Decision theory. Utility theory; Efficiency; Efficiency loss; Elasticity; Exact sciences and technology; Flows in networks. Combinatorial problems; Game theory; game/group decisions; Market mechanisms; Market prices; Mathematical vectors; Mechanism design; Nash equilibrium; networks/graphs; noncooperative; Operational research and scientific management; Operational research. Management science; Portfolio theory; Price efficiency; Resource allocation; Studies; theory; Utility functions; utility/preference; United States; Nash strategy; game/group decisions: noncooperative, bidding/auctions; Bidding; Scalability; Utility function; Worst case method; Nash equilibrium; Graph theory; Preference theory; Communication network; Flexibility; Game theory; utility/preference: theory; Social decision; Case study; Mechanism synthesis; Utility theory; Non cooperative game; networks/graphs: theory; Pricing; Telecommunication network; Game equilibrium; Large scale
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1080.0638

We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large-scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that Kelly's proportional allocation mechanism minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we construct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.