Profit Maximization in Mechanism Design

Abstract

Mechanism design is a subfield of game theory and microeconomics focused on incentive engineering. A mechanism is a protocol, typically taking the form of an auction, that is explicitly designed so that rational but non-cooperative agents, motivated solely by their self-interest, end up achieving the designer's goals. The challenge of mechanism design is to apply these methods to traditional computer science goals such as worst-case or competitive analysis. We consider two challenging problems related to mechanism design for profit maximization: the analysis of natural bidding strategies used by participants in sponsored search auctions, and the design of a mechanism for matroid procurement with provable performance guarantees. The sponsored search auctions of web search engines such as Google or Yahoo! use the generalized second-price (GSP) mechanism, in which bidders do not have a dominant strategy. We develop a framework for studying a variety of greedy bidding strategies and analyze their revenue, convergence and robustness properties. We compare the performance of greedy bidding strategies to that of a Nash equilibrium, quantifying how close these bidding strategies are to one of the most natural and rational stable points of the system. In the procurement problem a buyer is given a set of agents with values, along with a family of feasible sets over the agents. The goal is to procure a feasible set of maximum value, for minimum cost. Assuming that a buyer obtains a decreasing marginal benefit per feasible set procured, the problem is to determine the optimal number of feasible sets to procure in order to maximize the buyer's profit. We develop a mechanism that approximates the optimal profit to within a constant factor, when the set system is a matroid. Matroids are important structures in combinatorial optimization: for example, minimum spanning trees and node-weighted maximum matchings are both matroid problems. We also show that the well-known cost sharing revenue extraction mechanism is only truthful for matroid set systems, so that procurement problems over non-matroid set systems are not likely to be solved with current techniques.