Optimization in the private value model: competitive analysis applied to auction design

• Authors: Jason Daniel Hartline;Anna R. Karlin
• Venue: Optimization in the private value model: competitive analysis applied to auction design
• Year: 2003

We consider the study of a class of optimization problems with applications towards profit maximization. One feature of the classical treatment of optimization problems is that the space over which the optimization is being performed, i.e., the input description of the problem, is assumed to be publicly known to the optimizer. This assumption does not always accurately represent the situation in practical applications. Recently, with the advent of the Internet as one of the most important arenas for resource sharing between parties with diverse and selfish interests, this distinction has become more readily apparent. The inputs to many optimizations being performed are not publicly known in advance. Instead they must be solicited from companies, computerized agents, individuals, etc., that may act selfishly to promote their own self-interests. In particular, they may lie about their values or may not adhere to specified protocols if it benefits them. An auction is one of the simplest applications where the classical (a.k.a. public value) optimization approach fails to work as expected in the presence of selfish agents with private data. We consider casting profit optimization problems into the game theoretic framework of mechanism design and consider the design of auction mechanisms to maximize the profit of the auctioneer. We show how a competitive analysis can be used to gauge the performance of profit maximizing mechanisms. We develop a number of techniques for designing auctions and show how they can be extended to more complex profit maximization problems.