Techniques For Finding Nash Equilibria In Combinatorial Auctions

Abstract

Auctions that allow participants to bid on a combination of items rather than just the individual items are called combinatorial auctions. For items that exhibit complementarity and substitutability, combinatorial auctions can be used to reach economically efficient allocations of goods and services. There has been a surge of recent research on combinatorial auctions because of the wide variety of practical situations to which they can be applied.

There are several instances in which combinatorial auctions have already been applied to allocate scares resources, but there are still some challenging issues that need to be addressed before combinatorial auctions can be much more widely used in practice. Many different combinatorial auctions designs have been proposed by researchers and recently there has been a lot of work on studying the computational and strategic aspects of these auction designs. In this thesis, I analyze combinatorial auctions from a game theoretic perspective and propose techniques for determining pure strategy Nash equilibrium of combinatorial auctions. For a variety of reasons, combinatorial auctions pose serious computational challenges to compute Nash equilibria using current techniques. One problem is that the size of the strategy space in combinatorial auctions is very large and grows exponentially with the number of bidders and items. Another computational issue is that for combinatorial auctions it is computationally expensive to compute the payoffs of the players as a result of the joint actions. This makes it computationally expensive to determine the complete payoff matrix upfront and then determine Nash equilibrium. In this dissertation, we present techniques to overcome these problems. We present algorithms based on meta-heuristic search techniques, best response dynamics and linear programming to tackle these problems. We present empirical and theoretical results to support our claim that the algorithms perform well.