ITERATIVE COMBINATORIAL AUCTIONS : ACHIEVING ECONOMIC AND COMPUTATIONALEFFICIENCYDavid

ITERATIVE COMBINATORIAL AUCTIONS: ACHIEVING ECONOMIC AND COMPUTATIONAL EFFICIENCY David Christopher Parkes Supervisor: Lyle H. Ungar This thesis presents new auction-based mechanisms to coordinate systems of selfinterested and autonomous agents, and new methods to design such mechanisms and prove their optimality. Computation is increasingly carried out on open networks, with self-interested programs (\agents"), competing to derive the most utility for users. In addition, new interconnectivity and distributed computing is changing business practices. It is now possible to implement dynamic mechanisms to trade goods and services, both business-to-consumer (B2C) and business-to-business (B2B), and remove the ine ciencies in traditional marketplaces. Auctions o er great promise as simple and robust dynamic mechanisms for e cient resource allocation. There are already on-line consumer auctions, and nascent auctions for B2B trade in the supply-chain. However the majority of on-line auctions remain simple variations on standard auctions. My thesis is that it is necessary to take an explicitly computational approach to auction design. Auctions will be populated with automated bidding agents, and only auctions that are robust and present simple optimal bidding strategies will be successful. In addition, combinatorial auctions are important in many important applications, but present inherently hard computational problems for agents and for auctioneers. A combinatorial auction allows agents to bid for bundles of items. Consider a manufacturer that needs either components A and B, or just component C; consider a mobile agent that needs an interval of compute time; consider a train that needs a bundle of iii departure and arrival times on tracks across its route. Combinatorial auctions present two key computational problems: (1) the winner-determination problem, to compute a revenue-maximizing set of bids, is NP-hard; (2) agents often have hard valuation problems, for example local optimization problems, to compute the value of di erent bundles. I propose iBundle, an iterative combinatorial auction, that is economically e cient under a reasonable assumption about agent bidding strategies, minimizes agent valuation work, and allows the auctioneer to introduce approximate solutions for winnerdetermination. Iterative auctions allow agents to compute incremental values for items or bundles of items, in response to bids from other agents, and avoid valuation altogether on high priced bundles. In addition, the auctioneer can tradeo economic e ciency with computational e ciency. Increasing the bid increment decreases the number of rounds and the number of winner-determination problems to solve. Approximate algorithms for winnerdetermination can be introduced while maintaining incentives for agents to follow the same bidding strategy. iBundle is the rst iterative combinatorial auction that is optimal for a reasonable bidding strategy, in this case myopic best-response to current prices. Its optimality is proved through a fundamental connection with primal-dual optimization theory. iBundle maintains feasible primal and dual solutions to the resource allocation problem, the allocation and prices in the auction. The strong duality theorem of linear-programming states that primal and dual solutions are optimal if and only if they satisfy complementary slackness conditions, which express logical constraints between their values. Best-response bids from agents in iBundle provide enough information for the auctioneer to adjust prices so that the auction provably terminates with primal and dual solutions that satisfy complementary slackness conditions. The primal-dual interpretation of iBundle also suggests a method to boost the \strategyproofness" of the auction, adjusting the price after iBundle terminates towards prices that make myopic best-response an optimal strategy for rational self-interested agents. When successful, together with proxy bidding agents which constrain agent bidding strategies to (possibly untruthful) best-response bidding strategies, this \proxy and adjust" method makes iBundle an iterative, optimal, and non-manipulable auction. iv