Monte Carlo Approximation in Incomplete Information, Sequential Auction Games

We model sequential, possibly multiunit, sealed bid auctions as a sequential game with imperfect and incomplete information. We develop an agent that constructs a bidding policy by sampling the valuation space of its opponents, solving the resulting complete information game, and aggregating the samples into a policy. The constructed policy takes advantage of information learned in the early stages of the game and is flexible with respect to assumptions about the other bidders' valuations. Because the straightforward expansion of the complete information game is intractable, we develop a more concise representation that takes advantage of the sequential auctions' natural structure. We examine the performance of our agent versus agents that play perfectly, agents that also create policies using Monte Carlo, and other benchmarks. The technique performs quite well in these empirical studies, although the tractability of the problem is bounded by the ability to solve component games.

[1]  J. Harsanyi Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[2]  Michael P. Wellman,et al.  The 2001 trading agent competition , 2002, Electron. Mark..

[3]  Howard James Bampton Solving Imperfect Information Games Using the Monte Carlo Heuristic , 1994 .

[4]  D. Koller,et al.  The complexity of two-person zero-sum games in extensive form , 1992 .

[5]  Peter R. Wurman,et al.  Structural leverage and fictitious play in sequential auctions , 2002, AAAI/IAAI.

[6]  Nicholas R. Jennings,et al.  Decision procedures for multiple auctions , 2002, AAMAS '02.

[7]  LabElectrotechnical,et al.  Monte-Carlo Sampling in Games with Imperfect Information : Empirical Investigation and AnalysisIan FrankComplex Games , 1997 .

[8]  R. Weber Multiple-Object Auctions , 1981 .

[9]  R. Selten Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[10]  Avi Pfeffer,et al.  Representations and Solutions for Game-Theoretic Problems , 1997, Artif. Intell..

[11]  Klaus Winkelmann Conference on Innovative Applications of Artificial Intelligence , 1989, Künstliche Intell..

[12]  R. McAfee,et al.  Auctions and Bidding , 1986 .

[13]  A. U.S.,et al.  Computation of Equilibria in Noncooperative Games , 2005 .

[14]  P. Klemperer The Economic Theory of Auctions , 2000 .

[15]  R. McKelvey,et al.  Computation of equilibria in finite games , 1996 .

[16]  Peter Stone,et al.  Autonomous Bidding Agents in the Trading Agent Competition , 2001, IEEE Internet Comput..

[17]  Ashish Sureka,et al.  Mining for bidding strategies on ebay , 2003 .

[18]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[19]  B. Stengel,et al.  COMPUTING EQUILIBRIA FOR TWO-PERSON GAMES , 1996 .

[20]  Craig Boutilier,et al.  Sequential Auctions for the Allocation of Resources with Complementarities , 1999, IJCAI.

[21]  R. Palmer,et al.  Characterizing effective trading strategies: Insights from a computerized double auction tournament , 1994 .

[22]  A. Roth,et al.  Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet , 2002 .

[23]  Bernhard von Stengel,et al.  Fast algorithms for finding randomized strategies in game trees , 1994, STOC '94.

[24]  R. M. Stark,et al.  Auctions, Bidding, and Contracting: Uses and Theory , 1983 .

[25]  W. Hall,et al.  Autonomous Agents for Participating in Mulitple On-line Auctions , 2001 .

[26]  J. Nash Two-Person Cooperative Games , 1953 .

[27]  P. Klemperer Auction Theory: A Guide to the Literature , 1999 .

[28]  Nicholas R. Jennings,et al.  AUTONOMOUS AGENTS FOR PARTICIPATING IN MULTIPLE , 2001 .

[29]  Michael P. Wellman,et al.  Flexible double auctions for electronic commerce: theory and implementation , 1998, Decis. Support Syst..

[30]  Rajarshi Das,et al.  High-performance bidding agents for the continuous double auction , 2001, EC '01.

[31]  Kemal Guler,et al.  Bidding By Empirical Bayesians In Sealed Bid First Price Auctions , 2002 .

[32]  Dov Monderer,et al.  A Learning Approach to Auctions , 1998 .

[33]  Shou-De Lin,et al.  Designing the Market Game for a Trading Agent Competition , 2001, IEEE Internet Comput..

[34]  John H. Reif,et al.  Computation of equilibriain noncooperative games , 2005 .