research-article

Repeated Dollar Auctions: A Multi-Armed Bandit Approach

Authors:

Long Tran-Tranh,

Tomasz MichalakAuthors Info & Claims

AAMAS '16: Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems

Pages 579 - 587

Published: 09 May 2016 Publication History

Abstract

We investigate the repeated version of Shubik's dollar auctions, in which the type of the opponent and their level of rationality is not known in advance. We formulate the problem as an adversarial multi-armed bandit, and we show that a modified version of the ELP algorithm[25], tailored to our setting, can achieve Ṑ(√(|S_o| T)) performance loss (compared to the best fixed strategy), where S is the cardinality of the set of available strategies and T is the number of (sequential) auctions. We also show that under some further conditions, these bound can be improved to Ṑ(|S_o|^1/4√(T)) and Ṑ(√(T)), respectively. Finally, we consider the case of spiteful players. We prove that when a non-spiteful player bids against a malicious one, the game converges in performance to a Nash equilibrium if both players apply our strategy to place their bids.

References

[1]

R. Agrawal. Sample mean based index policies with o(log n) regret for the multi-armed bandit problem. Advances in Applied Probability, 27:1054--1078, 1995.

[2]

N. Alon, N. Cesa-Bianchi, C. Gentile, and Y. Mansour. From bandits to experts: A tale of domination and independence. In Advances in Neural Information Processing Systems, pages 1610--1618, 2013.

[3]

M. Aoyagi. Bid rotation and collusion in repeated auctions. Journal of Economic Theory, 112(1):79--105, 2003.

[4]

P. Auer, N. Cesa-Bianchi, and P. Fischer. Finite--time analysis of the multiarmed bandit problem. Machine Learning, 47:235--256, 2002.

Digital Library

[5]

P. Auer, N. Cesa-Bianchi, Y. Freund, and R. E. Schapire. Gambling in a rigged casino: The adversarial multi-armed bandit problem. In Foundations of Computer Science, 1995. Proceedings., 36th Annual Symposium on, pages 322--331. IEEE, 1995.

Digital Library

[6]

P. Auer, N. Cesa-Bianchi, Y. Freund, and R. E. Schapire. The nonstochastic multiarmed bandit problem. SIAM Journal on Computing, 32(1):48--77, 2002.

Digital Library

[7]

S. Bikhchandani. Reputation in repeated second-price auctions. Journal of Economic Theory, 46(1):97--119, 1988.

[8]

K. E. Boulding. Conflict and defense: A general theory. 1962.

[9]

F. Brandt, T. Sandholm, and Y. Shoham. Spiteful bidding in sealed-bid auctions. In Computing and Markets, 2005.

[10]

J. Campos, C. Martinho, and A. Paiva. Conflict inside out: A theoretical approach to conflict from an agent point of view. AAMAS '13, pages 761--768. International Foundation for Autonomous Agents and Multiagent Systems, 2013.

Digital Library

[11]

C. Castelfranchi. Conflict ontology. In Computational Conflicts, pages 21--40. Springer, 2000.

Digital Library

[12]

E. Dechenaux, D. Kovenock, and R. M. Sheremeta. A survey of experimental research on contests, all-pay auctions and tournaments. WZB Discussion Paper SP II 2012--109, Berlin, 2012.

[13]

G. Demange. Rational escalation. Annales d'Économie et de Statistique, (25/26):pp. 227--249, 1992.

[14]

D. DiPalantino and M. Vojnovic. Crowdsourcing and all-pay auctions. In EC'09, pages 119--128. ACM, 2009.

Digital Library

[15]

H. Fang. Lottery versus all-pay auction models of lobbying. Public Choice, 112(3--4):351--371, 2002.

[16]

A. M. Frieze. On the independence number of random graphs. Discrete Mathematics, 81(2):171--175, 1990.

Digital Library

[17]

Z. Han, R. Zheng, and H. V. Poor. Repeated auctions with bayesian nonparametric learning for spectrum access in cognitive radio networks. Wireless Communications, IEEE Transactions on, 10(3):890--900, 2011.

Digital Library

[18]

A. J. Jones. Game theory: Mathematical models of conflict. Elsevier, 2000.

[19]

J. H. Kagel and D. Levin. Auctions: a survey of experimental research, 1995--2008. 2008.

[20]

J. L. Knetsch, F.-F. Tang, and R. H. Thaler. The endowment effect and repeated market trials: Is the vickrey auction demand revealing? Experimental economics, 4(3):257--269, 2001.

[21]

T. Kocák, G. Neu, M. Valko, and R. Munos. Efficient learning by implicit exploration in bandit problems with side observations. In Advances in Neural Information Processing Systems, pages 613--621, 2014.

[22]

V. Krishna and J. Morgan. An analysis of the war of attrition and the all-pay auction. journal of economic theory, 72(2):343--362, 1997.

[23]

W. Leininger. Escalation and cooperation in conflict situations the dollar auction revisited. Journal of Conflict Resolution, 33(2):231--254, 1989.

[24]

Y. Lewenberg, O. Lev, Y. Bachrach, and J. S. Rosenschein. Agent failures in all-pay auctions. IJCAI/AAAI, 2013.

Digital Library

[25]

S. Mannor and O. Shamir. From bandits to experts: On the value of side-observations. In Advances in Neural Information Processing Systems, pages 684--692, 2011.

[26]

R. C. Marshall and L. M. Marx. Bidder collusion. Journal of Economic Theory, 133(1):374--402, 2007.

[27]

H. J. Müller and R. Dieng. On conflicts in general and their use in ai in particular. In Computational conflicts, pages 1--20. Springer, 2000.

Digital Library

[28]

J. Münster. Repeated contests with asymmetric information. Journal of Public Economic Theory, 11(1):89--118, 2009.

[29]

J. K. Murnighan. A very extreme case of the dollar auction. Journal of Management Education, 26(1):56--69, 2002.

[30]

M. Nanjanath and M. Gini. Repeated auctions for robust task execution by a robot team. Robotics and Autonomous Systems, 58(7):900--909, 2010.

Digital Library

[31]

B. O'Neill. International escalation and the dollar auction. Journal of Conflict Resolution, 30(1):33--50, 1986.

[32]

J. Poland. Fpl analysis for adaptive bandits. 3rd Symposium on Stochastic Algorithms, Foundations and Applications (SAGA'05), pages 58--69, 2005.

Digital Library

[33]

H. Robbins. Some aspects of the sequential design of experiments. Bulletin of the AMS, 55:527--535, 1952.

[34]

M. Shubik. The dollar auction game: A paradox in noncooperative behavior and escalation. Journal of Conflict Resolution, pages 109--111, 1971.

[35]

A. Skrzypacz and H. Hopenhayn. Tacit collusion in repeated auctions. Journal of Economic Theory, 114(1):153--169, 2004.

[36]

C. Tessier, L. Chaudron, and H. J. Müller. Agents' conflicts: New issues. In Conflicting Agents, volume 1 of Multiagent Systems, Artificial Societies, And Simulated Organizations, pages 1--30. Springer US, 2002.

Digital Library

[37]

W. W. Vasconcelos, M. J. Kollingbaum, and T. J. Norman. Normative conflict resolution in multi-agent systems. AAMAS'09, 19(2):124--152, 2009.

Digital Library

[38]

X. Vives. Technological competition, uncertainty, and oligopoly. Journal of Economic Theory, 48(2):386--415, 1989.

[39]

M. Waniek, A. Niescieruk, T. Michalak, and T. Rahwan. Spiteful bidding in the dollar auction. In Proceedings of the 24th International Conference on Artificial Intelligence, pages 667--673. AAAI Press, 2015.

Digital Library

[40]

D. Weyns and T. Holvoet. Regional synchronization for simultaneous actions in situated multi-agent systems. pages 497--510, 2003.

Digital Library

[41]

E. Wolfstetter. Auctions: an introduction. Journal of economic surveys, 10(4):367--420, 1996.

[42]

J. Y. Yu and S. Mannor. Piecewise-stationary bandit problems with side observations. In Proceedings of the 26th Annual International Conference on Machine Learning, pages 1177--1184. ACM, 2009.

Digital Library

Cited By

Waniek MTran-Thanh LMichalak TJennings NSingh SMarkovitch S(2017)The dollar auction with spiteful playersProceedings of the Thirty-First AAAI Conference on Artificial Intelligence10.5555/3298239.3298347(736-742)Online publication date: 4-Feb-2017
https://dl.acm.org/doi/10.5555/3298239.3298347

Index Terms

Repeated Dollar Auctions: A Multi-Armed Bandit Approach
1. Theory of computation
  1. Design and analysis of algorithms
    1. Online algorithms
      1. Online learning algorithms
  2. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
      1. Computational pricing and auctions

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cover image ACM Other conferences

AAMAS '16: Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems

May 2016

1580 pages

ISBN:9781450342391

General Chairs:
Catholijn M. Jonker
TU Delft, Netherlands
,
Stacy Marsella
University of Southern California, USA
,
Program Chairs:
John Thangarajah
RMIT University. Australia
,
Karl Tuyls
University of Liverpool, UK

Sponsors

IFAAMAS

In-Cooperation

SIGAI: ACM Special Interest Group on Artificial Intelligence

Publisher

International Foundation for Autonomous Agents and Multiagent Systems

Richland, SC

Publication History

Published: 09 May 2016

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UK Research Council
European Research Council

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AAMAS '16

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AAMAS '16: International Conference on Agents and Multiagent Systems

May 9 - 13, 2016

Singapore, Singapore

Acceptance Rates

AAMAS '16 Paper Acceptance Rate 137 of 550 submissions, 25%;

Overall Acceptance Rate 1,155 of 5,036 submissions, 23%

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Cited By

Waniek MTran-Thanh LMichalak TJennings NSingh SMarkovitch S(2017)The dollar auction with spiteful playersProceedings of the Thirty-First AAAI Conference on Artificial Intelligence10.5555/3298239.3298347(736-742)Online publication date: 4-Feb-2017
https://dl.acm.org/doi/10.5555/3298239.3298347

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