research-article

Bidding Games and Efficient Allocations

Authors:

Moshe TennenholtzAuthors Info & Claims

EC '15: Proceedings of the Sixteenth ACM Conference on Economics and Computation

Pages 113 - 130

https://doi.org/10.1145/2764468.2764526

Published: 15 June 2015 Publication History

Abstract

Bidding games are extensive form games, where in each turn players bid in order to determine who will play next. Zero-sum bidding games (also known as Richman games) have been extensively studied, focusing on the fraction of the initial budget that can guaranty the victory of each player [Lazarus et al.'99, Develin & Payne '10].

We extend the theory of bidding games to general-sum two player games, showing the existence of pure subgame-perfect Nash equilibria (PSPE), and studying their properties under various initial budgets.

We show that if the underlying game has the form of a binary tree (only two actions available to the players in each node), then there exists a natural PSPE with the following highly desirable properties: (a) players' utility is weakly monotone in their budget; (b) a Pareto-efficient outcome is reached for any initial budget; and (c) for any Pareto-efficient outcome there is an initial budget s.t. this outcome is attained. In particular, we can assign the budget so as to implement the outcome with maximum social welfare, maximum Egalitarian welfare, etc.

We show implications of this result for various games and mechanism design problems, including Centipede games, voting games, and combinatorial bargaining. For the latter, we further show that the PSPE above is fair, in the sense that an player with a fraction of $X\%$ of the total budget prefers her allocation to X% of the possible allocations.

References

[1]

Amir, O., Sharon, G., and Stern, R. 2015. Multi-agent pathfinding as a combinatorial auction. In AAAI'15.

[2]

Anbarci, N. 2006. Finite alternating-move arbitration schemes and the equal area solution. Theory and Decision 61, 1, 21--50.

[3]

Bae, J., Beigman, E., Berry, R., Honig, M. L., and Vohra, R. 2007. Efficiency bounds for sequential resource allocation auctions. In CDC'07. 765--770.

[4]

Blumrosen, L. and Nisan, N. 2007. Combinatorial auctions. In Algorithmic Game Theory, N. N. et al., Ed. Cambridge University Press.

[5]

Bnaya, Z., Stern, R., Felner, A., Zivan, R., and Okamoto, S. 2013. Multi-agent path finding for self interested agents. In SoCS'13. 38--46.

[6]

Chakraborty, T., Kearns, M., and Khanna, S. 2009. Network bargaining: Algorithms and structural results. In ACM-EC'09. 159--168.

Digital Library

[7]

De Clippel, G., Eliaz, K., and Knight, B. 2012. On the selection of arbitrators. Tech. rep., Working Paper, Brown University, Department of Economics.

[8]

Develin, M. and Payne, S. 2010. Discrete bidding games. The Electronic Journal of Combinatorics 17, 1, R85.

[9]

Fatima, S. S., Wooldridge, M., and Jennings, N. R. 2004. An agenda-based framework for multi-issue negotiation. Artificial Intelligence 152, 1, 1--45.

Digital Library

[10]

Gale, I. L. and Stegeman, M. 2001. Sequential auctions of endogenously valued objects. Games and Economic Behavior 36, 1, 74--103.

[11]

Huang, Z., Devanur, N. R., and Malec, D. 2012. Sequential auctions of identical items with budget-constrained bidders. arXiv preprint arXiv:1209.1698.

[12]

Kalai, E. 1977. Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica: Journal of the Econometric Society, 1623--1630.

[13]

Kalai, E. and Smorodinsky, M. 1975. Other solutions to Nash's bargaining problem. Econometrica, 513--518.

[14]

Lacy, D. and Niou, E. M. 2000. A problem with referendums. J. of The. Politics 12, 1, 5--31.

[15]

Lang, J. and Xia, L. 2009. Sequential composition of voting rules in multi-issue domains. Mathematical social sciences 57, 3, 304--324.

[16]

Lazarus, A. J., Loeb, D. E., Propp, J. G., Stromquist, W. R., and Ullman, D. H. 1999. Combinatorial games under auction play. Games and Economic Behavior 27, 2, 229--264.

[17]

Lazarus, A. J., Loeb, D. E., Propp, J. G., and Ullman, D. 1996. Richman games. Games of no chance 29, 439--449.

[18]

Leme, R. P., Syrgkanis, V., and Tardos, É. 2012. Sequential auctions and externalities. In SODA'12. 869--886.

Digital Library

[19]

Nash, J. F. 1950. The bargaining problem. Econometrica, 155--162.

[20]

Peres, Y., Schramm, O., Sheffield, S., and Wilson, D. B. 2007. Random-turn hex and other selection games. American Mathematical Monthly 114, 5, 373--387.

[21]

Powell, R. 2009. Sequential, nonzero-sum "blotto": Allocating defensive resources prior to attack. Games and Economic Behavior 67, 2, 611--615.

[22]

Rodriguez, G. E. 2009. Sequential auctions with multi-unit demands. The BE Journal of Theoretical Economics 9, 1.

[23]

Rosenthal, R. W. 1981. Games of perfect information, predatory pricing and the chain-store paradox. Journal of Economic Theory 25, 1, 92--100.

[24]

Rubinstein, A. 1982. Perfect equilibrium in a bargaining model. Econometrica: Journal of the Econometric Society, 97--109.

[25]

Sharon, G., Stern, R., Goldenberg, M., and Felner, A. 2012.small The increasing cost tree search for optimal multi-agent pathfinding. Artificial Intelligence 195, 470--495.

Digital Library

[26]

Silver, D. 2005. Cooperative pathfinding. In AIIDE. 117--122.

[27]

Sprumont, Y. 1993. Intermediate preferences and rawlsian arbitration rules. Social Choice and Welfare 10, 1, 1--15.

[28]

Winter, E. 1997. Negotiations in multi-issue committees. Journal of Public Economics 65, 3, 323--342.

[29]

Zlotkin, G. and Rosenschein, J. S. 1996. Mechanism design for automated negotiation, and its application to task oriented domains. Artificial Intelligence 86, 2, 195--244.

Digital Library

Cited By

Avni GHenzinger TIbsen-Jensen R(2018)Infinite-Duration Poorman-Bidding GamesWeb and Internet Economics10.1007/978-3-030-04612-5_2(21-36)Online publication date: 21-Nov-2018
https://doi.org/10.1007/978-3-030-04612-5_2
Aziz HGoldberg PWalsh T(2017)Equilibria in Sequential AllocationAlgorithmic Decision Theory10.1007/978-3-319-67504-6_19(270-283)Online publication date: 24-Sep-2017
https://doi.org/10.1007/978-3-319-67504-6_19

Index Terms

Bidding Games and Efficient Allocations
1. Computing methodologies
  1. Artificial intelligence
    1. Distributed artificial intelligence
      1. Multi-agent systems

Recommendations

Infinite-duration Bidding Games
Networking, Computational Complexity, Design and Analysis of Algorithms, Real Computation, Algorithms, Online Algorithms and Computer-aided Verification

<?tight?>Two-player games on graphs are widely studied in formal methods, as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common ...
Posted Pricing vs. Bargaining in Sequential Selling Process

We study the role of bargaining in a firm's sequential selling process. The seller firm under consideration sequentially sells a fixed amount of stock to a random arrival stream of potential buyers who are heterogeneous in product valuation. Based on ...
Naive Bidding

This paper presents an equilibrium explanation for the persistence of naive bidding. Specifically, we consider a common value auction in which a "naive" bidder (who ignores the winner's curse) competes against a fully rational bidder. We show that the ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

EC '15: Proceedings of the Sixteenth ACM Conference on Economics and Computation

June 2015

852 pages

ISBN:9781450334105

DOI:10.1145/2764468

General Chair:
Tim Roughgarden
Stanford University, USA
,
Program Chairs:
Michal Feldman
Tel Aviv University, Israel
,
Michael Schwarz
Google, USA

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGecom: Special Interest Group on Economics and Computation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 June 2015

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

EC '15

Sponsor:

SIGecom

EC '15: ACM Conference on Economics and Computation

June 15 - 19, 2015

Oregon, Portland, USA

Acceptance Rates

EC '15 Paper Acceptance Rate 72 of 220 submissions, 33%;

Overall Acceptance Rate 664 of 2,389 submissions, 28%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
159
Total Downloads

Downloads (Last 12 months)5
Downloads (Last 6 weeks)1

Reflects downloads up to 10 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Avni GHenzinger TIbsen-Jensen R(2018)Infinite-Duration Poorman-Bidding GamesWeb and Internet Economics10.1007/978-3-030-04612-5_2(21-36)Online publication date: 21-Nov-2018
https://doi.org/10.1007/978-3-030-04612-5_2
Aziz HGoldberg PWalsh T(2017)Equilibria in Sequential AllocationAlgorithmic Decision Theory10.1007/978-3-319-67504-6_19(270-283)Online publication date: 24-Sep-2017
https://doi.org/10.1007/978-3-319-67504-6_19

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents