Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article
Open access

Human-computer Coalition Formation in Weighted Voting Games

Published: 17 October 2020 Publication History

Abstract

This article proposes a negotiation game, based on the weighted voting paradigm in cooperative game theory, where agents need to form coalitions and agree on how to share the gains. Despite the prevalence of weighted voting in the real world, there has been little work studying people’s behavior in such settings. This work addresses this gap by combining game-theoretic solution concepts with machine learning models for predicting human behavior in such domains. We present a five-player online version of a weighted voting game in which people negotiate to create coalitions. We provide an equilibrium analysis of this game and collect hundreds of instances of people’s play in the game. We show that a machine learning model with features based on solution concepts from cooperative game theory (in particular, an extension of the Deegan-Packel Index) provide a good prediction of people’s decisions to join coalitions in the game. We designed an agent that uses the prediction model to make offers to people in this game and was able to outperform other people in an extensive empirical study. These results demonstrate the benefit of incorporating concepts from cooperative game theory in the design of agents that interact with people in group decision-making settings.

References

[1]
Y. Bachrach, P. Kohli, and T. Graepel. 2011. Ripoff: Playing the cooperative negotiation game. In Proceedings of the 10th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’11). 1179--1180.
[2]
J. F. Banzhaf. 1964. Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Rev. 19 (1964), 317--343.
[3]
M. Bitan, Y. Gal, S. Kraus, E. Dokow, and A. Azaria. 2013. Social rankings in human-computer committees. In Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI’13). 116--122.
[4]
C. F. Camerer. 2003. Behavioral Game Theory: Experiments in Strategic Interaction. Princeton University Press.
[5]
G. Chalkiadakis, E. Elkind, and M. Wooldridge. 2011. Computational Aspects of Cooperative Game Theory. Morgan-Claypool.
[6]
G. Chalkiadakis and M. Wooldridge. 2016. Weighted voting games. In Handbook of Computational Social Choice, F. Brandt, V. Conitzer, U. Endriss, A. D. Procaccia, and J. Lang (Eds.). Cambridge University Press, UK, Chapter 16.
[7]
J. Deegan and E. W. Packel. 1978. A new index of power for simple n-person games. Int. J. Game Theor. 7, 2 (1978), 113--123.
[8]
Greg d’Eon, Kate Larson, and Edith Law. 2019. The effects of single-player coalitions on reward divisions in cooperative games. In Proceedings of the 1st Workshop on Games, Agents and Incentives (GAIW) held at International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’19).
[9]
Dan S. Felsenthal and M. Machover. 2005. Voting power measurement: A story of misreinvention. Soc. Choice Welf. 25, 2 (2005), 485--506.
[10]
S. Ganzfried and T. Sandholm. 2011. Game theory-based opponent modeling in large imperfect-information games. In Proceedings of the 10th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’11). 533--540.
[11]
G. Haim, Y. Gal, B. Ann, and S. Kraus. 2017. Human-computer negotiation in a three player market setting. Artif. Intell. 246 (2017), 34--52.
[12]
J. S. Hartford, J. R. Wright, and K. Leyton-Brown. 2016. Deep learning for predicting human strategic behavior. In Proceedings of the 30th Annual Conference on Neural Information Processing Systems (NIPS’16). 2424--2432.
[13]
D. Leech. 2002. Designing the voting system for the Council of the European Union. Pub. Choice 113, 3--4 (2002), 437--464.
[14]
Michael Maschler, Bezalel Peleg, and Lloyd S. Shapley. 1979. Geometric properties of the kernel, nucleolus, and related solution concepts. Math. Op. Res. 4, 4 (1979), 303--338.
[15]
M. Mash, Y. Bachrach, Y. Gal, and Y. Zick. 2017. How to form winning coalitions in mixed human-computer settings. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI’17). 465--471.
[16]
N. Mattei and T. Walsh. 2013. PrefLib: A library of preference data. In Proceedings of the 3rd International Conference on Algorithmic Decision Theory (ADT’13). 259--270.
[17]
Patrick E. McKnight and Julius Najab. 2010. Mann-Whitney U test. In The Corsini Encyclopedia of Psychology. Wiley.
[18]
Timo Mennle, Michael Weiss, Basil Philipp, and Sven Seuken. 2015. The power of local manipulation strategies in assignment mechanisms. In Proceedings of the 24th International Joint Conference on Artificial Intelligence.
[19]
S. Merrill. 1978. Citizen voting power under the electoral college: A stochastic model based on state voting patterns. SIAM J. Appl. Math. 34, 2 (1978), 376--390.
[20]
J. F. Nash, R. Nagel, A. Ockenfels, and R. Selten. 2012. The agencies method for coalition formation in experimental games. Proc. Nat. Acad. Sci. United States Amer. 109, 50 (2012), 20358--20363.
[21]
H. Oosterbeek, R. Sloof, and K. G. Van De Kuilen. 2004. Cultural differences in ultimatum game experiments: Evidence from a meta-analysis. Exper. Econ. 7, 2 (2004), 171--188.
[22]
Y. Oshrat, R. Lin, and S. Kraus. 2009. Facing the challenge of human-agent negotiations via effective general opponent modeling. In Proceedings of the 8th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’09). 377--384.
[23]
L. S. Penrose. 1946. The elementary statistics of majority voting. J. Roy. Statist. Soc. 109, 1 (1946), 53--57.
[24]
A. Rapoport, J. P. Kahan, S. G. Funk, and A. D. Horowitz. 2012. Coalition Formation by Sophisticated Players. Springer-Verlag.
[25]
A. Rosenfeld and S. Kraus. 2016. Providing arguments in discussions on the basis of the prediction of human argumentative behavior. Trans. Interact. Intell. Syst. 6, 4 (2016), 30:1--30:33.
[26]
H. Sauermann. 1978. Coalition Forming Behavior. Vol. 8. Mohr Siebrek Ek.
[27]
L. S. Shapley and M. Shubik. 1954. A method for evaluating the distribution of power in a committee system. Amer. Polit. Sci. Rev. 48, 3 (1954), 787--792.
[28]
Yoav Shoham, Kevin Leyton-Brown, et al. 2009. Multiagent systems. Algorithmic, Game-Theoretic, and Logical Foundations (2009).
[29]
W. Słomczyński and K. Życzkowski. 2006. Penrose voting system and optimal quota. Acta Phys. Polon. B 37, 11 (2006), 3133--3143.
[30]
M. Tal, R. Meir, and Y. Gal. 2015. A study of human behavior in online voting. In Proceedings of the 14th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’15). 665--673.
[31]
Karine Van der Straeten, Jean-François Laslier, Nicolas Sauger, and André Blais. 2010. Strategic, sincere, and heuristic voting under four election rules: An experimental study. Soc. Choice Welf. 35, 3 (2010), 435--472.

Cited By

View all
  • (2024)Modeling of Small Groups in Computational Sciences: A Prospecting ReviewSmall Group Research10.1177/10464964241279164Online publication date: 27-Sep-2024
  • (2024)Network Selection over 5G-Advanced Heterogeneous Networks Based on Federated Learning and Cooperative Game TheoryIEEE Transactions on Vehicular Technology10.1109/TVT.2024.3373638(1-16)Online publication date: 2024

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Intelligent Systems and Technology
ACM Transactions on Intelligent Systems and Technology  Volume 11, Issue 6
Survey Paper and Regular Paper
December 2020
237 pages
ISSN:2157-6904
EISSN:2157-6912
DOI:10.1145/3424135
Issue’s Table of Contents
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 the author(s) 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].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 October 2020
Accepted: 01 June 2020
Revised: 01 May 2020
Received: 01 March 2019
Published in TIST Volume 11, Issue 6

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Negotiation and contract-based systems
  2. cooperative game theory

Qualifiers

  • Research-article
  • Research
  • Refereed

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)120
  • Downloads (Last 6 weeks)19
Reflects downloads up to 17 Oct 2024

Other Metrics

Citations

Cited By

View all
  • (2024)Modeling of Small Groups in Computational Sciences: A Prospecting ReviewSmall Group Research10.1177/10464964241279164Online publication date: 27-Sep-2024
  • (2024)Network Selection over 5G-Advanced Heterogeneous Networks Based on Federated Learning and Cooperative Game TheoryIEEE Transactions on Vehicular Technology10.1109/TVT.2024.3373638(1-16)Online publication date: 2024

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Get Access

Login options

Full Access

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media