Cited By
View all- Stoian MDas SPandis ISelçuk Candan KAmer-Yahia S(2023)Fast Joint Shapley ValuesCompanion of the 2023 International Conference on Management of Data10.1145/3555041.3589393(285-287)Online publication date: 4-Jun-2023
A Measure of Added Value in Groups
Authors: 
Bedoor K. Alshebli, Tomasz P. Michalak, Oskar Skibski, 
Michael Wooldridge, Talal RahwanAuthors Info & Claims
Article No.: 18, Pages 1 - 46
Abstract
The intuitive notion of added value in groups represents a fundamental property of biological, physical, and economic systems: how the interaction or cooperation of multiple entities, substances, or other agents can produce synergistic effects. However, despite the ubiquity of group formation, a well-founded measure of added value has remained elusive. Here, we propose such a measure inspired by the Shapley value—a fundamental solution concept from Cooperative Game Theory. To this end, we start by developing a solution concept that measures the average impact of each player in a coalitional game and show how this measure uniquely satisfies a set of intuitive properties. Then, building upon our solution concept, we propose a measure of added value that not only analyzes the interactions of players inside their group, but also outside it, thereby reflecting otherwise-hidden information about how these individuals typically perform in various groups of the population.
References
[1]
Karthik V. Aadithya, Tomasz P. Michalak, and Nicholas R. Jennings. 2011. Representation of coalitional games with algebraic decision diagrams. In Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems-Volume 3. International Foundation for Autonomous Agents and Multiagent Systems, 1121--1122.
[2]
Omer Ben-Porat and Moshe Tennenholtz. 2018. A game-theoretic approach to recommendation systems with strategic content providers. In Adv. Neural Inform. Proc. Syst 31 (NIPS’18). 1110--1120.
[3]
Gerhard Beneke, Willem Schurink, and Gert Roodt. 2007. Towards a substantive theory of synergy. SA J. Human Res. Manag. 5, 2 (2007).
[4]
Craig Boutilier and Holger H. Hoos. 2001. Bidding languages for combinatorial auctions. In Proceedings of the International Joint Conference on Artificial Intelligence, Vol. 17. Citeseer, 1211--1217.
[5]
Hans-Georg Breitinger. 2012. Drug Synergy—Mechanisms and Methods of Analysis. INTECH Open Access Publisher.
[6]
Georgios Chalkiadakis, Edith Elkind, and Michael Wooldridge. 2011. Computational aspects of cooperative game theory. Synth. Lect. Artific. Intell. Machine Learn. 5, 6 (2011), 1--168.
[7]
Gal Chechik, Amir Globerson, Mike J. Anderson, Eric D. Young, Israel Nelken, and Naftali Tishby. 2002. Group redundancy measures reveal redundancy reduction in the auditory pathway. In Adv. Neural Inform. Proc. Syst 15 (NIPS’01). 173--180.
[8]
Yann Chevaleyre, Ulle Endriss, Jérôme Lang, et al. 2006. Expressive Power of Weighted Propositional Formulas for Cardinal Preference Modelling. Institute for Logic, Language and Computation (ILLC), University of Amsterdam.
[9]
Vincent Conitzer and Tuomas Sandholm. 2006. Complexity of constructing solutions in the core based on synergies among coalitions. Artific. Intell. 170, 6 (2006), 607--619.
[10]
Peter A. Corning. 2005. Holistic Darwinism: Synergy, Cybernetics and the Bioeconomics of Evolution. University of Chicago Press.
[11]
Sylvie Coste-Marquis, Jérôme Lang, Paolo Liberatore, and Pierre Marquis. 2004. Expressive power and succinctness of propositional languages for preference representation. Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR’04) 4, 2004 (2004), 203--212.
[12]
Jeffrey S. Cox and Edmund H. Durfee. 2003. Discovering and exploiting synergy between hierarchical planning agents. In Proceedings of the 2nd International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS ’03). New York, NY, 281--288.
[13]
Aswath Damodaran. 1994. Damodaran on Valuation: Security Analysis for Investment and Corporate Finance. Wiley.
[14]
G. de Clippel and R. Serrano. 2008. Marginal contributions and externalities in the value. Econometrica 76, 6 (2008), 1413--1436.
[15]
A.C. Edmondson. 1987. A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller. Birkhäuser. Retrieved from: http://books.google.pl/books?id=UdTuAAAAMAAJ.
[16]
Edith Elkind, Leslie Ann Goldberg, Paul W. Goldberg, and Michael Wooldridge. 2009. A tractable and expressive class of marginal contribution nets and its applications. Math. Logic Quart. 55, 4 (2009), 362--376.
[17]
Edith Elkind and Michael Wooldridge. 2009. Hedonic coalition nets. In Proceedings of the 8th International Conference on Autonomous Agents and Multiagent Systems—Volume 1. International Foundation for Autonomous Agents and Multiagent Systems, 417--424.
[18]
Alexandre Fréchette, Lars Kotthoff, Tomasz Michalak, Talal Rahwan, Holger H. Hoos, and Kevin Leyton-Brown. 2016. Using the Shapley value to analyze algorithm portfolios. In Proceedings of the 30th AAAI Conference on Artificial Intelligence. AAAI Press, 3397--3403.
[19]
Milton Friedman. 1975. There’s No Such Thing as a Free Lunch. Open Court Publishing Company.
[20]
Nori Geary. 2013. Understanding synergy. Amer. J. Physiol. Endocrinol. Metab. 304 (2013), 237--253.
[21]
Michael Goold and Andrew Campbell. 1998. Desperately seeking synergy. Harvard Bus. Rev. 76, 5 (1998), 130--43.
[22]
M. Grabisch and M. Roubens. 1999. An axiomatic approach to the concept of interaction among players in cooperative games. Int. J. Game Theor. 28 (1999), 547--565.
[23]
T. Ryan Gregory. 2005. Synergy between sequence and size in large-scale genomics. Nature Rev. Gen. 6, 9 (2005), 699--708.
[24]
Virgil Griffith and Christof Koch. 2014. Quantifying synergistic mutual information. In Guided Self-Organization: Inception. Springer, 159--190.
[25]
J. C. Harsanyi. 1958. A Bargaining Model for the Cooperative N-person Game. Department of Economics, Stanford University.
[26]
Marta Horkov, Sarka Klementov, Pavel K?, Syam Krishna Balakrishna, Petr Patenka, Oksana Golovko, Pavlna Hjkov, and Petr Exnar. 2014. The synergistic effect of advanced oxidation processes to eliminate resistant chemical compounds. Surf. Coat. Technol. 241, 0 (2014), 154--158.
[27]
Ryo Ichimura, Takato Hasegawa, Suguru Ueda, Atsushi Iwasaki, and Makoto Yokoo. 2011. Extension of MC-net-based coalition structure generation: Handling negative rules and externalities. In Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems—Volume 3. International Foundation for Autonomous Agents and Multiagent Systems, 1173--1174.
[28]
S. Ieong and Y. Shoham. 2006. Marginal contribution nets: A compact representation scheme for coalitional games. In Proceedings of ACM Conference on Electronic Commerce (ACM EC’06). 170--179.
[29]
Edgar H. Johnson. 1910. The economics of Henry George’s “progress and poverty.” J. Polit. Econ. 18 (1910).
[30]
Jon Kleinberg, Christos H. Papadimitriou, and Prabhakar Raghavan. 2001. On the value of private information. In Proceedings of the 8th Conference on Theoretical Aspects of Rationality and Knowledge. Morgan Kaufmann Publishers, Inc., 249--257.
[31]
Lars Kotthoff, Alexandre Fréchette, Tomasz P. Michalak, Talal Rahwan, Holger H. Hoos, and Kevin Leyton-Brown. 2018. Quantifying algorithmic improvements over time. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI’18). 5165--5171.
[32]
James R. Larson. 2010. In Search of Synergy in Small Group Performance. Psychology Press.
[33]
Peter E. Latham and Sheila Nirenberg. 2005. Synergy, redundancy, and independence in population codes, revisited. J. Neurosci.: The Offic. J. Soc. Neurosci. 25, 21 (25 May 2005), 5195--5206.
[34]
Wen-Chung Lee. 2013. Assessing causal mechanistic interactions: A peril ratio index of synergy based on multiplicativity. PLoS ONE 8, 6 (2013).
[35]
Loet Leydesdorff and Han Woo Park. 2014. Can synergy in triple-helix relations be quantified? a review of the development of the triple-helix indicator. Retrieved from: CoRR abs/1401.2342.
[36]
Kevin Leyton-Brown and Yoav Shoham. 2008. Essentials of game theory: A concise multidisciplinary introduction. Synth. Lect. Artific. Intell. Machine Learn. 2, 1 (2008), 1--88.
[37]
Somchaya Liemhetcharat and Manuela Veloso. 2012. Weighted synergy graphs for role assignment in ad hoc heterogeneous robot teams. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. 5247--5254.
[38]
Jyrki Luukkanen, Jarmo Vehmas, Juha Panula-Ontto, Francesca Allievi, Jari Kaivo-oja, Tytti Pasanen, and Burkhard Auffermann. 2012. Synergies or trade-offs? A new method to quantify synergy between different dimensions of sustainability. Environ. Polic. Govern. 22, 5 (2012), 337--349.
[39]
Jean-Luc Marichal and Pierre Mathonet. 2008. Approximations of Lovsz extensions and their induced interaction index. Disc. Appl. Math. 156, 1 (2008), 11--24.
[40]
Mike Mesterton-Gibbons and Tom N. Sherratt. 2007. Coalition formation: A game-theoretic analysis. Behav. Ecol. 18, 2 (Mar. 2007), 277--286.
[41]
Tomasz Michalak, Dorota Marciniak, Marcin Szamotulski, Talal Rahwan, Michael Wooldridge, Peter McBurney, and Nicholas R. Jennings. 2010. A logic-based representation for coalitional games with externalities. In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: Volume 1. International Foundation for Autonomous Agents and Multiagent Systems, 125--132.
[42]
Tomasz P. Michalak, Piotr L. Szczepański, Talal Rahwan, Agata Chrobak, Simina Brânzei, Michael Wooldridge, and Nicholas R. Jennings. 2014. Implementation and computation of a value for generalized characteristic function games. ACM Trans. Econ. Comput. 2, 4, Article 16 (Oct. 2014), 35 pages.
[43]
Stefano Moretti. 2009. Game Theory applied to gene expression analysis. 4OR-A Quarterly Journal of Operations Research 7, 2 (2009), 195--198.
[44]
T. Murofushi and S. Soneda. 1993. Techniques for reading fuzzy measures (III): Interaction index. In Proceedings of the 9th Fuzzy System Symposium. 693--696.
[45]
Andre Nathan and Valmir C. Barbosa. 2008. V-like formations in flocks of artificial birds. Artific. Life 14, 2 (Apr. 2008), 179--188.
[46]
Sheila Nirenberg, Steve M. Carcieri, Adam L. Jacobs, and Peter E. Latham. 2001. Retinal ganglion cells act largely as independent encoders. Nature 411, 6838 (2001), 698.
[47]
Iersel Van and P. Joost. 2011. Europe 2020 and the future of the European Union. L’Europe en Formation 362, 4 (2011), 147--168.
[48]
Naoki Ohta, Vincent Conitzer, Ryo Ichimura, Yuko Sakurai, Atsushi Iwasaki, and Makoto Yokoo. 2009. Coalition structure generation utilizing compact characteristic function representations. In Proceedings of the International Conference on Principles and Practice of Constraint Programming (CP’09) (Lecture Notes in Computer Science), Ian P. Gent (Ed.), Vol. 5732. Springer, 623--638.
[49]
J. H. Ouyang, S. Sasaki, T. Murakami, and K. Umeda. 2004. The synergistic effects of CaF2 and Au lubricants on tribological properties of spark-plasma-sintered ZrO2 (Y2O3) matrix composites. Mat. Sci. Eng.: A 386, 1--2 (2004), 234--243.
[50]
G. Owen. 1972. Multilinear extensions of games. Manag. Sci. 18 (1972), 64--79.
[51]
Talal Rahwan, Tomasz P. Michalak, Michael Wooldridge, and Nicholas R. Jennings. 2015. Coalition structure generation: A survey. Artific. Intell. 229 (2015), 139--174.
[52]
Yuko Sakurai, Suguru Ueda, Atsushi Iwasaki, Shin-Ichi Minato, and Makoto Yokoo. 2011. A compact representation scheme of coalitional games based on multi-terminal zero-suppressed binary decision diagrams. In Proceedings of the International Conference on Principles and Practice of Multi-Agent Systems. Springer, 4--18.
[53]
Tuomas Sandholm, Kate Larson, Martin Andersson, Onn Shehory, and Fernando Tohmé. 1999. Coalition structure generation with worst case guarantees. Artific. Intell. 111, 1--2 (July 1999), 209--238.
[54]
Lloyd S. Shapley. 1953. A value for n-person games. In Contributions to the Theory of Games, Volume II, H. W. Kuhn and A. W. Tucker (Eds.). Princeton University Press, 307--317.
[55]
Roberta Sinatra, Dashun Wang, Pierre Deville, Chaoming Song, and Albert-László Barabási. 2016. Quantifying the evolution of individual scientific impact. Science 354, 6312 (2016), aaf5239.
[56]
Robert Steinmetz, Wanlop Chutipong, Naret Seuaturien, and Erb Chirngsaard. 2008. Community structure of large mammals in tropical montane and lowland forest in the Tenasserim-Dawna Mountains. Biotropica 40, 3 (May 2008), 344--353.
[57]
Suguru Ueda, Makoto Kitaki, Atsushi Iwasaki, and Makoto Yokoo. 2011. Concise characteristic function representations in coalitional games based on agent types. In Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems—Volume 3. International Foundation for Autonomous Agents and Multiagent Systems, 1271--1272.
[58]
William Morton Wheeler. 1911. The ant-colony as an organism. J. Morphol. 22, 2 (1911), 307--325.
[59]
P. L. Williams and R. D. Beer. 2010a. Nonnegative decomposition of multivariate information. Retrieved from: CoRR abs/1004.2515.
[60]
Paul L. Williams and Randall D. Beer. 2010b. Nonnegative decomposition of multivariate information. Retrieved from: arXiv preprint arXiv:1004.2515 (2010).
[61]
Anita W. Woolley, Christopher F. Chabris, Alex Pentland, Nada Hashmi, and Thomas W. Malone. 2010. Evidence for a collective intelligence factor in the performance of human groups. Science 330, 6004 (2010), 686--688.
[62]
H. P. Young. 1985. Monotonic solutions of cooperative games. Int. J. Game Theor. 14, 2 (1985), 65--72.
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Publication History
Published: 23 July 2019
Accepted: 01 March 2019
Received: 01 August 2018
Published in TAAS Volume 13, Issue 4
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View all- Stoian MDas SPandis ISelçuk Candan KAmer-Yahia S(2023)Fast Joint Shapley ValuesCompanion of the 2023 International Conference on Management of Data10.1145/3555041.3589393(285-287)Online publication date: 4-Jun-2023
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