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.
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- Gerhard Beneke, Willem Schurink, and Gert Roodt. 2007. Towards a substantive theory of synergy. SA J. Human Res. Manag. 5, 2 (2007).Google Scholar
- 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. Google Scholar
Digital Library
- Hans-Georg Breitinger. 2012. Drug Synergy—Mechanisms and Methods of Analysis. INTECH Open Access Publisher.Google Scholar
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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.Google Scholar
- 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. Google Scholar
Digital Library
- Peter A. Corning. 2005. Holistic Darwinism: Synergy, Cybernetics and the Bioeconomics of Evolution. University of Chicago Press.Google Scholar
Cross Ref
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- Aswath Damodaran. 1994. Damodaran on Valuation: Security Analysis for Investment and Corporate Finance. Wiley.Google Scholar
- G. de Clippel and R. Serrano. 2008. Marginal contributions and externalities in the value. Econometrica 76, 6 (2008), 1413--1436.Google Scholar
Cross Ref
- A.C. Edmondson. 1987. A Fuller Explanation: The Synergetic Geometry of R. Buckminster Fuller. Birkhäuser. Retrieved from: http://books.google.pl/books?id=UdTuAAAAMAAJ. Google Scholar
Digital Library
- 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.Google Scholar
Cross Ref
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- Milton Friedman. 1975. There’s No Such Thing as a Free Lunch. Open Court Publishing Company.Google Scholar
- Nori Geary. 2013. Understanding synergy. Amer. J. Physiol. Endocrinol. Metab. 304 (2013), 237--253.Google Scholar
Cross Ref
- Michael Goold and Andrew Campbell. 1998. Desperately seeking synergy. Harvard Bus. Rev. 76, 5 (1998), 130--43.Google Scholar
- 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.Google Scholar
Cross Ref
- T. Ryan Gregory. 2005. Synergy between sequence and size in large-scale genomics. Nature Rev. Gen. 6, 9 (2005), 699--708.Google Scholar
Cross Ref
- Virgil Griffith and Christof Koch. 2014. Quantifying synergistic mutual information. In Guided Self-Organization: Inception. Springer, 159--190.Google Scholar
- J. C. Harsanyi. 1958. A Bargaining Model for the Cooperative N-person Game. Department of Economics, Stanford University.Google Scholar
- 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.Google Scholar
Cross Ref
- 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. Google Scholar
Digital Library
- 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.Google Scholar
- Edgar H. Johnson. 1910. The economics of Henry George’s “progress and poverty.” J. Polit. Econ. 18 (1910).Google Scholar
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- James R. Larson. 2010. In Search of Synergy in Small Group Performance. Psychology Press.Google Scholar
- 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.Google Scholar
- Wen-Chung Lee. 2013. Assessing causal mechanistic interactions: A peril ratio index of synergy based on multiplicativity. PLoS ONE 8, 6 (2013).Google Scholar
- 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.Google Scholar
- 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. Google Scholar
Digital Library
- 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.Google Scholar
Cross Ref
- 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.Google Scholar
Cross Ref
- Jean-Luc Marichal and Pierre Mathonet. 2008. Approximations of Lovsz extensions and their induced interaction index. Disc. Appl. Math. 156, 1 (2008), 11--24. Google Scholar
Digital Library
- Mike Mesterton-Gibbons and Tom N. Sherratt. 2007. Coalition formation: A game-theoretic analysis. Behav. Ecol. 18, 2 (Mar. 2007), 277--286.Google Scholar
Cross Ref
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- Stefano Moretti. 2009. Game Theory applied to gene expression analysis. 4OR-A Quarterly Journal of Operations Research 7, 2 (2009), 195--198.Google Scholar
- T. Murofushi and S. Soneda. 1993. Techniques for reading fuzzy measures (III): Interaction index. In Proceedings of the 9th Fuzzy System Symposium. 693--696.Google Scholar
- Andre Nathan and Valmir C. Barbosa. 2008. V-like formations in flocks of artificial birds. Artific. Life 14, 2 (Apr. 2008), 179--188. Google Scholar
Digital Library
- 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.Google Scholar
- Iersel Van and P. Joost. 2011. Europe 2020 and the future of the European Union. L’Europe en Formation 362, 4 (2011), 147--168.Google Scholar
- 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. Google Scholar
Digital Library
- 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.Google Scholar
Cross Ref
- G. Owen. 1972. Multilinear extensions of games. Manag. Sci. 18 (1972), 64--79. Google Scholar
Digital Library
- Talal Rahwan, Tomasz P. Michalak, Michael Wooldridge, and Nicholas R. Jennings. 2015. Coalition structure generation: A survey. Artific. Intell. 229 (2015), 139--174. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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. Google Scholar
Digital Library
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
Cross Ref
- 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. Google Scholar
Digital Library
- William Morton Wheeler. 1911. The ant-colony as an organism. J. Morphol. 22, 2 (1911), 307--325.Google Scholar
Cross Ref
- P. L. Williams and R. D. Beer. 2010a. Nonnegative decomposition of multivariate information. Retrieved from: CoRR abs/1004.2515.Google Scholar
- Paul L. Williams and Randall D. Beer. 2010b. Nonnegative decomposition of multivariate information. Retrieved from: arXiv preprint arXiv:1004.2515 (2010).Google Scholar
- 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.Google Scholar
Cross Ref
- H. P. Young. 1985. Monotonic solutions of cooperative games. Int. J. Game Theor. 14, 2 (1985), 65--72.Google Scholar
Cross Ref
Index Terms
A Measure of Added Value in Groups
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