Abstract
Coalitional games, including Coalition Structure Generation (CSG), have been attracting considerable attention from the AI research community. Traditionally, the input of a coalitional game is a black-box function called a characteristic function. Previous studies have found that many problems in coalitional games tend to be computationally intractable in this black-box function representation. Recently, several concise representation schemes for a characteristic function have been proposed. Among them, a synergy coalition group (SCG) has several good characteristics, but its representation size tends to be large compared to other representation schemes.
We propose a new concise representation scheme for a characteristic function based on a Zero-suppressed Binary Decision Diagram (ZDD) and a SCG. We show our scheme (i) is fully expressive, (ii) can be exponentially more concise than the SCG representation, (iii) can solve core-related problems in polynomial time in the number of nodes, and (iv) can solve a CSG problem reasonably well by utilizing a MIP formulation. A Binary Decision Diagram (BDD) has been used as unified infrastructure for representing/manipulating discrete structures in such various domains in AI as data mining and knowledge discovery. Adapting this common infrastructure brings up the opportunity of utilizing abundant BDD resources and cross-fertilization with these fields.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aadithya, K., Michalak, T., Jennings, N.: Representation of Coalitional Games with Algebraic Decision Diagrams. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 1121–1122 (2011)
Airiau, S., Sen, S.: On the stability of an optimal coalition structure. In: Proceeding of the 19th European Conference on Artificial Intelligence (ECAI 2010), pp. 203–208 (2010)
Akers, S.B.: Binary decision diagrams. IEEE Transactions on Computers C-27(6), 509–516 (1978)
Aumann, R.J., Dreze, J.H.: Cooperative games with coalition structures. International Journal of Game Theory 3, 217–237 (1974)
Bachrach, Y., Elkind, E., Meir, R., Pasechnik, D., Zuckerman, M., Rothe, J., Rosenschein, J.S.: The Cost of Stability in Coalitional Games. In: Mavronicolas, M., Papadopoulou, V.G. (eds.) SAGT 2009. LNCS, vol. 5814, pp. 122–134. Springer, Heidelberg (2009)
Berghammer, R., Bolus, S.: Problem Solving on Simple Games via BDDs. In: Proceedings of the 3rd International Workshop on Computation Social Choice, COMSOC 2010 (2010)
Bryant, R.E.: Symbolic Boolean Manipulation with Ordered Binary Decision Diagrams. ACM Computing Surveys 24(3), 293–318 (1992)
Conitzer, V., Sandholm, T.: Complexity of constructing solutions in the core based on synergies among coalitions. Artificial Intelligence 170(6), 607–619 (2006)
Elkind, E., Goldberg, L.A., Goldberg, P.W., Wooldridge, M.: A tractable and expressive class of marginal contribution nets and its applications. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2008), pp. 1007–1014 (2008)
Engel, Y., Wellman, M.P.: Generalized value decomposition and structured multiattribute auctions. In: Proceedings of the 8th ACM Conference on Electronic Commerce (EC 2007), pp. 227–236 (2007)
Faigle, U., Fekete, S.P., Hochstättler, W., Kern, W.: On the complexity of testing membership in the core of min-cost spanning tree games. International Journal of Game Theory 26, 361–366 (1997)
Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Mathematica 182, 105–142 (1999)
Ieong, S., Shoham, Y.: Marginal contribution nets: a compact representation scheme for coalitional games. In: Proceedings of the 5th ACM Conference on Electronic Commerce (EC 2005), pp. 193–202 (2005)
Knuth, D.: The art of computer programming 4, Fascicle 1 (2009)
Loekito, E., Bailey, J.: Fast mining of high dimensional expressive contrast patterns using zero-suppressed binary decision diagrams. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2006), pp. 307–316 (2006)
Minato, S.: Zero-suppressed bdds for set manipulation in combinatorial problems. In: Proceedings of the 30th Design Automation Conference (DAC 1993), pp. 272–277 (1993)
Minato, S.: Arithmetic boolean expression manipulator using bdds. Formal Methods in System Design 10(2/3), 221–242 (1997)
Ohta, N., Conitzer, V., Ichimura, R., Sakurai, Y., Iwasaki, A., Yokoo, M.: Coalition Structure Generation Utilizing Compact Characteristic Function Representations. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 623–638. Springer, Heidelberg (2009)
Sandholm, T., Larson, K., Andersson, M., Shehory, O., Tohmé, F.: Coalition structure generation with worst case guarantees. Artificial Intelligence 111(1-2), 209–238 (1999)
Shrot, T., Aumann, Y., Kraus, S.: On agent types in coalition formation problems. In: Proceedings of the 9th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), pp. 757–764 (2010)
Uckelman, J., Chevaleyre, Y., Endriss, U., Lang, J.: Representing utility functions via weighted goals. Mathematical Logic Quarterly 55(4), 341–361 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sakurai, Y., Ueda, S., Iwasaki, A., Minato, SI., Yokoo, M. (2011). A Compact Representation Scheme of Coalitional Games Based on Multi-Terminal Zero-Suppressed Binary Decision Diagrams. In: Kinny, D., Hsu, J.Yj., Governatori, G., Ghose, A.K. (eds) Agents in Principle, Agents in Practice. PRIMA 2011. Lecture Notes in Computer Science(), vol 7047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25044-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-25044-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25043-9
Online ISBN: 978-3-642-25044-6
eBook Packages: Computer ScienceComputer Science (R0)