A linear approximation method for the Shapley value

Artificial Intelligence

Volumn 172, Issue 14, 2008, Pages 1673-1699

  Fatima, Shaheen S ^a   Wooldridge, Michael ^b   Jennings, Nicholas R ^c  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

^c UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Approximation method; Coalitional game theory; Shapley value

Indexed keywords

ADDITION REACTIONS; APPROXIMATION THEORY; BOOLEAN FUNCTIONS; EIGENVALUES AND EIGENFUNCTIONS; GAME THEORY; POLYNOMIAL APPROXIMATION; WEIGHING;

#P-COMPLETE; (ALGORITHMIC) COMPLEXITY; (N-1) CRITERION; APPROXIMATION ERRORS; APPROXIMATION METHODS; COALITIONAL GAMES; COMPARATIVE STUDIES; GENERAL (CO); LINEAR APPROXIMATION METHOD; LINEAR EXTENSIONS; MAJORITY VOTING; MEAN WEIGHT; PERCENTAGE ERROR; SHAPLEY VALUES; TIME COMPLEXITIES; VOTING GAMES;

APPROXIMATION ALGORITHMS;

EID: 47649117256     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.artint.2008.05.003     Document Type: Article

References (39)

1. Algaba E., Bilbao J.M., Garcia J.R., and Lopez J.J. Computing power indices in weighted multiple majority games. Mathematical Social Sciences 46 (2003) 63-80
2. Aumann R. Acceptable Points in General Cooperative n-Person Games. Contributions to the Theory of Games vol. IV (1959), Princeton University Press
3. Ausiello G., Crescenzi P., Gambosi G., Kann V., Marchetti-Spaccamela A., and Protasi M. Complexity and Approximation: Combinatorial Optimization Problems and their Approximability Properties (2003), Springer
4. Y. Bachrach, J. Rosenschein, Approximating power indices, in: Proceedings of the Seventh International Conference on Autonomous Agents and Multi-Agent Systems, 2008
5. Bilbao J.M., Fernandez J.R., Jimenez N., and Lopez J.J. Voting power in the European union enlargement. Journal of Operational Research 143 (2002) 181-196
6. Bilbao J.M., Fernandez J.R., Losada A.J., and Lopez J.J. Generating functions for computing power indices efficiently. Top 8 2 (2000) 191-213
7. Bork P., Grote H., Notz D., and Regler M. Data Analysis Techniques in High Energy Physics Experiments (1993), Cambridge University Press
8. Brams S., and Affuso P.J. Power and size: A new paradox. Theory and Decision 7 (1976) 29-56
9. V. Conitzer, T. Sandholm, Computing Shapley values, manipulating value division schemes, and checking core membership in multi-issue domains, in: Proceedings of the National Conference on Artificial Intelligence, San Jose, California, 2004, pp. 219-225
10. Conitzer V., and Sandholm T. Complexity of constructing solutions in the core based on synergies among coalitions. Artificial Intelligence Journal 170 (2006) 607-619
11. Cormen T.H., Leiserson C.E., Rivest R.L., and Stein C. An Introduction to Algorithms (2003), The MIT Press, Cambridge, MA
12. Deng X., and Papadimitriou C.H. On the complexity of cooperative solution concepts. Mathematics of Operations Research 19 2 (1994) 257-266
13. E. Elkind, L.A. Goldberg, P. Goldberg, M. Wooldridge, Computational complexity of weighted threshold games, in: Proceedings of the National Conference on Artificial Intelligence (AAAI-2007), 2007
14. S.S. Fatima, M. Wooldridge, N.R. Jennings, A randomized method for the Shapley value for the voting game, in: Proceedings of the Sixth International Conference on Autonomous Agents and Multi-Agent Systems, 2007, pp. 955-962
15. Francis A. Advanced Level Statistics (1979), Stanley Thornes Publishers p. 425
16. S. Ieong, Y. Shoham, Marginal contribution nets: A compact representation scheme for coalitional games, in: Proceedings of the Sixth ACM Conference on Electronic Commerce, Vancouver, Canada, 2005, pp. 193-202
17. S. Ieong, Y. Shoham, Multi-attribute coalition games, in: Proceedings of the Seventh ACM Conference on Electronic Commerce, Ann Arbor, Michigan, 2006, pp. 170-179
18. Kahan J.P., and Rapoport A. Theories of Coalition Formation (1984), Lawrence Erlbaum Associates Publishers
19. Leech D. Computing power indices for large voting games. Management Science 49 6 (2003) 831-837
20. I. Mann, L.S. Shapley, Values for large games IV: Evaluating the electoral college by Monte Carlo techniques, Technical report, The RAND Corporation, Santa Monica, 1960
21. I. Mann, L.S. Shapley, Values for large games IV: Evaluating the electoral college exactly, Technical report, The RAND Corporation, Santa Monica, 1962
22. MasColell A., Whinston M., and Green J.R. Microeconomic Theory (1995), Oxford University Press
23. Osborne M.J., and Rubinstein A. A Course in Game Theory (1994), The MIT Press
24. Owen G. Multilinear extensions of games. Management Science 18 5 (1972) 64-79
25. Papadimitriou C.H. Computational Complexity (1994), Addison Wesley Longman
26. Rahwan T., and Jennings N.R. An algorithm for distributing coalitional value calculations among cooperating agents. Artificial Intelligence Journal 171 (2007) 535-567
27. Rapoport A. N-Person Game Theory: Concepts and Applications (2001), Dover Publications, Mineola, NY
28. Rosenschein J.S., and Zlotkin G. Rules of Encounter (1994), MIT Press
29. Roth A.E. Introduction to the Shapely value. In: Roth A.E. (Ed). The Shapley Value (1988), University of Cambridge Press, Cambridge 1-27
30. Sandholm T., Larson K., Andersson M., Shehory O., and Tohme F. Coalition structure generation with worst case guarantees. Artificial Intelligence Journal 111 (1999) 209-238
31. Sandholm T., and Lesser V. Coalitions among computationally bounded agents. Artificial Intelligence Journal 94 1 (1997) 99-137
32. Shapley L.S. A value for n person games. In: Roth A.E. (Ed). The Shapley Value (1988), University of Cambridge Press, Cambridge 31-40
33. O. Shehory, S. Kraus, A kernel-oriented model for coalition-formation in general environments: Implementation and results, in: Proceedings of the National Conference on Artificial Intelligence (AAAI-96), 1996, pp. 131-140
34. Shehory O., and Kraus S. Methods for task allocation via agent coalition formation. Artificial Intelligence Journal 101 2 (1998) 165-200
35. Tanenbaum P. Power in weighted voting games. The Mathematica Journal 7 (1997) 58-63
36. Taylor J.R. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (1982), University Science Books
37. Underhill W.V. Finding bounds for definite integrals. The College Mathematics Journal 15 5 (1984) 426-429
38. Wilf H.S. Generatingfunctionology (1994), Academic Press
39. G. Zlotkin, J. Rosenschein, Coalition, cryptography, and stability: mechanisms foe coalition formation in task oriented domains, in: Proceedings of the National Conference on Artificial Intelligence (AAAI-94), 1994, pp. 432-437