Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions

European Journal of Operational Research

Volumn 211, Issue 1, 2011, Pages 148-159

  Carreras, Francesc ^a   Giménez, José Miguel ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Cooperative game; Multilinear extension; Potential; Power; Semivalue

Indexed keywords

COOPERATIVE GAME; MULTILINEAR EXTENSION; POTENTIAL; POWER; SEMIVALUE;

VECTOR SPACES;

EID: 79551496649     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.11.002     Document Type: Article

References (39)

1. J.M. Alonso, F. Carreras, and M.G. Fiestras The multilinear extension and the symmetric coalition Banzhaf value Theory and Decision 59 2005 111 126
2. R. Amer, and J.M. Giménez Modification of semivalues for games with coalition structures Theory and Decision 54 2003 185 205
3. J.F. Banzhaf Weighted voting doesn't work: A mathematical analysis Rutgers Law Review 19 1965 317 343
4. R. van den Brink, and G. van der Laan Potential and reduced games for share functions Discrete Mathematics 307 2007 2385 2399
5. E. Calvo, and J.C. Santos Potentials in cooperative TU games Mathematical Social Sciences 34 1997 175 190
6. F. Carreras, and J. Freixas Semivalue versatility and applications Annals of Operations Research 109 2002 343 358
7. F. Carreras, and A. Magaña The multilinear extension of the quotient game Games and Economic Behavior 18 1997 22 31
8. F. Carreras, and M.A. Puente A parametric family of mixed coalitional values A. Seeger, Recent Advances in Optimization Lecture Notes in Economics and Mathematical Systems 2006 Springer-Verlag 323 339
9. F. Carreras, J. Freixas, and M.A. Puente Semivalues as power indices European Journal of Operational Research 149 2003 676 687
10. F. Carreras, M.D. Llongueras, and M.A. Puente Partnership formation and binomial semivalues European Journal of Operational Research 192 2009 487 499
11. J.S. Coleman Control of collectivities and the power of a collectivity to act B. Lieberman, Social Choice 1971 Gordon and Breach New York 269 300
12. I. Dragan New mathematical properties of the Banzhaf value European Journal of Operational Research 95 1996 451 463
13. I. Dragan, Some recursive definitions of the Shapley value and other linear values of cooperative TU games, Working Paper 328, University of Texas at Arlington, United States of America, 1997.
14. I. Dragan Potential and consistency for semivalues of finite cooperative TU games International Journal of Mathematics, Game Theory and Algebra 9 1999 85 97
15. I. Dragan Potential, balanced contributions, recursion formula, Shapley blueprint properties for values of cooperative TU games H. de Swart, Logic, Game Theory and Social Choice 1999 Tilburg University Press 57 67
16. I. Dragan, and J.E. Martinez-Legaz On the semivalues and the power core of cooperative TU games International Game Theory Review 3 2001 127 139
17. T.S.H. Driessen, E. Calvo, A multiplicative potential approach to solutions for cooperative TU-games, Memorandum No. 1570, Faculty of Mathematical Sciences, University of Twente Enschede, The Netherlands, 2001.
18. P. Dubey, and L.S. Shapley Mathematical properties of the Banzhaf power index Mathematics of Operations Research 4 1979 99 131
19. P. Dubey, A. Neyman, and R.J. Weber Value theory without efficiency Mathematics of Operations Research 6 1981 122 128
20. E. Einy Semivalues of simple games Mathematics of Operations Research 12 1987 185 192
21. V. Feltkamp Alternative axiomatic characterizations of the Shapley and Banzhaf values International Journal of Game Theory 24 1995 179 186
22. J.M. Giménez, Contributions to the study of solutions for cooperative games, Ph.D. Thesis, Technical University of Catalonia, Spain, 2001 (in Spanish).
23. J.C. Harsanyi A bargaining model for the cooperative n-person games A.W. Tucker, R.D. Luce, Contributions to the Theory of Games vol. IV 1959 Princeton University Press 325 356
24. S. Hart, and A. Mas-Colell The potential of the Shapley value A.E. Roth, The Shapley Value: Essays in Honor of Lloyd S. Shapley 1988 Cambridge University Press 127 137
25. S. Hart, and A. Mas-Colell Potential, value and consistency Econometrica 57 1989 589 614
26. E. Kalai, and D. Samet On weighted Shapley values International Journal of Game Theory 16 1987 205 222
27. G. Owen Multilinear extensions of games Management Science 18 1972 64 79
28. G. Owen Evaluation of a presidential election game American Political Science Review 69 1975 947 953
29. G. Owen Multilinear extensions and the Banzhaf value Naval Research Logistics Quarterly 22 1975 741 750
30. G. Owen Characterization of the Banzhaf-Coleman index SIAM Journal of Applied Mathematics 35 1978 315 327
31. G. Owen, and E. Winter Multilinear extensions and the coalition value Games and Economic Behavior 4 1992 582 587
32. L.S. Penrose The elementary statistics of majority voting Journal of the Royal Statistical Society 109 1946 53 57
33. M.A. Puente, Contributions to the representability of simple games and to the calculus of solutions for this class of games, Ph.D. Thesis, Technical University of Catalonia, Spain, 2000 (in Spanish).
34. T. Radzik, and T.S.H. Driessen An axiomatic approach to probabilistic efficient values for cooperative games Homo Oeconomicus 19 2002 399 411
35. L.M. Ruiz, F. Valenciano, and J.M. Zarzuelo The family of least square values for transferable utility games Games and Economic Behavior 24 1998 109 130
36. L.S. Shapley A value for n-person games H.W. Kuhn, A.W. Tucker, Contributions to the Theory of Games II 1953 Princeton University Press 307 317
37. L.S. Shapley, and M. Shubik A method for evaluating the distribution of power in a committee system American Political Science Review 48 1954 787 792
38. R.J. Weber Subjectivity in the valuation of games O. Moeschlin, D. Pallaschke, Game Theory and Related Topics 1979 North-Holland 129 136
39. R.J. Weber Probabilistic values for games A.E. Roth, The Shapley Value: Essays in Honor of Lloyd S. Shapley 1988 Cambridge University Press 101 119