In this paper, we discuss the egalitarianism solution (ES) and center-of-gravity of the imputation-set value (CIV) for bicooperative games, which can be seen as the extensions of the solutions for traditional games given by Dutta and Ray [1] and Driessen and Funaki [2]. Furthermore, axiomatic systems for the given values are proposed. Finally, a numerical example is offered to illustrate the player ES and CTV.
[1] B. Dutta and D. Ray, A concept of egalitarianism under participation
constraints, Econometrica 57 (1989) 615-635.
[2] T. S. H. Driessen and Y. Funaki, Coincidence of and collinearity between
game theoretic solutions, OR Spektrum 13 (1991) 15-30.
[3] R. van den Brink and Y. Funaki, Axiomatizations of a class of equal
surplus sharing solutions for TU-games, Theory and Decision 67 (2009)
303-340.
[4] B. Dutta and D. Ray, Constrained egalitarian allocations, Games and
Economic Behavior 3 (1991) 403-422.
[5] B. Dutta, The egalitarian solution and reduced game properties in convex
games, International Journal of Game Theory 19 (1990) 153-169.
[6] S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica
57 (1989) 589-614.
[7] M. Davis and M. Maschler, The kernel of a cooperative game, Naval
Research Logistics Quarterly 12 (1965) 223-259.
[8] J. Arin and E. Inarra, Consistency and egalitarianism: the egalitarian
set, D.P. 163, Dpto. Fundamentos del Analisis Economico UPV-EHU,
Spain, 1997.
[9] F. Klijn, M. Slikker, S. Tijs and J. Zarzuelo, The egalitarian solution for
convex games: some characterizations, Mathematical Social Sciences 40
(2000) 111-121.
[10] J. Arin, J. Kuipers and D. Vermeulen. Some characterizations of egalitarian
solutions on classes of TU-games, Mathematical Social Sciences
46 (2003) 327-345.
[11] R. van den Brink, Null or nullifying players: The difference between the
Shapley value and equal division solutions, Journal of Economic Theory
136 (2007) 767-775.
[12] H. Salonen, Egalitarian solutions for n-person bargaining games, Mathematical
Social Sciences 35 (1998) 291-306.
[13] R. Branzei, D. Dimitrov and S. Tijs, Egalitarianism in convex fuzzy
games, Mathematical Social Sciences 47 (2004) 313-325.
[14] H. Peters and H. Zank, The egalitarian solution for multichoice games,
Annals of Operations Research 137 (2005) 399-409.
[15] J. M. Bilbao, J. Fernndez, N. Jimnez and J. J. Lpez, The Shapley value
for bicooperative games, Annals of perations Research 158 (2008) 99-
115.
[16] J. M. Bilbao, J. R. Fernndez, N. Jimnez and J. J. Lpez, The Banzhaf
power index for ternary bicooperative games, Discrete Applied Mathematics
158 (2010) 967-980.
[17] M. Grabisch and C. Labreuche, Bi-capacities-I:definition, Mobius transform
and interaction, Fuzzy sets and systems 151 (2005) 211-236.
[18] X. H. Yu and Q. Zhang, The Shapley value for fuzzy bi-cooperative
games, International Conference on Intelligent Systems and Knowledge
Engineering 2007.
[19] M. Tsurumi, T. Tanino and M. Inuiguchi, A Shapley function on a class
of cooperative fuzzy games, European Journal of Operational Research
129 (2001) 596-618.
[1] B. Dutta and D. Ray, A concept of egalitarianism under participation
constraints, Econometrica 57 (1989) 615-635.
[2] T. S. H. Driessen and Y. Funaki, Coincidence of and collinearity between
game theoretic solutions, OR Spektrum 13 (1991) 15-30.
[3] R. van den Brink and Y. Funaki, Axiomatizations of a class of equal
surplus sharing solutions for TU-games, Theory and Decision 67 (2009)
303-340.
[4] B. Dutta and D. Ray, Constrained egalitarian allocations, Games and
Economic Behavior 3 (1991) 403-422.
[5] B. Dutta, The egalitarian solution and reduced game properties in convex
games, International Journal of Game Theory 19 (1990) 153-169.
[6] S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica
57 (1989) 589-614.
[7] M. Davis and M. Maschler, The kernel of a cooperative game, Naval
Research Logistics Quarterly 12 (1965) 223-259.
[8] J. Arin and E. Inarra, Consistency and egalitarianism: the egalitarian
set, D.P. 163, Dpto. Fundamentos del Analisis Economico UPV-EHU,
Spain, 1997.
[9] F. Klijn, M. Slikker, S. Tijs and J. Zarzuelo, The egalitarian solution for
convex games: some characterizations, Mathematical Social Sciences 40
(2000) 111-121.
[10] J. Arin, J. Kuipers and D. Vermeulen. Some characterizations of egalitarian
solutions on classes of TU-games, Mathematical Social Sciences
46 (2003) 327-345.
[11] R. van den Brink, Null or nullifying players: The difference between the
Shapley value and equal division solutions, Journal of Economic Theory
136 (2007) 767-775.
[12] H. Salonen, Egalitarian solutions for n-person bargaining games, Mathematical
Social Sciences 35 (1998) 291-306.
[13] R. Branzei, D. Dimitrov and S. Tijs, Egalitarianism in convex fuzzy
games, Mathematical Social Sciences 47 (2004) 313-325.
[14] H. Peters and H. Zank, The egalitarian solution for multichoice games,
Annals of Operations Research 137 (2005) 399-409.
[15] J. M. Bilbao, J. Fernndez, N. Jimnez and J. J. Lpez, The Shapley value
for bicooperative games, Annals of perations Research 158 (2008) 99-
115.
[16] J. M. Bilbao, J. R. Fernndez, N. Jimnez and J. J. Lpez, The Banzhaf
power index for ternary bicooperative games, Discrete Applied Mathematics
158 (2010) 967-980.
[17] M. Grabisch and C. Labreuche, Bi-capacities-I:definition, Mobius transform
and interaction, Fuzzy sets and systems 151 (2005) 211-236.
[18] X. H. Yu and Q. Zhang, The Shapley value for fuzzy bi-cooperative
games, International Conference on Intelligent Systems and Knowledge
Engineering 2007.
[19] M. Tsurumi, T. Tanino and M. Inuiguchi, A Shapley function on a class
of cooperative fuzzy games, European Journal of Operational Research
129 (2001) 596-618.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53257", author = "Fan-Yong Meng and Yan Wang", title = "Equal Sharing Solutions for Bicooperative Games", abstract = "In this paper, we discuss the egalitarianism solution (ES) and center-of-gravity of the imputation-set value (CIV) for bicooperative games, which can be seen as the extensions of the solutions for traditional games given by Dutta and Ray [1] and Driessen and Funaki [2]. Furthermore, axiomatic systems for the given values are proposed. Finally, a numerical example is offered to illustrate the player ES and CTV.
", keywords = "Bicooperative games, egalitarianism solution, center of- gravity of the imputation-set value.", volume = "5", number = "12", pages = "1862-4", }
