\. {0, 0, 5. for each h ? H, for each x p ? L p \ {0}, v ? 1.(b) ,P (1 ?h,p , 0 h , x p ) = 0, 6. for each i ? I \ {2}, for each x p ? L p \ {0}

, P (1 ?p , x p ) = 0, 2. v ? 1.(c) ,P (1 ?p , 0 p ) = 0, 3. v ? 1.(c) ,P (1 ?2,p , 0 2 , 1 p ) = 1.5, 4. v ? 1.(c) ,P (1 ?1,p , 0 1 , 1 p ) = 5, 5. for each i ? I\{1, 2}, for each x p ? L p \{0}, v ? 1.(c) ,P (1 ?i,p , 0 i , x p ) = v ? 1.(c) ,P (1 ?p , x p ) = 0. By taking the balanced collection B as defined above, Consider any mapping of rights ? 1.(c) , then I = U . Furthermore assume thatx i p = 2 we have: 1. for each x p ? L p \ {0}, v ? 1.(c)

J. and H. , Consider any mapping of rights ? 2.(d) such that

?. , P (1 ?p , 0 p ) = 0, 3. for each x p ? L p \ {0}, v ? 2.(d) ,P (1 ?2,p , 0 2 , x p ) = 1.5, 4. for each h ? H, for each x p ? L p \ {0}, v ? 2.(d) ,P (1 ?h,p , 0 h , x p ) = 0, 5. for each j ? J \{2}, for each x p ? L p \{0}, v ? 2.(d) ,P (1 ?j,p , 0 j , x p ) = v ? 2.(d) ,P (1 ?p , x p ) = 0. References Aivazian VA, Then we obtain, 1. for each x p ? L p \ {0}, v ? 1.(b) ,P (1 ?p , x p ) = 0, 2. v ? 2.(d), vol.24, pp.175-181, 1981.

S. Ambec and Y. Kervinio, Cooperative decision-making for the provision of a locally undesirable facility, Social Choice and Welfare, vol.46, issue.1, pp.119-155, 2016.

L. Anderlini and L. Felli, Costly bargaining and renegotiation, Econometrica, vol.69, issue.2, pp.377-411, 2001.

F. Bloch and A. Van-den-nouweland, Expectation formation rules and the core of partition function games, Games and Economic Behavior, vol.88, pp.339-353, 2014.

O. Bondareva, The theory of the core in an n-person game, Vestnik Leningrad Univ, vol.13, pp.141-142, 1962.

J. S. Chipman and G. Tian, Detrimental externalities, pollution rights, and the "coase theorem, Economic Theory, vol.49, issue.2, pp.309-327, 2012.

R. H. Coase, The problem of social cost, Journal of Law and Economics, vol.3, issue.2, pp.1-44, 1960.

T. Ellingsen and E. Paltseva, Confining the coase theorem: contracting, ownership, and free-riding, The Review of Economic Studies, vol.83, issue.2, pp.547-586, 2016.

Y. Funaki and T. Yamato, The core of an economy with a common pool resource: A partition function form approach, International Journal of Game Theory, vol.28, issue.2, pp.157-171, 1999.

S. Gonzalez, A. Marciano, and P. Solal, The social cost problem, rights, and the (non) empty core, Journal of Public Economic Theory, vol.21, issue.2, pp.347-365, 2019.

M. Grabisch and L. Xie, A new approach to the core and weber set of multichoice games, Mathematical Methods of Operations Research, vol.66, issue.3, pp.491-512, 2007.

C. R. Hsiao and T. Raghavan, Monotonicity and dummy free property for multi-choice cooperative games, International Journal of Game Theory, vol.21, issue.3, pp.301-312, 1992.

C. R. Hsiao and T. Raghavan, Shapley value for multichoice cooperative games, i, Games and economic behavior, vol.5, issue.2, pp.240-256, 1993.

L. Hurwicz, What is the coase theorem?, Japan and the World Economy, vol.7, issue.1, pp.49-74, 1995.

Y. A. Hwang and Y. H. Liao, The multi-core, balancedness and axiomatizations for multichoice games, International Journal of Game Theory, vol.40, issue.4, pp.677-689, 2011.

A. Van-den-nouweland, S. Tijs, J. Potters, and J. Zarzuelo, Cores and related solution concepts for multi-choice games, Zeitschrift für Operations Research, vol.41, issue.3, pp.289-311, 1995.

A. C. Pigou, The Economics of Welfare, 1920.

L. S. Shapley, On balanced sets and cores, Naval research logistics quarterly, vol.14, issue.4, pp.453-460, 1967.

L. S. Shapley and M. Shubik, On the core of an economic system with externalities, The American Economic Review, vol.59, issue.4, pp.678-684, 1969.

G. J. Stigler, The theory of price, 1966.

J. Zhao, A reexamination of the coase theorem, The Journal of Mechanism and Institution Design, vol.3, issue.1, pp.111-132, 2018.