The modeling of coalition for environmental protection within co-utility framework

Abstract

The game theoretic modelling of coalition for environmental protection within the framework of a new concept of co-utility is discussed. The co-utility concept contains mainly two elements. Firstly, agents can increase their payoffs by collaborating with each-other. Secondly, the outcome of collaboration is robust towards internal and external disturbances. The advantages of using of co-utility are two-fold. Primarily, the co-utility concept is broad and can serve as an umbrella concept in all applications where agents have a space for simultaneous improvement of payoffs. Secondly the co-utility concept can be associated with different stability concept such as myopic or farsighted stability. The myopic and farsighted co-utile sets are defined and their element-co-utile outcomes are found.

Keywords:

• Coalition formation
• co-utility
• game theory
• farsighted stability
• myopic stability
• integrated assessment modelling

Acknowledgements

The views in this paper belongs to the author and do not necessarily reflect the views of the Templeton World Charity Foundation.

Notes

No potential conflict of interest was reported by the authors.

1 A player (which is outside of coalition) satisfies the negative spillover property if he decreases his profit when coalition increases its size.

2 Please note that sub-coalition domination is always of indirect domination in nature; in any simple sub-coalition domination there are always two steps; on the first step, some countries leave the coalition, and on the second one some countries join it. External (or internal) domination can be of a direct nature too; for example, two countries join the coalition (or leave it), and the coalition domination process ends.

3 The algorithms of Tables A.1 and A.2 in [12] (see Appendix 1) fully describe the procedure of finding single farsightedly stable coalitions. As mentioned before we do not find it necessary to repeat them here. One of the reasons is to keep the length of the paper to a reasonable size.

4 In open membership games, the definition of myopic stability requests only that a country that joins a coalition reduces its profit [4]. It is more realistic (as an exclusive membership game in our case) to add the second part that a previous member of the coalition reduces his profit.

5 The discussion in this section is more relevant for farsighted stability, but it can somehow be applied to myopic stability too. We simply grant members of myopic stable coalitions the possibility of choosing between different myopic stable coalitions (which is an ad-hoc assumption).

Additional information

Funding

This work was supported by Templeton World Charity Foundation [grant number TWCF0095/AB60 CO-UTILITY].