Abstract
In this paper we consider a two-stage game where at stage 1 the members of two groups of countries decide whether they should form a coalition and then at stage 2 determine their contribution to a global public good cooperatively within their respective group. After describing the Nash equilibria of public good provision at stage 2, which result either after unilateral or bilateral coalition building at stage 1, we provide some characterization of the subgame-perfect equilibria of the entire game. Especially, we show that in many situations the coalition formation game at stage 1 will be of the chicken type, but that other game structures may emerge as well. Since partial cooperation by a smaller group of countries may undermine the willingness of a larger group to form a coalition some paradoxical effects can also be observed.
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Appendix: Derivation of the Threshold Level in Proposition 11
Appendix: Derivation of the Threshold Level in Proposition 11
It directly follows from Eq. (19) that
which is positive since \( {e}_1^K>0 \), \( {e}_1^M>0 \), \( {e}_2^K<0 \) and \( w-{e}^K \) is a member of K’s private consumption which is positive in the equilibrium E B I (k, m) by definition. Inserting (29) into
gives
Then an upper bound \( \underline{\chi}>{\underline{\xi}}_B(m) \) which has the properties required by Proposition 11 exist since at \( \xi ={\underline{\xi}}_B(m) \) we have \( w-{e}^K=0 \). Hence, because of \( {e}_1^M>0 \) and \( {e}_2^K<0 \), the numerator is of (30) is negative there so that continuity implies that u BK I must also be falling for all ξ close to \( {\underline{k}}_B(m) \).QED
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Buchholz, W., Eichenseer, M. (2017). Strategic Coalition Formation in Global Public Good Provision. In: Buchholz, W., Rübbelke, D. (eds) The Theory of Externalities and Public Goods. Springer, Cham. https://doi.org/10.1007/978-3-319-49442-5_4
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DOI: https://doi.org/10.1007/978-3-319-49442-5_4
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