Minimum Participation Rules with Heterogeneous Countries

Abstract

Almost all international environmental agreements include a minimum participation rule. Under such rule an agreement becomes legally binding if and only if a certain threshold in terms of membership or contribution is reached. We analyse a cartel game with open membership and heterogeneous countries to study the endogenous choice of a minimum participation rule and its role for the success of international environmental agreements. While a full participation requirement would be efficient, we find (sequential) equilibria with a minimum participation rule that allows at least one country to free ride. Free riding may occur if a country can exploit some bargaining power in the negotiation of the minimum participation rule.

Appendix

Proof of Proposition 2

To determine whether $q_N^\varnothing -q_i^\varnothing$ is acceptable we have to distinguish two cases: the grand coalition is either ($i)$ stable or (ii) unstable.

($i$):

If $V_N (N)\ge \sum _{j=i+1}^n {V_j (\varnothing )} +\sum _{j=1}^i {V_j (N_{-j} )}$, the grand coalition is stable given $\bar{{q}}=q_N^\varnothing -q_i^\varnothing$. By positive spillovers, if acceptable, no other proposal will give a larger payoff to country $i$ as it receives at least the outside option payoff $V_i (N_{-i} )$. Acceptability implies $V_N (N)\ge \sum _{j=i+1}^n {E_j^r } +\sum _{j=1}^i {V_j (N_{-j} )}$ because pivotal countries would reject $\bar{{q}}=q_N^\varnothing -q_i^\varnothing$ if they will not receive at least $E_j^r$ under the grand coalition. If the proposal $q_N^\varnothing -q_i^\varnothing$ is unacceptable, $q_N^\varnothing$ is proposed and part (ii) of the proof of Fact 9 applies.

(ii):

If the grand coalition is unstable given $\bar{{q}}=q_N^\varnothing -q_i^\varnothing$, then by proposing $\bar{{q}}=q_N^\varnothing -q_i^\varnothing$ country $i$ can still secure $V_i (N_{-i} )$, if the proposal is acceptable. The further course of play will then be ${\upsigma } _i =0$ at stage 2 and others’ best response is ${\upsigma } _j =1$ for all $j\ne i$. Hence, coalition $N_{-i}$ is formed. $N_{-i}$ is stable as all its members are pivotal under $\bar{{q}}=q_N^\varnothing -q_i^\varnothing$. In this case acceptability requires $V_{N_{-i} } (N_{-i} )\ge \sum _{j\in N_{-i} } {E_j^r }$. If the proposal $q_N^\varnothing -q_i^\varnothing$ is unacceptable, $q_N^\varnothing$ is proposed and part (ii) of the proof of Fact 9 applies.$\square$