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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.

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Notes

  1. 1.

    The recent literature on IEAs has been surveyed by Brandt (2002), Barrett (2003, 2007), Carraro and Marchiori (2003) and Finus (2003, 2008).

  2. 2.

    In this paper, the term signatories refers to sovereign states that have ratified the agreement.

  3. 3.

    Diamantoudi and Sartzetakis (2006) have shown that some of Barrett’s (1994) results only hold if the level of abatement is not restricted by emissions.

  4. 4.

    The assumptions are more formally described by Folmer and von Mouche (2000) in Definition 1 and are assumed to hold also for coalitions acting jointly at this stage.

  5. 5.

    One possible interpretation of our model is that the all-singletons Nash equilibrium abatements reflect the historical abatement/emissions levels used by Kyoto protocol to formulate the 55 % condition.

  6. 6.

    The latter option would result in a quite different type of game where not just participation but contributions matter for the effectiveness of coalition formation. Such games have been explored by e.g. Bagnoli and Lipman (1989) and Admati and Perry (1991).

  7. 7.

    Our analysis employs Nash equilibrium (and sequential equilibrium; Kreps and Wilson 1982) as solution concepts. Hence, we do not consider multiple deviations and coalition proof Nash equilibrium (cf. Bernheim and Peleg 1987).

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Acknowledgments

We dedicate this article to the memory of Mika Widgrén. Mika has provided stimulating comments on an earlier version this paper just a few weeks before he passed away. The paper has further benefitted from suggestions by Erik Ansink, Michael Finus and three anonymous reviewers. We thank the German Science Foundation (DFG) for supporting our research cooperation.

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Correspondence to Hans-Peter Weikard.

Appendix

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.\(\square \)

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Weikard, HP., Wangler, L. & Freytag, A. Minimum Participation Rules with Heterogeneous Countries. Environ Resource Econ 62, 711–727 (2015). https://doi.org/10.1007/s10640-014-9861-1

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Keywords

  • Minimum participation rules
  • International environmental agreements
  • Coalition formation
  • Transboundary pollution
  • Environmental policy coordination

JEL Classification

  • D62
  • H41
  • D02
  • C72