Strategic Behavior and the Environment > Vol 2 > Issue 2

Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria

Melanie Heugues, Fondazione Eni Enrico Mattei, Italy,
Suggested Citation
Melanie Heugues (2012), "Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria", Strategic Behavior and the Environment: Vol. 2: No. 2, pp 133-158.

Publication Date: 30 Jul 2012
© 2012 M. Heugues
Climate Change,  Game Theoretic Models/Cooperation/Noncooperation,  Pollution/Abatement
Climate changeNon-cooperative gameGlobal pollutionStrategic interactionsEndogenous timingSupermodular game theory


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In this article:
The Extended Global Emission Game 
Definition, Existence and Characterization of Equilibria in the Constituent Game 
Results: Subgame Perfect Equilibria of the Extended Game and Their Respective Environmental Consequences 
Appendix A: Definitions and Main Theorems of Lattice Theory 
Appendix B: Proofs 


In the framework of international cooperation on climate change to control green-house gas emissions (GHG), this paper aims to shed new light on the eventuality of the emergence of a country (or a group of countries) behaving as a leader in the implementation of its environmental policy. The sequence of moves in the existing literature is usually an exogenous assumption — known as the Cournot assumption (if countries take action simultaneously) and the Stackelberg assumption (if they act sequentially, the latter observing the strategy of the former). The main purpose here is to make the timing endogenous. To do so, we introduce a pre-play stage in the basic two-country game. Then we provide different sets of minimal conditions — on the benefit and damage functions linked to GHG emissions into the atmosphere, yielding respectively the simultaneous and the two sequential modes of play. While the results essentially confirmthe prevalence of the former, they also indicate that the latter are natural under some robust conditions: a leader can emerge endogenously when implementing its environmental policy. Finally we provide sufficient conditions for a specific leader to appear. All the results come with an analysis in terms of global emissions and global welfare. The analysis makes crucial use of the basic results from the theory of supermodular games.