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

The paper analyzes the strategic interactions between countries in pollution control, comparing simultaneous (Cournot-Nash) and sequential (Stackelberg) move equilibria. By introducing a pre-play stage where countries choose their timing, the author demonstrates that while simultaneous play is prevalent when strategies are substitutable, a leader can emerge endogenously when strategic complementarities exist. The study finds that sequential play under complementarity leads to lower global emissions and higher welfare than simultaneous play. The analysis utilizes supermodular game theory to avoid restrictive assumptions like concavity or uniqueness of equilibria.

• When countries' strategies are strategic substitutes (defined by a strictly convex damage function), the only subgame perfect Nash equilibrium of the extended game is for countries to act simultaneously, resulting in a Cournot-Nash equilibrium.
• In cases of strategic substitutability, the environmental impact of simultaneous play versus sequential play depends on the strength of the substitutability; simultaneous play is globally preferable if substitutability is weak, but not if it is strong.
• Sequential play under strategic complementarity is environmentally superior to simultaneous play, as both the leader and the follower reduce their individual emission levels compared to the Cournot-Nash outcome.
• If one country's payoff function exhibits strategic substitutability while the other's exhibits strategic complementarity, the country with substitutable strategies will endogenously emerge as the leader.
• The emergence of a leader is economically rational if there are reinforcement effects between countries' economic activities, such as imitation, technology transfers, or increasing returns to scale.

APA

Heugues, M. (2011). Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria. Basque Centre for Climate Change. https://www.bc3research.org/h6T8Uy8Nm4gFs0O/201102281237151591195905.pdf

Chicago

Heugues, Melanie. Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria. Basque Centre for Climate Change, 2011. https://www.bc3research.org/h6T8Uy8Nm4gFs0O/201102281237151591195905.pdf.

Wikipedia

{{cite report |last1=Heugues |first1=Melanie |title=Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria |publisher=Basque Centre for Climate Change |date=February 2011 |url=https://www.bc3research.org/h6T8Uy8Nm4gFs0O/201102281237151591195905.pdf |access-date=23 October 2026 |via=Climate Insights Directory}}

BibTeX

@techreport{heugues2011endogenous, author = {Heugues, Melanie}, title = {{Endogenous Timing in Pollution Control: Stackelberg versus Cournot-Nash Equilibria}}, institution = {Basque Centre for Climate Change}, year = {2011}, month = feb, url = {https://www.bc3research.org/h6T8Uy8Nm4gFs0O/201102281237151591195905.pdf}, urldate = {2026-10-23}, note = {Indexed by Climate Insights Directory} }