Voluntary agreements as correlated equilibria of a subscription game

I develop a subscription game, modified so as to represent firms' incentives to participate to an environmental Voluntary Agreement (VA). Specifically, I assume the VA is preemptive, i.e. it occurs under the threat of a mandatory regulation. I suggest the use of a correlating device to strengthen firms participation, formalized by the concept of correlated equilibrium (CE). I characterize the multiple pure and mixed Nash equilibria (NE) of the game without the correlating device. I find that such a device not only solves the problem raised by multiplicity of NE, but also ensures that a higher expected aggregate payoff is reached for any given level of threat. I provide a full comparative efficiency analysis after the optimal CE is characterized, and study the impact of the threat stringency. Finally, I illustrate the general results in a specified example of pollution abatement model.