Abstract
We consider a normal-form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players. We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are stated and we identify conditions under which the various equilibrium concepts are equivalent. We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly, typically, a merger paradox emerges in the partial cooperative equilibrium. The paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.
Highlights
We consider a game theoretic framework for understanding collaborative decision situations embedded in competitive environments
We show that the cartel benefits in comparison with the standard Nash equilibrium outcome if it has a clear leadership position: An improvement only occurs in the leadership equilibrium, not in the partial cooperative equilibrium
In Nash equilibrium, all countries achieve the same utility levels, under partial cooperation, the independent countries have a higher utility than the cooperators, since they act as free riders, enjoying the environmental pollution abatement imposed through the treaty
Summary
We consider a game theoretic framework for understanding collaborative decision situations embedded in competitive environments Often, these kinds of agreements on a specific economic issue involve a single group of decision makers who cooperate. The utilitarian aggregator is imposed, for example, in the theory of (standard) partial cooperative games as seminally developed in Mallozzi and Tijs (2009). We consider the effects of international pollution abatement treaties Such treaties are best described as partial cooperative agreements: A single coalition of treaty countries writes a binding agreement on certain aspects of the spectrum of economic controls at the disposal of a country’s government. Cooperators choose the amount of labour freely, but form a cooperative agreement with regard to the amount of pollutants In this context, there is no difference between the partial cooperative equilibrium and the leadership one, but both differ from the Nash outcome. All non-treaty countries act as free riders in these equilibrium situations
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