Partial Cooperation in Strategic Decision Situations

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. These collective actions typically represent a certain number of dimensions in the players’ strategy space. The actions represented by the other dimensions of the strategy space remain under the complete, individual control of the players.<br/>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 developed for these new equilibrium concepts. We identify conditions on these partial cooperative games under which the various equilibrium concepts are equivalent.<br/>We apply this game theoretic 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, which vanishes if the cartel of collaborators exploits its leadership position. Our application to international pollution abatement treaties shows that 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.<br/>