I just added a new working paper on partial cooperation in non-cooperative games on the economic theory page. It addresses how to consider a group of decision makers to coordinate certain strategic actions, while all other actions remain purely non-cooperative. The paper generalises the existing contributions to this partial cooperation problem to include more complex decision situations.
We provide two applications of this framework. First, we look at cartel formation in a multi-market oligopoly. In this case the cartel operates only in one market, while all cartel members and other firms remain competitive in the other markets. Interestingly, we show that the merger paradox vanishes if the cartel takes a leadership position in determining its actions.
Second, we consider the writing of international treaties to curb environmental pollution. In particular, in our framework we can now study how a group of countries can agree on emissions control, while other countries do not participate. Furthermore, all countries remain competitive in the production of non-polluting goods. We show that even when few countries participate, emissions control efforts are Pareto improving.