Cycles and Third-Party Payments in the Partnership Formation Problem

We characterize the core of the partnership formation problem (Talman and Yang, Journal of Mathematical Economics 47, 2011) using cycles in the solution of a linear programming problem. The cycles also lead us to a new and intuitive sufficient condition for the existence of equilibrium, generalizing known results. We then introduce the partnership-stable equilibrium, a weakened solution concept in the sense that each equilibrium is also a partnership-stable equilibrium, and find sufficient and necessary conditions for its existence. Finally, we conduct a simulation study to see how often existence is an issue and which factors affect the rate at which problems have solutions.