Modeling Compromise at the International Table

A number of people have modeled Putnam's (1988) analogy of the two-level game to better understand the interaction between domestic and international politics. Milner and Rosendorff's model (1997) has taken on particular significance in this area of research. By applying a Nash bargaining solution to a standard spatial model, they were able to make specific predictions of bargaining behavior with and without domestic constraints. In this paper, I argue that some compromise should be expected in the bargaining, compromise that the Nash bargaining solution does not allow when paired with a linear utility assumption. I present a number of theoretical alternatives for which some degree of compromise is predicted. General solutions are derived given the unidimensional spatial model for the Nash (1950), the Kalai—Smorodinsky (1975), and the Felsenthal—Diskin (1982) bargaining solutions with linear and with quadratic equations. Given the unidimensional spatial context, more compromise is proposed under a given bargaining solution when using quadratic utilities rather than linear utilities. The most compromise is proposed by the Felsenthal—Diskin bargaining solution, followed by the Kalai—Smorodinsky, and then the Nash bargaining solutions.