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.
Butler, Christopher K. (2004) Modeling Compromise at the International Table, Conflict Management and Peace Science 21 (3): 159–177.