A Nash bargaining model for simple exchange networks

Starting from exogenously given negotiation networks, sociological exchange theories explain bilateral divisions of fixed surpluses (e.g., cake, dollar) as consequences of the partners’ structural embeddedness. In accordance with the available experimental evidence, we focus on simple exchange networks and present a formal model for predicting profit splits from such structures. In contrast to other approaches, we combine the generalized Nash bargaining solution from game theory with the assumption that both relational features and network positions affect exchange outcomes. The resulting point predictions for profit splits correspond closely with experimental results obtained by Cook et al. [Cook, K.S., Emerson, R.M., Gillmore, M.R., Yamagishi, T., 1983. The distribution of power in exchange networks: theory and experimental results. American Journal of Sociology 89, 275–305], Lovaglia et al. [Lovaglia, M.J., Skvoretz, J., Willer, D., Markovsky, B., 1995. Negotiated exchanges in social networks. Social Forces 74, 123–155], Markovsky et al. [Markovsky, B., Willer, D., Patton, T., 1988. Power relations in exchange networks. American Sociological Review 53, 220–236], Simpson and Willer [Simpson, B., Willer, D., 1999. A new method for finding power structures. In: Willer, D. (Ed.), Network Exchange Theory. Praeger, Westport, CT, pp. 270–284], Skvoretz and Fararo [Skvoretz, J., Fararo, T.J., 1992. Power and network exchange: an essay toward theoretical unification. Social Networks 14, 325–344], Skvoretz and Willer [Skvoretz, J., Willer, D., 1993. Exclusion and power: a test of four theories of power in exchange networks. American Sociological Review 58, 801–818] as well as Yamagishi et al. [Yamagishi, T., Gillmore, M.R., Cook, K.S., 1988. Network connections and the distribution of power in exchange networks. American Journal of Sociology 93, 833–851].