A Theory of Disagreement in Repeated Games with Renegotiation

This paper develops the concept of contractual equilibrium for repeated games with transferable utility, whereby the players negotiate cooperatively over their continuation strategies at the start of each period. Players may disagree in the negotiation phase, and continuation play may be suboptimal under disagreement. Under agreement, play is jointly optimal in the continuation game, and the players split the surplus (according to fixed bargaining weights) relative to what they would have attained under disagreement. Contractual equilibrium outcomes also arise from subgame perfect equilibria in a class of models with noncooperative bargaining, under some assumptions on the endogenous meaning of cheap-talk messages. Contractual equilibria exist for all discount factors, and for any given discount factor all contractual equilibria attain the same aggregate utility. Patient players attain efficiency under simple sufficient conditions; necessary and sufficient conditions are also provided. The allocation of bargaining power can dramatically affect aggregate utility. The theory extends naturally to games with more than two players, imperfect public monitoring, and heterogeneous discount factors. JEL: C71 , C72 , C73 , C78 ∗We thank seminar participants at Collegio Carlo Alberto, Columbia, Florida International, the International Food Policy Research Institute, Penn, Toronto, UCLA, UCSD, UC Davis, USC, USC Marshall School of Business, Western Ontario, the 2009 NBER Organizational Economics Working Group Meeting (especially Sylvain Chassang), the Third World Congress of the Game Theory Society, the 2008 Southwest Economic Theory Conference, and the 2008 Stony Brook Workshop on Recent Advances in Repeated Games, for valuable comments and suggestions. Jacob Johnson and Jong-Myun Moon provided excellent research assistance. Both authors: Dept. of Economics, 9500 Gilman Dr. #0508, La Jolla, CA 92093–0508. Miller thanks Yale University and the Cowles Foundation for Research in Economics for hospitality and financial support, and Partha Dasgupta for inspiration to pursue this topic. Watson thanks the National Science Foundation (SES-0095207) and the National Oceanic and Atmospheric Administration (Southwest Fisheries Science Center), and the Cowles Foundation at Yale for financial support and hospitality.