Aeory of Disagreement in Repeated Games with Bargaining

is paper proposes a new approach to the problem of equilibrium selection in repeated games with transfers, by supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (which follows a generalized alternating-offer protocol), sharp predictions arise from three axioms. Two axioms allow the players to meaningfully discuss whether to deviate from their plan; the third embodies a “theory of disagreement”—that play under disagreement should not vary with the manner in which bargaining broke down. Equilibria satisfying these axioms exist for all discount factors and are simple to construct, and all equilibria attain the same joint value. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efciency depends on both the stage game and the bargaining power that they derive from the details of the bargaining protocol. e theory extends naturally to games with imperfect public monitoring and heterogeneous discount factors, and yields new insights into classic relational contracting questions. JEL Classi cations: C71 , C72 , C73 , C78 *We thank Sylvain Chassang, Marina Halac, Jin Li, Larry Samuelson, and Garey Ramey for valuable comments and suggestions, along with seminar participants at Carlo Alberto, Columbia, Duke-Fuqua, ETH Zurich, Florida International, IFPR, Penn, Santa Fe Institute, Toronto, UCLA, UCSD, UC Davis, USC, USC-Marshall, Western Ontario, and Yale; and conference participants at the GTS 3rdWorld Congress, SWET 2008, the 2008 Stony BrookWorkshops, the 2009 NBER Organizational Economics Working Group, and NAWMES 2011. Jacob Johnson, Jong-Myun Moon, and Aniela Pietrasz provided excellent research assistance. Miller thanks Yale and the Cowles Foundation for hospitality and nancial support, and Partha Dasgupta for inspiration to pursue this topic. Watson thanks NSF (SES-0095207), NOAA Fisheries Service, and the Cowles Foundation at Yale for hospitality and nancial support.