We thank Nageeb Ali, Jim Andreoni, Sylvain Chassang, Vince Crawford, Marina Halac, Matt Jackson, Sebastian Kranz, Ola Kvaløy, Jin Li, Garey Ramey, Larry Samuelson, Joel Sobel, and several anonymous referees for valuable comments and suggestions, along with seminar participants at Arizona, Collegio Carlo Alberto, Columbia, Duke-Fuqua, ETH Zurich, Florida International, IFPR, Johns Hopkins, Microsoft Research, Penn, Santa Fe Institute, Toronto, UCLA, UCSD, UC Davis, USC, USC-Marshall, Washington University, Western Ontario, and Yale, and conference participants at the GTS Third World Congress, SWET 2008, the 2008 Stony Brook Workshops, the 2009 NBER Organizational Economics Working Group, and NAWMES 2011. Jacob Johnson, Jong-Myun Moon, and Aniela Pietrasz provided excellent research assistance. Miller thanks the NSF (SES-1127643), Microsoft Research, Yale, and the Cowles Foundation for hospitality and financial support; Partha Dasgupta for inspiration to pursue this topic; and his former colleagues at UCSD for all their support. Watson thanks the NSF (SES-0095207 and SES-1227527), the NOAA Fisheries Service, Yale, the Cowles Foundation, and the Center for Advanced Study in the Behavioral Sciences at Stanford for hospitality and financial support.
A Theory of Disagreement in Repeated Games With Bargaining
Article first published online: 13 NOV 2013
© 2013 The Econometric Society
Volume 81, Issue 6, pages 2303–2350, November 2013
How to Cite
Miller, D. A. and Watson, J. (2013), A Theory of Disagreement in Repeated Games With Bargaining. Econometrica, 81: 2303–2350. doi: 10.3982/ECTA10361
- Issue published online: 13 NOV 2013
- Article first published online: 13 NOV 2013
- Manuscript received October, 2011; final revision received March, 2013.
- Relational contracts;
- repeated games;
- equilibrium selection;
This paper proposes a new approach to equilibrium selection in repeated games with transfers, supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (following 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 that satisfy these axioms exist for all discount factors and are simple to construct; all equilibria generate the same welfare. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining protocol. The theory extends naturally to games with imperfect public monitoring and heterogeneous discount factors, and yields new insights into classic relational contracting questions.