Reputational Bargaining With Minimal Knowledge of Rationality


  • Alexander Wolitzky

    1. Dept. of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305, U.S.A.;
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    • I thank the editor and three anonymous referees for helpful comments. I thank my advisors, Daron Acemoglu, Glenn Ellison, and Muhamet Yildiz, for extensive discussions and comments as well as continual advice and support. For additional helpful comments, I thank Sandeep Baliga, Abhijit Banerjee, Alessandro Bonatti, Matthew Elliott, Jeff Ely, Drew Fudenberg, Xavier Gabaix, Bob Gibbons, Michael Grubb, Peter Klibanoff, Anton Kolotilin, Mihai Manea, Parag Pathak, Jeroen Swinkels, Juuso Toikka, Iván Werning, and (especially) Gabriel Carroll, as well as many seminar audiences. I thank the National Science Foundation for financial support.


Two players announce bargaining postures to which they may become committed and then bargain over the division of a surplus. The share of the surplus that a player can guarantee herself under first-order knowledge of rationality is determined (as a function of her probability of becoming committed), as is the bargaining posture that she must announce in order to guarantee herself this much. This “maxmin” share of the surplus is large relative to the probability of becoming committed (e.g., it equals 30% if the commitment probability is 1 in 10 and equals 13% if the commitment probability is 1 in 1000), and the corresponding bargaining posture simply demands this share plus compensation for any delay in reaching agreement.