Identi cation of Stochastic Sequential Bargaining Models1

Stochastic sequential bargaining games (Merlo and Wilson (1995, 1998)) have found wide applications in various \u85elds including political economy and macroeconomics due to their exibility in explaining delays in reaching an agreement. In this paper, we present new results in nonparametric identi\u85cation of such models under di¤erent scenarios of data availability. First, we give conditions for an observed distribution of playersdecisions and agreed allocations of the surplus, or the "cake", to be rationalized by a sequential bargaining model. We show the common discount rate is identi\u85ed, provided the surplus is monotonic in unobservable states (USV) given observed ones (OSV). Then the mapping from states to surplus, or the "cake function", is also recovered under appropriate normalizations. Second, when the cake is only observed under agreements, the discount rate and the impact of observable states on the cake can be identi\u85ed, if the distribution of USV satis\u85es some exclusion restrictions and the cake is additively separable in OSV and USV. Third, if data only report when an agreement is reached but never report the size of the cake, we propose a simple algorithm that exploits shape restrictions on the cake function and the independenc