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Identification of Stochastic Sequential Bargaining Models, Second Version


  • Antonio Merlo

    () (Department of Economics, University of Pennsylvania)

  • Xun Tang

    () (Department of Economics, University of Pennsylvania)


Stochastic sequential bargaining games (Merlo and Wilson (1995, 1998)) have found wide applications in various fields including political economy and macroeconomics due to their flexibility in explaining delays in reaching an agreement. In this paper, we present new results in nonparametric identification of such models under different scenarios of data availability. First, we give conditions for an observed distribution of players’ decisions and agreed allocations of the surplus, or the "cake", to be rationalized by a sequential bargaining model. We show the common discount rate is identified, 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 identified, if the distribution of USV satisfies 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 independence of USV to recover all rationalizable probabilities for agreements under counterfactual state transitions. Numerical examples show the set of rationalizable counterfactual outcomes so recovered can be informative.

Suggested Citation

  • Antonio Merlo & Xun Tang, 2009. "Identification of Stochastic Sequential Bargaining Models, Second Version," PIER Working Paper Archive 10-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Mar 2010.
  • Handle: RePEc:pen:papers:10-008

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    Nonparametric identification; non-cooperative bargaining; stochastic sequential bargaining; rationalizable counterfactual outcomes;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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