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A time consistent dynamic bargaining procedure in differential games with hterogeneous discounting


  • Anna Castañer

    (Universitat de Barcelona)

  • Jesús Marín-Solano

    (Universitat de Barcelona
    Universitat de Barcelona)

  • Carmen Ribas

    (Universitat de Barcelona)


We study cooperative solutions for differential games where players consume a common property resource. Players are asymmetric, in the sense that they have different preferences and, in particular, different time preferences. We propose a new time-consistent dynamic bargaining procedure for this class of games. This solution concept, which is defined as the time-consistent dynamic bargaining (TCB) solution, extends the recursive Nash bargaining solution introduced in Sorger (J Econ Dyn Control 30:2637–2659, 2006) to a continuous time setting. The underlying idea is that, in case of disagreement, the threat is that players will play a noncooperative Markov Perfect Nash equilibrium just during a very small period of time, since new negotiations can take place at every future moment and, in particular, immediately later. Conditions for interior TCB solutions are derived. To illustrate the results, two common property resource games are analyzed in detail.

Suggested Citation

  • Anna Castañer & Jesús Marín-Solano & Carmen Ribas, 2021. "A time consistent dynamic bargaining procedure in differential games with hterogeneous discounting," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 555-584, June.
  • Handle: RePEc:spr:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00742-0
    DOI: 10.1007/s00186-021-00742-0

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    References listed on IDEAS

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