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

Anna Castañer (), Jesús Marín-Solano () and Carmen Ribas ()
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Anna Castañer: Universitat de Barcelona
Jesús Marín-Solano: Universitat de Barcelona
Carmen Ribas: Universitat de Barcelona

Mathematical Methods of Operations Research, 2021, vol. 93, issue 3, No 5, 555-584

Abstract: Abstract 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.

Keywords: Differential games; Time-consistency; Dynamic bargaining; Asymmetric players; Heterogeneous discounting; Common property resource games (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00186-021-00742-0

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