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A time consistent dynamic bargaining procedure in differential games with heterogeneous discounting
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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 de ned as the time-consistent dynamic bargaining (TCB) solution, extends the recursive Nash bargaining solution introduced in Sorger (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.
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CASTAÑER, Anna, MARÍN SOLANO, Jesús and RIBAS MARÍ, Carme. A time consistent dynamic bargaining procedure in differential games with heterogeneous discounting. Mathematical Methods of Operations Research. 2021. Vol. 93, num. 3, pags. 555-584. ISSN 1432-2994. [consulted: 30 of June of 2026]. Available at: https://hdl.handle.net/2445/179057