Abstract
We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.
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The authors thank János Flesch, Dinard van der Laan, Ad Ridder, Klaus Ritzberger and Eilon Solan and several participants of the Conference on Economics Design 2009, the Conference of the Society for the Advancement of Economic Theory 2011, GAMES 2012, SAET 2013, the World Congress of the Econometric Society 2015 and GAMES 2016 for valuable comments.
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Herings, P.JJ., Houba, H. Costless delay in negotiations. Econ Theory 74, 69–93 (2022). https://doi.org/10.1007/s00199-021-01373-6
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DOI: https://doi.org/10.1007/s00199-021-01373-6