Imperfect information processing in sequential bargaining games with present biased preferences

This paper studies an alternating-offers bargaining game between a time-consistent player and a time-inconsistent player who processes information on future self-preferences imperfectly. Time-inconsistency and information processing are modeled by using cognitive and mood state approaches, respectively. This model structure allows for the learning of the partially naive time-inconsistent agent. The results characterize the relationship among the level of naivete, the level of learning probability and the equilibrium. We find critical values of the model parameters that specify whether the agreement is delayed and characterize the probabilistic nature of the agreement. In addition, comparative static results are reported with respect to time preferences.