On time-consistent equilibrium stopping under aggregation of diverse discount rates
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This work studies the central planner’s decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with a smooth aggregation preference to incorporate all heterogeneous discount rates with an attitude function that reﬂects the aggregation rule in the same spirit of ambiguity aversion in the smooth ambiguity preference proposed in Klibanoﬀ et al. (2005). The optimal stopping problem renders to be time inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent equilibria as ﬁxed points of an operator in the setting of one-dimensional diﬀusion processes. We provide some suﬃcient conditions on both the underlying models and the attitude function such that the smallest equilibrium attains the optimal equilibrium in which the attitude function becomes equivalent to the linear aggregation rule as of diversity neutral. When the suﬃcient condition of the attitude function is violated, we can illustrate by various examples that the characterization of the optimal equilibrium may diﬀer signiﬁcantly from some existing results for an individual agent, which now sensitively depends on the attitude function and the diversity distribution of discount rates.