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This paper studies the central planner's decision making on behalf of a groupof members with diverse discount rates. In the context of optimal stopping, wework with a smooth aggregation preference to incorporate all heterogeneousdiscount rates with an attitude function that reflects the aggregation rule inthe same spirit of ambiguity aversion in the smooth ambiguity preferenceproposed in Klibanoff et al.(2005). The optimal stopping problem renders to betime inconsistent, for which we develop an iterative approach using consistentplanning and characterize all time-consistent equilibria as fixed points of anoperator in the setting of one-dimensional diffusion processes. We provide somesufficient conditions on both the underlying models and the attitude functionsuch that the smallest equilibrium attains the optimal equilibrium in which theattitude function becomes equivalent to the linear aggregation rule as ofdiversity neutral. In addition, we show that the optimal equilibrium is a weakequilibrium in the existing literature. When the sufficient condition of theattitude function is violated, we can illustrate by various examples that thecharacterization of the optimal equilibrium may differ significantly from someexisting results for an individual agent.

On time-consistent equilibrium stopping under aggregation of diverse discount rates