On Time-Consistent Equilibrium Stopping Under Aggregation of Diverse Discount Rates

This paper studies a 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 an aggregation preference to incorporate all discount rates via an attitude function that reflects the aggregation rule chosen by the central planner. The resulting optimal stopping problem is time-inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent mild equilibria as fixed points of an operator in the setting of one-dimensional diffusion processes. We provide some sufficient conditions on the underlying models and the attitude function such that the smallest mild equilibrium attains the optimal equilibrium. In addition, we show that the optimal equilibrium is a weak equilibrium. When the sufficient condition of the attitude function is violated, we illustrate by various examples that the characterization of the optimal equilibrium may differ significantly from some existing results for a single agent, which now sensitively depends on the attitude function and the diversity distribution of discount rates within the group.

Funding: S. Deng is supported by a Hong Kong University of Science and Technology startup grant [Grant R9826]. X. Yu is supported by the Hong Kong RGC General Research Fund (GRF) [Grant 15304122] and by the Research Centre for Quantitative Finance at the Hong Kong Polytechnic University [Grant P0042708]. J. Zhang is supported by a Chinese University of Hong Kong startup grant [Grant 4937261].