Econ Papers Daily / 期刊论文
未来盲视与乘积拓扑
Future-blindness and the product topology
摘要
We study future-blind preferences, which are preferences that heavily discount the future, within the space of infinite consumption streams. We give two definitions: N-blindness, where agents ignore periods beyond a fixed date N, and eventual blindness, where all but finitely many dates are neglected. Using a topological approach, we show that the finest topology ensuring eventual blindness coincides with the product topology. This provides a behavioral foundation for continuity in the product topology, which was considered for studying equilibrium existence in infinite-dimensional spaces. Finally, we characterize the dual spaces under these topologies.
中文摘要
我们研究未来盲偏好，即在无限消费流空间中，对未来给予高度贴现的偏好。我们给出两个定义：N-盲，即代理人忽略固定日期N之后的时期；以及最终盲，即除有限多个日期外，其余日期均被忽略。采用拓扑方法，我们证明，确保最终盲的最精细拓扑与乘积拓扑一致。这为乘积拓扑中的连续性提供了行为基础，而该连续性曾被用于研究无限维空间中的均衡存在性。最后，我们刻画了这些拓扑下的对偶空间。