Extension of Monotonic Functions and Representation of Preferences

• 成果类型: Article
• 署名作者: Evren, Ozgur; Husseinov, Farhad
• 署名单位: New Economic School; Ministry of Education of Azerbaijan Republic; ADA University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1095
• 发表日期: 2021
• 页码: 1430-1451
• 关键词: utility-functions; EXISTENCE; completeness; rationality; continuity; economies; THEOREMS; SPACES; MODEL

摘要

Consider a dominance relation (a preorder) >= on a topological space X, such as the greater than or equal to relation on a function space or a stochastic dominance relation on a space of probability measures. Given a compact set K subset of X, we study when a continuous real function on K that is strictly monotonic with respect to >= can be extended to X without violating the continuity and monotonicity conditions. We show that such extensions exist for translation invariant dominance relations on a large class of topological vector spaces. Translation invariance or a vector structure are no longer needed when X is locally compact and second countable. In decision theoretic exercises, our extension theorems help construct monotonic utility functions on the universal space X starting from compact subsets. To illustrate, we prove several representation theorems for revealed or exogenously given preferences that are monotonic with respect to a dominance relation.