Sandwich games

• 成果类型: Article
• 署名作者: Lehrer, Ehud; Teper, Roee
• 署名单位: Tel Aviv University; INSEAD Business School; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0796-7
• 发表日期: 2015
• 页码: 545-557
• 关键词: subjective-probability; cores

摘要

The extension of set functions (or capacities) in a concave fashion, namely a concavification, is an important issue in decision theory and combinatorics. It turns out that some set-functions cannot be properly extended if the domain is restricted to be bounded. This paper examines the structure of those capacities that can be extended over a bounded domain in a concave manner. We present a property termed the sandwich property that is necessary and sufficient for a capacity to be concavifiable over a bounded domain. We show that when a capacity is interpreted as the product of any sub group of workers per a unit of time, the sandwich property provides a linkage between optimality of time allocations and efficiency.