Sandwich games

Ehud Lehrer, Roee Teper*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)545-557
Number of pages13
JournalMathematical Programming
Issue number1-2
StatePublished - 24 Aug 2015


  • 28B20
  • 46N10
  • 52A41
  • 91A12
  • 91B06


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