On the Formation of Unions in n-Person Games
Abstract
A union in an n-person cooperative game is a group of players who agree to act only in unison. Unions may combine to form further unions, and sub-unions may form within a union thereby generating a union structure. The effect on the core of the game is, if anything, to enlarge it by removing potential blocking coalitions. It is shown that appropriate union structures will generate a non-empty core for any game which is monotonic in zero- normalised form (such as a superadditive game). The authors give simple numerical examples of games which require more than one union and indeed more than one 'level' of unions to generate a non-empty core. Finally the authors characterise the complexity of the union structure required for different sizes of games, in particular for symmetric games. The authors conclude with some remarks on which union structures are likely to form.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1974
- Accession Number
- ADA008359
Entities
People
- Abraham Charnes
- S. C. Littlechild
Organizations
- University of Texas at Austin