Symmetric solutions of some production economies

Sergiu Hart*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A symmetric n-person game (n, k) (for positive integer k) is defined in its characteristic function form by v(S)=[|S|/k], where |S| is the number of players in the coalition S and [x] denotes the largest integer not greater than x, (i.e., any k players, but not less, can "produce" one unit). It is proved that in any imputation in any symmetric von Neumann-Morgenstern solution of such a game, a blocking coalition of p=n-k+1 players who receive the largest payoffs is formed, and their payoffs are always equal. Conditions for existence and uniqueness of such symmetric solutions with the other k-1 payoffs equal too are proved; other cases are discussed thereafter.

Original languageEnglish
Pages (from-to)53-62
Number of pages10
JournalInternational Journal of Game Theory
Volume2
Issue number1
DOIs
StatePublished - Dec 1973
Externally publishedYes

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