Linear transformation of products: Games and economies

J. Timmer*, P. Borm, J. Suijs

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

In this paper, we introduce situations involving the linear transformation of products (LTP). LTP situations are production situations where each producer has a single linear transformation technique. First, we approach LTP situations from a (cooperative) game theoretical point of view. We show that the corresponding LTP games are totally balanced. By extending an LTP situation to one where a producer may have more than one linear transformation technique, we derive a new characterization of (nonnegative) totally balanced games: each totally balanced game with nonnegative values is a game corresponding to such an extended LTP situation. The second approach to LTP situations is based on a more economic point of view. We relate (standard) LTP situations to economies in two ways and we prove that the economies are standard exchange economies (with production). Relations between the equilibria of these economies and the cores of cooperative LTP games are investigated.

Original languageEnglish
Pages (from-to)677-706
Number of pages30
JournalJournal of optimization theory and applications
Volume105
Issue number3
DOIs
Publication statusPublished - 1 Jan 2000
Externally publishedYes

Keywords

  • Economies
  • Linear transformation
  • Price equilibria
  • Cooperative games

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