Convexity of production, common pool and oligopoly games: a survey

Theo Driessen, Holger Meinhardt

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


The paper surveys a uniform proof technique of the convexity property for three different cooperative TU games arising from three different economical settings. The production economy, common pool situation and oligopoly framework involve a cost function, but different production functions. Each of the three corresponding game theoretic models refers to some maximization problem described by optimizing a certain net profit function over all feasible production levels. The current mathematical proof of the convexity of any of three cooperative TU games is strongly based on the interchangeability of maximizers for the underlying maximization problems. This uniform proof technique is inspired by the interchangeability of two players concerning the convexity condition in terms of the marginal contributions of both players in the TU game.
Original languageUndefined
Title of host publicationGame Theory and Mathematical Economics
EditorsA. Wieczorek, M. Malawski, A. Wiszniewska-Matyszkiel
Place of PublicationWarsaw, Poland
PublisherBanach Center Publications 71.
Number of pages10
ISBN (Print)0137-6934
Publication statusPublished - 2006
EventInternational Conference on Game Theory and Mathematical Economics - Warsaw, Poland
Duration: 6 Sept 200410 Sept 2004

Publication series

NameBanach Center Publications
PublisherInstitute of Mathematics, Polish Academy of Sciences
ISSN (Print)0137-6934


ConferenceInternational Conference on Game Theory and Mathematical Economics
Other6-10 September 2004


  • MSC-91A12
  • MSC-91A40
  • IR-63652
  • METIS-239249
  • EWI-8035

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