Convexity of production, common pool and oligopoly games: a survey
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.
- Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Institute for Statistics and Economic Theory, University of Karlsruhe, Zirkel 2, D-76128 Karlsruhe, Germany