(Average-) convexity of common pool and oligopoly TU-games

Theo Driessen, H. Meinhardt

Research output: Book/ReportReportOther research output

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Abstract

The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages18
Publication statusPublished - 2000

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1558
ISSN (Print)0169-2690

Fingerprint

Common pool
Oligopoly
TU game
Convexity
Cost function
Joint production
Production function
Demand function
Cooperative game
Cooperative TU games
Average cost
Guarantee
Convex games
Inverse demand
Marginal cost

Keywords

  • MSC-91D12
  • IR-65745
  • EWI-3378
  • MSC-91D40

Cite this

Driessen, T., & Meinhardt, H. (2000). (Average-) convexity of common pool and oligopoly TU-games. (Memorandum; No. 1558). Enschede: University of Twente, Department of Applied Mathematics.
Driessen, Theo ; Meinhardt, H. / (Average-) convexity of common pool and oligopoly TU-games. Enschede : University of Twente, Department of Applied Mathematics, 2000. 18 p. (Memorandum; 1558).
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Driessen, T & Meinhardt, H 2000, (Average-) convexity of common pool and oligopoly TU-games. Memorandum, no. 1558, University of Twente, Department of Applied Mathematics, Enschede.

(Average-) convexity of common pool and oligopoly TU-games. / Driessen, Theo; Meinhardt, H.

Enschede : University of Twente, Department of Applied Mathematics, 2000. 18 p. (Memorandum; No. 1558).

Research output: Book/ReportReportOther research output

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AB - The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function.

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Driessen T, Meinhardt H. (Average-) convexity of common pool and oligopoly TU-games. Enschede: University of Twente, Department of Applied Mathematics, 2000. 18 p. (Memorandum; 1558).