### Abstract

Original language | English |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 18 |

Publication status | Published - 2000 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1558 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

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

### Cite this

*(Average-) convexity of common pool and oligopoly TU-games*. (Memorandum; No. 1558). Enschede: University of Twente, Department of Applied Mathematics.

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*(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.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - (Average-) convexity of common pool and oligopoly TU-games

AU - Driessen, Theo

AU - Meinhardt, H.

N1 - Imported from MEMORANDA

PY - 2000

Y1 - 2000

N2 - 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.

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.

KW - MSC-91D12

KW - IR-65745

KW - EWI-3378

KW - MSC-91D40

M3 - Report

T3 - Memorandum

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

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -