The Pre-Kernel as a Fair Division Rule for Some Cooperative Game Models

Chapter
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Abstract

Rather than considering fairness as some private property or a subjective feeling of an individual, we study fairness on a set of principles (axioms) which describes the pre-kernel. Apart from its appealing axiomatic foundation, the pre-kernel also qualifies in accordance with the recent findings of Meinhardt (The pre-kernel as a tractable solution for cooperative games: an exercise in algorithmic game theory. Springer, Berlin, 2013b) as an attractive fair division rule due to its ease of computation by solving iteratively systems of linear equations. To advance our understanding of compliance on non-binding agreements, we start our analysis with a Cournot situation to derive four cooperative game models well introduced in the literature, where each of it represents different aspiration levels of partners involved in a negotiation process of splitting the monopoly proceeds. In this respect, we demonstrate the bargaining difficulties that might arise when agents are not acting self-constraint, and what consequences this impose on the stability of a fair agreement.

Keywords

Convex analysis Convex games Fenchel-Moreau conjugation Indirect function Pre-kernel Stable agreement 
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Notes

Acknowledgements

We are very grateful to Jingang Zhao for his helpful comments and suggestions of improvements. Of course, the usual disclaimer applies.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of Operations Research, Karlsruhe Institute of TechnologyKarlsruheGermany

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