Link Monotonic Allocation Schemes

Tilburg University, CentER Discussion Paper Series No. 1999-6

Posted: 16 Aug 1999

See all articles by Marco Slikker

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering

Date Written: 1999

Abstract

A network is a graph where the nodes represent players and the links represent bilateral interaction between the players. A reward game assigns a value to every network on a fixed set of players. An allocation scheme specifies how to distribute the worth of every network among the players. This allocation scheme is link monotonic if extending the network does not decrease the payoff of any player. We characterize the class of reward games that have a link monotonic allocation scheme. Two allocation schemes for reward games are studied, the Myerson allocation scheme and the position allocation scheme, which are both based on allocation rules for communication situations. We introduce two notions of convexity in the setting of reward games and with these notions of convexity we characterize the classes of reward games where the Myerson allocation scheme and the position allocation scheme are link monotonic. As a by-product we find a characterization of the Myerson value and the position value on the class of reward games using potentials.

JEL Classification: C71

Suggested Citation

Slikker, Marco, Link Monotonic Allocation Schemes (1999). Tilburg University, CentER Discussion Paper Series No. 1999-6, Available at SSRN: https://ssrn.com/abstract=166497

Marco Slikker (Contact Author)

Eindhoven University of Technology (TUE) - School of Industrial Engineering ( email )

P.O. Box 513
5600 MB Eindhoven
Netherlands

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