A Dual Description Of The Class Of Games With A Population Monotonic Allocation Scheme

10.1142/s0219198903001112 ◽

2003 ◽

Vol 05 (04) ◽

pp. 385-390

Author(s):

RUUD HENDRICKX

Keyword(s):

Cooperative Games ◽

Transferable Utility ◽

Allocation Scheme ◽

Population Monotonic Allocation Schemes

Monotonic Allocation Scheme ◽

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept, mainly because it implies some very nice and handy properties. One of these is that every extended marginal vector constitutes a population monotonic allocation scheme. In this note, this well-known result is generalised to games with nontransferable utility.

INFORMATION SHARING GAMES

10.1142/s0219198903000842 ◽

2003 ◽

Vol 05 (01) ◽

pp. 1-12 ◽

Cited By ~ 11

Author(s):

MARCO SLIKKER ◽

HENK NORDE ◽

STEF TIJS

Keyword(s):

Information Sharing ◽

Cooperative Game ◽

Cooperative Games ◽

Allocation Scheme ◽

In this paper we study information sharing situations. For every information sharing situation we construct an associated cooperative game, which we call an information sharing game. We show that the class of information sharing games coincides with the class of cooperative games with a population monotonic allocation scheme.

A dual description of the class of games with a population monotonic allocation scheme

Games and Economic Behavior ◽

10.1016/s0899-8256(02)00506-7 ◽

2002 ◽

Vol 41 (2) ◽

pp. 322-343 ◽

Cited By ~ 9

Author(s):

Henk Norde ◽

Hans Reijnierse

Keyword(s):

Allocation Scheme ◽

FISHERY MANAGEMENT GAMES: HOW TO ADMIT NEW MEMBERS AND REDUCE HARVESTING LEVELS

10.1142/s0219198908001960 ◽

2008 ◽

Vol 10 (03) ◽

pp. 319-333 ◽

Cited By ~ 2

Author(s):

KIM HANG PHAM DO ◽

HENK FOLMER ◽

HENK NORDE

Keyword(s):

Game Theory ◽

Nash Equilibrium ◽

Shapley Value ◽

Fishery Management ◽

Proportional Rule ◽

Allocation Scheme ◽

New Members ◽

Management Games ◽

This paper applies game theory to address the problem of allocating profits among fishing nations, once the countries concerned have expressed an interest in achieving an agreement through a Regional Fishery Management Organization (RFMO). Proposing the population monotonic allocation scheme as management rule for division of profits, we argue that existing RFMOs can be expanded by means of the Shapley value. We also show that adjustment from the Nash equilibrium to sustainable or more efficient can be achieved by means of the proportional rule without harming any of the countries involved.

LINK MONOTONIC ALLOCATION SCHEMES

10.1142/s021919890500065x ◽

2005 ◽

Vol 07 (04) ◽

pp. 473-489 ◽

Cited By ~ 20

Author(s):

MARCO SLIKKER

Keyword(s):

Allocation Scheme ◽

Myerson Value ◽

Allocation Rules ◽

A Value ◽

Position Value ◽

Communication Situations ◽

Fixed Set ◽

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.