Cooperative Games on Antimatroids

AMS classification: 90D12;game theory;cooperative games;antimatroids

Spatially explicit risk analysis: a new solution to contamination problems in the Metropolitan Delta

In the current paper a new conceptual outline for the ecological risk assessment of contamination will be adressed. In the first place risk assessment has to be spatially explicit, taking in account the spatial structure of the landscape (landscape ecotoxicology). Secondly the concept of SSRA (spatially structured risk assessment) being introduced: it is aimed at minimising the contact between organisms and contaninants by spatially structuring the landscape so that organisms will not forage at contaminated site

Axiomatizations of the Shapley Value for Cooperative Games on Antimatroids

AMS classification: 91A12

Axiomatizations of the Shapley Value for Cooperative Games on Antimatroids

AMS classification: 91A12;cooperative games;antimatroid;permission structure;Shapley value

Axiomatizations of two types of Shapley values for games on union closed systems

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication. © 2010 The Author(s)