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, Volume 25, Issue 1, pp 42–44 | Cite as

Comments on: Games with a permission structure - A survey on generalizations and applications

  • Juan Vidal-Puga
Discussion
  • 103 Downloads

Van den Brink presents an excellent survey on how a permission structure affects the sharing of benefits from cooperation among a finite set of players. The survey covers from the simplest and most intuitive permission structure, given by a directed graph, to a more general one, given by the abstract concept of normal antimatroid (Dilworth 1940). This generalization allows to include very particular cases such as the one presented in Example 2, where permission is held not by a fixed set of players but as the result of a voting game. I believe normal antimatroids could be the most general concept that maintains the essential ideas of a permission structure.

On the other hand, and despite the fact that other solution concepts are briefly commented in the concluding remarks section, the results are focused on the Shapley value. The Shapley value is already considered as (one of) the most relevant solution concept(s) in transferable utility (TU) games. Yet, I believe it is specially...

Keywords

Dependence Relation Preference Structure Vote Game Balance Game Transferable Utility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Dilworth RP (1940) Lattices with unique irreducible decompositions. Ann Math 41(4):771–777CrossRefGoogle Scholar
  2. Graham DA, Marshall RC, Richard J-F (1990) Differential payments within a bidder coalition and the Shapley value. Am Econ Rev 80(3):493–510Google Scholar
  3. Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2(3):225–229CrossRefGoogle Scholar
  4. van den Brink R (2017) Games with a permission structure: a survey on generalizations and applications. TOP. doi: 10.1007/s11750-017-0440-9
  5. Young HP (1985) Monotonic solutions of cooperative games. Int J Game Theory 14(2):65–72CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.Universidade de VigoVigoSpain

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