Fuzzy Optimization and Decision Making

, Volume 15, Issue 3, pp 281–306 | Cite as

A fundamental study for partially defined cooperative games

  • Satoshi Masuya
  • Masahiro Inuiguchi


The payoff of each coalition has been assumed to be known precisely in the conventional cooperative games. However, we may come across situations where some coalitional values remain unknown. This paper treats cooperative games whose coalitional values are not known completely. In the cooperative games it is assumed that some of coalitional values are known precisely but others remain unknown. Some complete games associated with such incomplete games are proposed. Solution concepts are studied in a special case where only values of the grand coalition and singleton coalitions are known. Through the investigations of solutions of complete games associated with the given incomplete game, we show a focal point solution suggested commonly from different viewpoints.


Cooperative game Lower game Upper game Reference point game Shapley value Nucleolus 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of Business AdministrationDaito Bunka UniversityItabashi-kuJapan
  2. 2.Graduate School of Engineering ScienceOsaka UniversityToyonakaJapan

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