Fuzzy Core and Equilibria of Games Defined in Strategic Form

  • Jean-Pierre Aubin


Let us consider a n-person game \({\left\{ {{\text{X}}\left( {\text{A}} \right),{{\text{F}}^{\text{A}}}} \right\}_{{\text{A}}\,\,\,\,\, \in \,\,\,\,\alpha }}\) described in strategic form by
  1. 1)

    a family α of coalitions A C N, where \({\text{N}} = \left\{ {1,2, \ldots ,{\text{n}}} \right\}\) is the whole set of players

  2. 2)

    multistrategy subsets X(A) of \({{\text{X}}^{\text{A}}} = \mathop \Pi \limits_{{\text{i}}\,\,\, \in \,\,\,{\text{A}}} \,\,\,{{\text{x}}^{\text{i}}}\) of the coalition A

  3. 3)

    multiloss operators FA = \({{\text{F}}^{\text{A}}} = {\left\{ {{\text{f}}_{\text{i}}^{\text{A}}} \right\}_{{\text{i}}\,\,\,\, \in \,\,\,\,\,{\text{A}}}}\) where \({\text{f}}_{\text{i}}^{\text{A}}\,\,:\,\,{{\text{X}}^{\text{i}}}\,\, \to \,\,\mathbb{R}\) is the loss function of player i behaving as member of coalition A.



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Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.Université Paris-IX DauphineParis Cedex 16France

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