# Fuzzy Core and Equilibria of Games Defined in Strategic Form

• Jean-Pierre Aubin
Chapter

## Abstract

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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