strong core allocation

That the allocation $x$ is a strong core allocation is

• $y_i{\succsim }_i{x}_i\forall i\in T$
• $y_j{\succ }_j{x}_j\exists j\in T$
• $\{y_i:i\in T\}=\{w_i:i\in T\}$ There must be no $T\subseteq I$ and $y\in X$ that satisfy
• Mechanism Design (Book) p.138

If it is a strong core allocation, it is efficient and individual rationality.

Individual Rationality:$x_i{\succsim }_i{w}_i\forall i\in I$

• $w_i$ is the initial holding

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