strong core allocation

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

• $y_i \succsim_i x_i \quad \forall i \in T$
• $y_j \succ_j x_j \quad \exists j \in T$
• ${y_i: i \in T} = { w_i: i \in T}$ 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:$x_i \succsim_i w_i \quad \forall i \in I$

• $w_i$ is the initial holding

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