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
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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