Core allocations may not be Walras allocations in any large finite economy with indivisible commodities

We consider an exchange economy where every commodity can be consumed only in integer amounts. Inoue [Inoue, T., 2005. Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only. Journal of Mathematical Economics 41, 571-601] proved that in such an economy with a continuum of agents, the core coincides with the set of Walras allocations. We show that this equivalence holds only in an atomless economy by giving two examples of the sequence of replica economies such that in any replica economy, there exists a core allocation that is not a Walras allocation. -- Indivisible commodities ; Core ; Walras equilibrium ; Strong core ; Cost-minimized Walras equilibrium