Abstract
Since the precore violates (weak) converse consistency, two converse consistent enlargements are proposed. These two converse consistent enlargements are the smallest (weak) converse consistent solutions that contain the precore. On the other hand, we turn to a different notion of the reduction by considering the players and the activity levels simultaneously. Based on such revised reductions, we offer several axiomatizations of the precore.
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Notes
By the fact “ if \(x\in C_P(N,m,v)\) then for all \(y \in C(S,m_S,v_{S,x}^\mathrm{DM} )\), \((y, x|_{N{\setminus } S}) \in C_P(N,m,v)\) where \(S\subset N\) ”, one could verify that \(\sigma \) satisfies DMCON. This is left to reader.
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Liao, YH. The precore: converse consistent enlargements and alternative axiomatic results. TOP 26, 146–163 (2018). https://doi.org/10.1007/s11750-017-0463-2
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DOI: https://doi.org/10.1007/s11750-017-0463-2