= Core of a glove game
{title2=$\ell_i=\theta,\quad r_j=\omega-\theta$}
If there are fewer left owners than right owners, deleting any right owner leaves the grand-coalition value unchanged. The complement's core constraint and efficiency force that owner's payoff to be zero. Mixed-pair inequalities then require every left owner to receive at least $\omega$, and efficiency makes all these payoffs exactly $\omega$. Reverse the types when right owners are scarce. If both counts equal $k$, sum all $k^2$ mixed-pair inequalities. Their total is exactly $k$ times the grand-coalition payoff, so each pair sum is $\omega$. Hence all left owners receive a common $\theta\in[0,\omega]$ and all right owners $\omega-\theta$. Such allocations meet every coalition constraint because $\theta u+(\omega-\theta)v\geq\omega\min(u,v)$. This proves the complete <core> description.
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