Shapley limit in a buyer-heavy exchange market ($s_k\to 1,b_k\to 0$)

For $k$ unit sellers and $3k$ unit buyers with unit surplus per trade, a coalition's value is the smaller of its seller and buyer counts. Give each player an independent uniform arrival time. Conditional on a specified seller arriving at time $t$, the previous buyers and other sellers have independent binomial counts $B\sim \mathrm{Bin}(3k,t)$ and $S\sim \mathrm{Bin}(k-1,t)$. The seller contributes one exactly when $B>S$. For fixed positive $t$ this probability tends to one; a Chebyshev bound and a split near $t=0$ also give an explicit uniform integral estimate. Averaging gives seller Shapley value tending to one. Efficiency and role symmetry give $s_k+3b_k=1$, hence the buyer value tends to zero.