The equilibrium-value convergence for the multiple-partners game
研究了多伙伴博弈的复制版本，证明当复制次数趋于无穷时，沙普利值收敛到竞争均衡收益，且该结果对一大类半值也成立。
We study the assignment game (Shapley and Shubik, 1972) and its generalization of the multiple-partners game (Sotomayor, 1992), the simplest many-to-many extension. Our main result is that the Shapley value of a replicated multiple-partners game converges to a competitive equilibrium payoff when the number of replicas tends to infinity. The result also holds for a large subclass of semivalues since we prove that they converge to the same value as the replica becomes large. Furthermore, in supermodular and monotonic assignment games, the asymptotic Shapley value coincides with the mean stable imputation. The proof of our theorem relies on Hall's theorem.