Many interactions from linear production problems, financial markets, or sequencing problems are modeled by cooperative games where payoffs to a coalition of players is a random variable. For this class of cooperative games, we introduce a two-stage value as an ex-ante agreement among players. Players are first promised their prior Shapley shares which are exactly their respective shares by the Shapley value of the expectation game. The final payoff vector is obtained by equally re-allocating the surplus when a realization of the random payoff of the grand coalition is observed. In support of the tractability of the newly introduced value called equal-surplus Shapley value, we provide a simple and compact formula. Depending on which probability distributions over the sample spaces are admissible, we present several characterization results of the equal-surplus Shapley value. This is achieved by using some classical axioms together with some other appealing axioms such as the independence of local duplication which simply requires that individual shares in a game remain unchanged when only certain events are duplicated in the sample space of a coalition without altering the probability of observing the others.

线性生产问题，金融市场或排序问题产生的许多相互作用都是通过合作博弈来建模的，在这种博弈中，玩家联盟的收益是一个随机变量。对于此类合作游戏，我们引入两个阶段的价值作为玩家之间的事前协议。首先通过期望游戏的Shapley值向玩家保证其先前的Shapley份额恰好是其各自的份额。当观察到大联盟的随机收益的实现时，通过均等地重新分配剩余来获得最终收益向量。为了支持新引入的等值Shapley值的易处理性，我们提供了一个简单紧凑的公式。根据样本空间上哪些概率分布是可接受的，我们给出了等盈余Shapley值的几个表征结果。这是通过使用一些经典公理以及一些其他有吸引力的公理（例如局部复制的独立性）来实现的，该公理仅要求在联盟的样本空间中仅复制某些事件时，游戏中的各个份额保持不变，而不会改变观察其他人。