For general-sum, n-player, strategic games with transferable utility, the Harsanyi-Shapley value provides a computable method to both 1) quantify the strategic value of a player; and 2) make cooperation rational through side payments. We give a simple formula to compute the HS value in normal-form games. Next, we provide two methods to generalize the HS values to stochastic (or Markov) games, and show that one of them may be computed using generalized Q-learning algorithms. Finally, an empirical validation is performed on stochastic grid-games with three or more players. Source code is provided to compute HS values for both the normal-form and stochastic game setting.

翻译：对于具有可转移效用的n人一般和战略博弈，Harsanyi-Shapley值提供了一种可计算方法，既能1)量化玩家的战略价值，又能2)通过旁支付使合作具有合理性。我们给出了正规型博弈中计算HS值的简单公式。接着，我们提出了两种将HS值推广到随机（或马尔可夫）博弈的方法，并表明其中一种方法可以通过广义Q学习算法进行计算。最后，我们在三个或更多玩家的随机网格博弈上进行了实证验证。提供了用于计算正规型和随机博弈设定下HS值的源代码。