Theory and Decision ( IF 0.802 ) Pub Date : 2023-09-12 , DOI: 10.1007/s11238-023-09954-8 Zeguang Cui , Erfang Shan , Wenrong Lyu
The principle of differential marginality (Casajus in Theory and Decis 71(2):163-–174) for cooperative games is a very appealing property that requires equal productivity differentials to translate into equal payoff differentials. In this paper we apply this property to axiomatic characterizations of values. We show that differential marginality implies additivity and symmetry under certain conditions. Based on this result, we propose new characterizations of the equal division and the equal surplus division values. Finally, we characterize two classes of convex combinations of values, i.e., \(\alpha\)-egalitarian Shapley values and \(\alpha\)-equal surplus division values, by employing differential marginality and establishing the uniqueness of these values on inessential games.
中文翻译:
微分边际性、非本质博弈和凸价值组合
合作博弈的差别边际原则(Casajus in Theory and Decis 71(2):163-–174)是一个非常有吸引力的特性,它需要相等的生产率差异才能转化为相等的支付差异。在本文中,我们将此属性应用于值的公理表征。我们证明,微分边际性意味着在某些条件下的可加性和对称性。基于这一结果,我们提出了等分和等余分值的新特征。最后,我们通过利用微分边际性并在非本质上建立这些值的唯一性,刻画了两类凸值组合,即\(\alpha\)-均等Shapley值和\(\alpha\)-相等剩余分值。游戏。