Econ Papers Daily / 期刊论文
学位必要性的本质
Essentiality of degree
摘要
Cooperative game theory has proposed different notions of powerful players. For example, big-boss games (Muto et al. 1988 On Big Boss Games. In: The economic studies quarterly 39.4:303–321")) and clan games (Potters et al. 1989 Clan Games. In: Games and Economic Behavior 1.3:275–293")) are particular cases of veto games (Bahel 2016 On the Core and Bargaining Set of a Veto Game. In: International Journal of Game Theory 45.3:543–566")). The present paper extends these veto games by assuming that there is a given subset of powerful (or essential) players, but only a few (as opposed to all) essential players are required for a coalition to have a positive group value. The resulting games, which are called r -essential games, encompass convex games (Shapley 1971 Cores of Convex Games. In: International Journal of Game Theory 1.1:11–26")) and veto games. We show that r -essential games have a nonempty core. We give a recursive description of the core. Moreover, it is shown that the core and the bargaining set are equivalent for r -essential games. An application to networks is provided. Similar content being viewed by others
中文摘要
合作博弈理论提出了多种关于强有力参与者的概念。例如，大老板博弈（Muto等，1988，《论大老板博弈》，载于《经济研究季刊》第39卷第4期，第303-321页）和宗族博弈（Potters等，1989，《宗族博弈》，载于《博弈与经济行为》第1卷第3期，第275-293页）是否决博弈（Bahel，2016，《否决博弈的核心与谈判集》，载于《国际博弈论杂志》第45卷第3期，第543-566页）的特例。本文通过假设存在一个给定的强有力（或关键）参与者子集，但仅需少数（而非全部）关键参与者即可使联盟具有正群体价值，从而扩展了这些否决博弈。由此产生的博弈被称为r-关键博弈，它涵盖了凸博弈（Shapley，1971，《凸博弈的核心》，载于《国际博弈论杂志》第1卷第1期，第11-26页）和否决博弈。我们证明r-关键博弈具有非空核心，并给出了核心的递归描述。此外，研究表明对于r-关键博弈，核心与谈判集是等价的。本文还提供了在网络中的应用。