Abstract

We propose a network formation model using the theory of stochastic games with random terminal time. Initially, the leader proposes a joint project in the form of a network to the players. Then the players have opportunities to form new links with each other to update the network proposed by the leader. Any player’s payoff is determined at any step by the network structure. It is also assumed that the formation of the links proposed by the players is random. The duration of the game is random as well. As a result of the players’ actions and the implementation of random steps of the Nature, a network is formed. We consider a cooperative approach to network formation and use the CIS-value as a cooperative solution. In this paper, we obtain a recursive formula to derive this value in any cooperative subgame. The paper also investigates the dynamic consistency of the CIS-value. The theoretical results are illustrated by a numerical example.

中文翻译：

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非对称参与者网络形成的随机模型

摘要

我们使用具有随机终端时间的随机博弈理论提出了一个网络形成模型。最初，领导者以网络的形式向玩家提出一个联合项目。然后玩家有机会彼此形成新的链接来更新领导者提出的网络。任何参与者的收益都由网络结构在任何步骤决定。还假设玩家提议的链接的形成是随机的。游戏的持续时间也是随机的。由于玩家的行为和自然随机步骤的执行，网络就形成了。我们考虑网络形成的合作方法，并使用 CIS 值作为合作解决方案。在本文中，我们获得了一个递归公式来在任何合作子博弈中推导出这个值。本文还研究了 CIS 值的动态一致性。理论结果通过一个数值例子来说明。