In this paper we study a model of weighted network formation. The bilateral interaction is modeled as a Tullock contest game with the possibility of a draw. We describe stable networks under different concepts of stability. We show that a Nash stable network is either the empty network or the complete network. The complete network is not immune to bilateral deviations. When we allow for limited farsightedness, a stable network immune to bilateral deviations must be a complete $M$‐partite network, with partitions of different sizes. We provide several comparative statics results illustrating the importance of the structure of stable networks in mediating the effects of shocks and interventions. In particular, we show that an increase in the likelihood of a draw has a nonmonotonic effect on the level of wasteful contest spending in the society. To the best of our knowledge, this paper is the first attempt to model weighted network formation when the actions of individuals are neither strategic complements nor strategic substitutes.

中文翻译：

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竞赛网络形成的非合作模型

在本文中，我们研究了加权网络形成的模型。双边互动被建模为Tullock竞赛游戏，有可能平局。我们描述了不同稳定性概念下的稳定网络。我们表明，纳什稳定网络可以是空网络，也可以是完整网络。完整的网络无法避免双边偏差。如果我们只允许有限的远见，那么一个稳定的，不受双边偏差影响的网络必须是完整的$\mathrm{中号}$分区网络，具有不同大小的分区。我们提供了一些比较静态的结果，这些结果说明了稳定网络结构在调解电击和干预措施影响方面的重要性。特别是，我们表明，抽奖可能性的增加对社会上浪费的比赛支出水平具有非单调的影响。据我们所知，当个人的行动既不是战略补充也不是战略替代品时，本文是对加权网络形成进行建模的首次尝试。