The competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks. In this model, two different paradigms or interests compete with each other to dominate the network's relations and impose their own values. In this paper, using the mean-field method, we examine the thermal behavior of the competitive balance model. Our results show that under a certain temperature, the symmetry between two competing interests will spontaneously break which leads to a discrete phase transition. So, starting with a heterogeneous signed network, if agents aim to decrease tension stemming from competitive balance theory, evolution ultimately chooses only one of the existing interests and stability arises where one paradigm dominates the system. The critical temperature depends linearly on the number of nodes, which is a linear dependence in the thermal balance theory as well. Finally, the results obtained through the mean-field method are verified by a series of simulations.

中文翻译：

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竞争均衡理论中签名网络临界行为的均值解

竞争性余额模型已被提议作为平衡模型的扩展，以解决已签名网络中的利益冲突。在此模型中，两个不同的范式或利益相互竞争，以支配网络的关系并施加自己的价值。在本文中，我们采用均值场方法研究了竞争平衡模型的热行为。我们的结果表明，在一定温度下，两个相互竞争的利益之间的对称性将自发地破裂，从而导致离散的相变。因此，从异类签名网络开始，如果代理商旨在降低竞争均衡理论所产生的压力，则进化最终只会选择一种现有利益，而在一种范式主导系统的情况下会出现稳定性。临界温度与节点数成线性关系，这在热平衡理论中也呈线性关系。最后，通过一系列模拟验证了通过均值场方法获得的结果。