  Competitive balance model has been proposed as an extension to the balance
model to address the conflict of interests in signed networks arXiv:2001.04664
. In this model two different paradigms compete with each other due to the
competitive interests to dominate the system and impose their own values. Using
mean-field solution method in this paper, we examine the thermal behavior of
the competitive balance model. Our results show that under a certain
temperature, the symmetry between two competitive interests will spontaneously
break which leads to a discrete phase transition. So, starting with a
heterogeneous signed network, if agents aim to ultimately decrease tension
stemming from balance theory, evolution ultimately chooses only one of the
existing interests and stability arises where one paradigm dominates the
network. The critical temperature depends linearly on the number of nodes,
which was a linear dependence in the thermal balance theory as well. Finally
the results obtained through the mean-field theory are verified by a series of
simulations.
