Competitive balance theory: Modeling conflict of interest in a heterogeneous network

The dynamics of networks on Heider's balance theory moves toward reducing the tension by constantly reevaluating the interactions to achieve a state of balance. Conflict of interest, however, is inherent in most complex systems; frequently, there are multiple ideals or states of balance, and moving towards one could work against another. In this paper, by introducing the competitive balance theory, we study the evolution of balance in the presence of conflicts of interest. In our model, the assumption is that different states of balance compete in the evolution process to dominate the system. We ask whether, through these interactions, different states of balance compete to prevail their own ideals or a set of coexisting ideals in a balanced condition is a possible outcome. The results show that although there is a symmetry in the type of balance the system either evolves towards a symmetry breaking, where one of the states of balance dominates the system, or, less frequently, the competing states of balance coexist in a jammed state.