Optimizing strategic blocks with asymmetric bilateral propensities with symmetric propensities

Abstract

There are models taken from physics that have been used to explain the formation of coalitions or blocks of agents. Such models are useful to understand how alliances (in wars, political parties, etc.) tend to cluster friends in same blocks and enemies in separate blocks by minimizing the total frustration. All of these models assume reciprocal interactions between agents, since this is the most common case in physics. However, we point out the important fact that human interactions are, in general, not reciprocal, i.e., there is no “social Newton ́s third law”. Here we show that this fundamental flaw of coalition models can be solved by constructing effective symmetric interactions (in which well-known physical models work) from non-reciprocal interactions. For various model cases with asymmetrical propensities we propose several qualitative strategies to achieve effective symmetric interactions. In many of these strategies we employ the symmetric average value in which propensities compete in strength to keep some partial information of the asymmetrical propensities. Keywords: 87.23.Ge Dynamics of social systems, 89.75.Fb Structures and organization in complex systems, 75.50Lk Spin glasses and other random magnets.