Heterogeneity of Some Cooperation/Competition Properties

We show that the heterogeneity index, which was proposed by Hu and Wang [Physica A 387 (2008) 3769], can be used to describe the disparity of the cooperation sharing or competition gain distributions, which is very important for understanding the dynamics of a cooperation/competition system. An analytical relation between the distribution parameters and the heterogeneity index is derived, which is in good agreement with the empirical results. Our theoretical and empirical analyses also show that the relation between the distribution parameters can be analytically derived from the so-called Zhang-Chang model [Physica A 360 (2006) 599; 383 (2007) 687). This strongly recommends a possibility to create a general dynamic cooperation/competition model.