Economic description of tolerance in a society with asymmetric social cost functions

The evolutionary game dynamics of social tolerance among heterogeneous economic agents have been discussed in an economic interaction model with asymmetric social cost functions, where the individual cost depends only on the share of intolerant people in the opposite group. We show that, very different from the symmetric function case studied previously , economic interactions between individuals in a society with asymmetric social cost functions can be exactly solved in phase plane, and rich behaviours can be revealed by using algebraic approach. Our contribution consists in offering the explicit formula of evolutionary trajectories in the phase plane for the first time. The property of equilibrium is shown to be closely related to the group populations. Based on the explicit formula in the phase plane, the equilibriums of the evolutionary dynamics can be easily identified, and the evolutionary trajectory can be exactly analysed. We also show that the explicit solutions obtained would be especially suited to effective control of the evolutionary dynamics of social tolerance. The necessary and sufficient conditions of the full tolerance equilibrium under asymmetric social cost function are also discussed, which provides guidance and reference to set policies and development strategy of social tolerance.