Chapter 9 - Stochastic Noncooperative and Cooperative Evolutionary Game Strategies of a Population of Biological Networks Under Natural Selection

Abstract

In this chapter, noncooperative and cooperative evolutionary game strategies are discussed from the stochastic Nash game perspective to investigate and compare their phenotypic robustness and network evolvability to get an insight into the evolutionary game theory of stochastic biological networks under natural selection. The noncooperative evolutionary game strategy can be transformed to an equivalent multiobjective optimization problem and significantly improve network robustness to tolerate more genetic variations and buffer more environmental disturbances to maintain the phenotypic trait longer in the evolutionary process than the cooperative evolutionary game strategy. However, the noncooperative game strategy needs to be solved with more efforts and compromises with these conflicting players than the cooperative evolutionary game strategy. In order to overcome the difficulty of solving two nonlinear stochastic evolutionary game strategies, the global linearization technique is employed to simplify the solution procedure of two evolutionary strategies. Finally, a simple example of a stochastic evolutionary metabolic pathway is given with a simulation to illustrate the solution procedure of two evolutionary game strategies and to confirm and compare their network evolutionary results in the evolutionary process.