Game theoretic model for control of gene regulatory networks

The intervention in gene regulatory networks has been modelled as the Markov decision process problem. However, this approach only allows one external control, which is inadequate in many situations such as drug and gene therapies. In this paper, we propose the non-cooperative stochastic game model for intervention in the genetic regulatory networks as the generalization of the Markov decision process approach and formulate the intervention problem into solving the Nash equilibrium. The definition of equilibrium has been proposed and the existences for both infinite and finite horizon cases have been proven. We provide the numerical example for using non-cooperative stochastic game model on the mammalian cell cycle network. We also compare the results under the Nash equilibrium and independent Markov decision process approach.