On stability in dynamical Prisoner’s dilemma game with non-uniform interaction rates M.I.Shehata Mathematics Department, Faculty of Science, Mansoura 35516, EGYPT E-mail: mishehata@yahoo.com Abstract Introduction arXiv:1103.5150v1 [q-bio.PE] 26 Mar 2011 1 Stability of evolutionary dynamics of non-repeated Prisoner’s Dilemma game with non-uniform interaction rates [1], via benefit and cost dilemma is studied . Moreover , the stability condition ( $^{b}$+c b$_{−}$$_{c}$) 2 < r$_{1}$r$_{3}$ is derived in case of coexistence between cooperators and defectors .If r$_{1}$, r$_{3}$ −→ ∞ cooperation is the dominant strategy and defectors can no longer exploit cooperators. Key words: Prisoner’s Dilemma game , non-uniform interaction rates and Dynamical Prisoner’s Dilemma game. Evolutionary game theory[3] was first introduced by John Maynard Smith in 1973[2]. He invented the important concept of an evolutionarily stable strat- egy (ESS) that resist invasion of other strategies in infinitely large populations. Prisoner’s dilemma (PD) game[4] studies cooperation between unrelated indi- viduals. In non-repeated PD,individuals are either cooperators or defectors, acting accordingly whenever two of them interact. They both receive R upon mutual cooperation and P upon mutual defection. A defector exploiting a co- operator gets an amount T and the exploited cooperator receives S, such that