ρ = b + c b − c and ρ > 1 . (7) If r$_{1}$r$_{3}$ < ( b + c b − $_{c}$) 2 then defection is the dominant strategy. When r$_{1}$r$_{3}$ = ( b + c b − $_{c}$) $^{2}$. we have the bifurcation [8] point at If r$_{1}$r$_{3}$ > ( b + c b − $_{c}$) 2 the two interior equilibria (6) move symmetrically away from the bifurcation point (8) toward the end points. As r$_{1}$ and r$_{3}$ increase the stable interior equilibrium point moves from the bifurcation point (8) closer toward 1.Whereas, unstable interior equilibrium point moves from the bifurcation point (8) closer toward 0.As r$_{1}$, r$_{3}$ −→ ∞ we recover the case where r$_{2}$ = 0 and cooperation is the dominant strategy as defectors can no longer exploit cooperators. x ∗ = √ r$_{3}$ √ r$_{1}$ + √ r$_{3}$ (8) 3 Conclusion For the non-repeated PD game, coexistence between cooperators and defectors is possible if the ratio of homogeneous r$_{1}$, r$_{3}$ over heterogeneous r$_{2}$ interaction rates exceeds a critical value. If r$_{1}$ = r$_{3}$ = ρ , then the pair of equilibria ap- proaches cooperator frequency of x = 1 2 which is entirely independent of the payoff matrix, as long as b > b − c > 0 > − c . Both equilibria are stable, one consists of defectors alone, and the other consists of a mixture of defectors and cooperators. References [1] Taylor C,Nowak M.A ,2006. Evolutionary game dynamics with non-uniform interaction rates. Theor Popul Biol 69: 243-252. 5