of generality, assume that r$_{2}$ = 1. The fitness of individuals is determined by the average payoff over a large number of interactions. Therefore, the fitness of C and D players are non-linear functions of x and y , given by The replicator equations can be reduced to where, f C = ( b − c ) r$_{1}$x − cy r$_{1}$x + y , f D = bx x + r$_{3}$y (4) ˙ x = x (1 − x )( f C − f D ) (5) f C − f D = (( b − c ) r$_{1}$x − cy )( x + r$_{3}$y $^{)}$− ( bx )( r$_{1}$x + y ) ( r$_{1}$x + y )( x + r$_{3}$y ) The equilibrium points are either on the boundary or in the interior. The boundary points x = 0 is stable equilibrium while x = 1 is unstable equilibrium. If f C − f D = 0 and x + y = 1then we have two interior equilibrium are given by where, In case of non- uniform interaction rate ,the selection dynamics depend on the size of r$_{1}$r$_{3}$ relative to ρ $^{2}$.[1] where, x ∗ = − ( α − 2 γ $^{)}$± √ α 2 − 4 βγ 2( β + γ − α ) (6) α = r$_{1}$r$_{3}$ ( b − c $^{)}$− ( b + c ) , β = − r$_{1}$c , γ = − r$_{3}$c α 2 > 4 βγ , β + γ < α , α > 2 γ , α > 2 β 4