Nonlinearities in the cost and benefit functions affect the convergence stability and resistance to invasion of a candidate solution to the cost–benefit game. In (

*a*,

*b*), the

*x*-axis lies on

and the

*y*-axis lies on

. Thus, each of these functions is positive in the regions shown, satisfying the conditions that benefits are positive and costs are negative. For a given

*b*_{2} and

*c*_{2}, a candidate solution is given by equation . The line with circles (

*S*_{1}=0) separates the space into regions where the candidate solution for

*u*_{1} is either a maximum (

*S*_{1}<0) or a minimum (

*S*_{1}>0) on its adaptive landscape. The line with stars (

*S*_{2}=0) separates the space into regions where the candidate solution for

*u*_{1} is either convergent stable (

*S*_{2}<0) or convergent unstable (

*S*_{2}>0). Arrows indicate the direction that values for

*S*_{1} or

*S*_{2} are positive. The solid line indicates the values for

*b*_{2} and

*c*_{2} that will generate a candidate solution of

*u*_{1}=0.6 when (i)

*b*_{1}=6 and

*c*_{1}=4 or (ii)

*b*_{1}=2 and

*c*_{1}=4. Moving from lower left to upper right along the candidate solution curve

*u*_{1}=0.6 in (

*a*), the solution shifts from being a convergent-stable minimum (not an ESS) to a convergent-stable maximum (an ESS). Moving from lower left to upper right along the candidate solution curve

*u*_{1}=0.6 in (

*b*), the solution shifts from being an unstable minimum to an unstable maximum (neither are an ESS).

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