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demanding that- if W(x′,x∗)=W(x∗,x∗) for some x′≠x∗ then W(x′,x′)<W(x∗,x′). A Nash equilibrium strategy x* satisfies this second condition. 2. If the resident population is perturbed away from x* then natural selection will lead back to x*. When the trait x is one-dimensional, this will happen if