Public goods games often assume that the effect of the public good is a linear function of the\nnumber of contributions. In many cases, however, especially in biology, public goods have nonlinear\neffects, and nonlinear games are known to have dynamics and equilibria that can differ dramatically\nfrom linear games. Here I explain how to analyze nonlinear public goods games using the properties\nof Bernstein polynomials, and how to approximate the equilibria. I use mainly examples from the\nevolutionary game theory of cancer, but the approach can be used for a wide range of nonlinear\npublic goods games.
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