How to analyze models of nonlinear public goods

Marco Archetti

doi:10.3390/g9020017

How to analyze models of nonlinear public goods

Marco Archetti

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

24 Downloads (Pure)

Abstract

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

Original language	English
Article number	17
Journal	Games
Volume	9
Issue number	2
DOIs	https://doi.org/10.3390/g9020017
Publication status	Published - 4 Apr 2018

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

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10.3390/g9020017Licence: CC BY

Published manuscript
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Final published version, 5.38 MBLicence: CC BY

http://www.mdpi.com/2073-4336/9/2/17Licence: CC BY

Cite this

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

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