Abstract
We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner.
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We thank two referees, Ulrich Witt and audiences in Tilburg, Amsterdam and Stony Brook for comments and suggestions for improvement.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Joosten, R., Roorda, B. On evolutionary ray-projection dynamics. Math Meth Oper Res 74, 147–161 (2011). https://doi.org/10.1007/s00186-010-0342-1
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DOI: https://doi.org/10.1007/s00186-010-0342-1