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The projection dynamic and the replicator dynamic

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  • Sandholm, William H.
  • DokumacI, Emin
  • Lahkar, Ratul

Abstract

We investigate a variety of connections between the projection dynamic and the replicator dynamic. At interior population states, the standard microfoundations for the replicator dynamic can be converted into foundations for the projection dynamic by replacing imitation of opponents with "revision driven by insecurity" and direct choice of alternative strategies. Both dynamics satisfy a condition called inflow-outflow symmetry, which causes them to select against strictly dominated strategies at interior states; still, because it is discontinuous at the boundary of the state space, the projection dynamic allows strictly dominated strategies to survive in perpetuity. The two dynamics exhibit qualitatively similar behavior in strictly stable and null stable games. Finally, the projection and replicator dynamics both can be viewed as gradient systems in potential games, the latter after an appropriate transformation of the state space.

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  • Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, vol. 64(2), pages 666-683, November.
  • Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:666-683
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    3. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    4. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    5. Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
    6. Dai Zusai, 2018. "Net gains in evolutionary dynamics: A unifying and intuitive approach to dynamic stability," Papers 1805.04898, arXiv.org, revised Oct 2023.
    7. Sylvain Sorin, 2023. "Continuous Time Learning Algorithms in Optimization and Game Theory," Dynamic Games and Applications, Springer, vol. 13(1), pages 3-24, March.
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    9. Laraki, Rida & Mertikopoulos, Panayotis, 2013. "Higher order game dynamics," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2666-2695.
    10. Konstantin Avrachenkov & Vivek S. Borkar, 2019. "Metastability in Stochastic Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 9(2), pages 366-390, June.
    11. Marc Harper & Dashiell Fryer, 2015. "Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex," Dynamic Games and Applications, Springer, vol. 5(3), pages 318-333, September.
    12. Jie Jin & Jun Zhuang & Qiuhong Zhao, 2018. "Supervision after Certification: An Evolutionary Game Analysis for Chinese Environmental Labeled Enterprises," Sustainability, MDPI, vol. 10(5), pages 1-22, May.
    13. Fujishima, Shota, 2013. "Growth, agglomeration, and urban congestion," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1168-1181.
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