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The target projection dynamic

Author

Listed:
  • Tsakas, Elias

    (Department of Economics)

  • Voorneveld, Mark

    (Dept. of Economics, Stockholm School of Economics)

Abstract

This paper studies the target projection dynamic, which is a model of myopic adjustment for population games. We put it into the standard microeconomic framework of utility maximization with control costs. We also show that it is well-behaved, since it satisfies the desirable properties: Nash stationarity, positive correlation, and existence, uniqueness, and continuity of solutions. We also show that, similarly to other well-behaved dynamics, a general result for elimination of strictly dominated strategies cannot be established. Instead we rule out survival of strictly dominated strategies in certain classes of games. We relate it to the projection dynamic, by showing that the two dynamics coincide in a subset of the strategy space. We show that strict equilibria, and evolutionarily stable strategies in $2\times2$ games are asymptotically stable under the target projection dynamic. Finally, we show that the stability results that hold under the projection dynamic for stable games, hold under the target projection dynamic too, for interior Nash equilibria.

Suggested Citation

  • Tsakas, Elias & Voorneveld, Mark, 2007. "The target projection dynamic," SSE/EFI Working Paper Series in Economics and Finance 670, Stockholm School of Economics, revised 13 Aug 2007.
    • Handle: RePEc:hhs:hastef:0670
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    Cited by:

    1. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
    2. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    3. Sylvain Sorin, 2023. "Continuous Time Learning Algorithms in Optimization and Game Theory," Dynamic Games and Applications, Springer, vol. 13(1), pages 3-24, March.
    4. Minyu Shen & Feng Xiao & Weihua Gu & Hongbo Ye, 2024. "Cognitive Hierarchy in Day-to-day Network Flow Dynamics," Papers 2409.11908, arXiv.org, revised Jun 2025.
    5. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 147-161, October.
    6. Sylvain Sorin & Cheng Wan, 2016. "Finite composite games: Equilibria and dynamics," Post-Print hal-02885860, HAL.
    7. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Philipps University Marburg, Department of Geography.
    8. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.

    More about this item

    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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