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The target projection dynamic

  • Tsakas, Elias

    (Department of Economics)

  • Voorneveld, Mark


    (Dept. of Economics, Stockholm School of Economics)

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.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 670.

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Length: 21 pages
Date of creation: 13 Aug 2007
Date of revision: 13 Aug 2007
Handle: RePEc:hhs:hastef:0670
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  1. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
  2. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
  3. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.
  4. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  5. 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.
  6. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  7. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," NajEcon Working Paper Reviews 625018000000000226,
  8. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  9. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  10. Mark Voorneveld, 2006. "Probabilistic Choice in Games: Properties of Rosenthal’s t-Solutions," International Journal of Game Theory, Springer, vol. 34(1), pages 105-121, April.
  11. 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.
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