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The target projection dynamic

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series 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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Keywords: target projection dynamic; noncooperative games; adjustment;

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  1. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  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. Voorneveld, Mark, 2003. "Probabilistic choice in games: properties of Rosenthal's t-solutions," Working Paper Series in Economics and Finance 542, Stockholm School of Economics, revised 31 Oct 2003.
  4. 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.
  5. 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.
  6. 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.
  7. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
  8. Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
  9. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  10. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  11. 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.
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Cited by:
  1. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Max Planck Institute of Economics, Evolutionary Economics Group.
  2. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Computational Statistics, Springer, vol. 74(2), pages 147-161, October.
  3. 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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