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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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References

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  1. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2141-2166, November.
  2. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, American Economic Association, vol. 93(5), pages 1830-1836, December.
  3. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  4. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, Elsevier, vol. 124(2), pages 149-170, October.
  5. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  6. Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(2), pages 666-683, November.
  7. Voorneveld, Mark, 2003. "Probabilistic choice in games: properties of Rosenthal's t-solutions," Working Paper Series in Economics and Finance, Stockholm School of Economics 542, Stockholm School of Economics, revised 31 Oct 2003.
  8. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  9. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2265-2294, November.
  10. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, Elsevier, vol. 41(1), pages 61-78, October.
  11. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(2), pages 565-590, November.
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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, Elsevier, vol. 64(2), pages 565-590, November.
  2. 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.
  3. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Computational Statistics, Springer, Springer, vol. 74(2), pages 147-161, October.

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