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Log-linear Dynamics and Local Potential

  • Daijiro Okada

    ()

    (Rutgers)

  • Olivier Tercieux

    ()

    (Ecole Normale Suprieure)

We show that local potential maximizer (\cite{morris+05}) with constant weights is stochastically stable in the log-linear dynamics provided that the payoff function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of our main results as well as other concepts closely related to local potential maximizer: weighted potential maximizer, p-dominance. We also discuss the log-linear processes where each player's stochastic choice rule converges to the best response rule at different rates. For 2 player 2 action games, we examine a modified log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically stable. This in particular implies that for 2 player 2 action games a strict (p1,p2)-dominant equilibrium with p1+p2

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Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200807.

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Length: 20 pages
Date of creation: 04 Dec 2008
Date of revision:
Handle: RePEc:rut:rutres:200807
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  1. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  2. Carlos Alos-Ferrer & Nick Netzer, 2008. "The Logit-Response Dynamics," TWI Research Paper Series 28, Thurgauer Wirtschaftsinstitut, Universit�t Konstanz.
  3. Deisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Vienna Economics Papers 0318, University of Vienna, Department of Economics.
  4. David M. Frankel & Stephen Morris & Ady Pauzner, 2001. "Equilibrium Selection in Global Games with Strategic Complementarities," Cowles Foundation Discussion Papers 1336, Cowles Foundation for Research in Economics, Yale University.
  5. James Bergin & B. L. Lipman, 1994. "Evolution with state-dependent mutations," Working Papers 199411, School of Economics, University College Dublin.
  6. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  8. Daisuke Oyama & Olivier Tercieux, 2009. "Iterated potential and robustness of equilibria," Post-Print halshs-00754349, HAL.
  9. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  10. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  12. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers 1394, Cowles Foundation for Research in Economics, Yale University.
  13. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  14. Lawrence Blume, 1996. "Population Games," Game Theory and Information 9607001, EconWPA.
  15. S. Morris & R. Rob & H. Shin, 2010. "p-dominance and Belief Potential," Levine's Working Paper Archive 505, David K. Levine.
  16. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
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