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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. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  2. Josef Hofbauer & Daisuke Oyama & Satoru Takahashi, 2004. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Econometric Society 2004 North American Winter Meetings 339, Econometric Society.
  3. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
  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. smorris & Takashi Ui, 2004. "Generalized Potentials and Robust Sets of Equilibria," Econometric Society 2004 North American Winter Meetings 45, Econometric Society.
  6. Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
  7. S. Morris & R. Rob & H. Shin, 2010. "p-dominance and Belief Potential," Levine's Working Paper Archive 505, David K. Levine.
  8. repec:ner:tilbur:urn:nbn:nl:ui:12-154416 is not listed on IDEAS
  9. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  10. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
  11. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
  12. Lawrence Blume, 1996. "Population Games," Game Theory and Information 9607001, EconWPA.
  13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  14. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
  15. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  16. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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