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Log-linear Dynamics and Local Potential

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Author Info

  • Daijiro Okada

    ()
    (Rutgers)

  • Olivier Tercieux

    ()
    (Ecole Normale Suprieure)

Abstract

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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Bibliographic Info

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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Related research

Keywords: Log-linear dynamics; Stochastic stability; Local potential maximizer; Equilibrium selection; Comparison of Markov Chains;

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References

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  1. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-80, September.
  2. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
  4. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January.
  5. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
  6. Lawrence Blume, 1996. "Population Games," Game Theory and Information 9607001, EconWPA.
  7. 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.
  8. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
  9. Carlsson, H. & Damme, E.E.C. van, 1993. "Global games and equilibrium selection," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154416, Tilburg University.
  10. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  11. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  12. 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.
  13. Carlos Alos-Ferrer & Nick Netzer, 2008. "The Logit-Response Dynamics," TWI Research Paper Series 28, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
  14. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  15. 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.
  16. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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Citations

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Cited by:
  1. Oyama, Daisuke & Tercieux, Olivier, 2004. "Iterated Potential and Robustness of Equilibria," MPRA Paper 1599, University Library of Munich, Germany.
  2. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
  3. Carlos Alós–Ferrer & Nick Netzer, 2012. "Robust stochastic stability," ECON - Working Papers 063, Department of Economics - University of Zurich, revised Jan 2014.
  4. Carlos Alos-Ferrer & Nick Netzer, 2008. "The Logit-Response Dynamics," TWI Research Paper Series 28, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
  5. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
  6. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.

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