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Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

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  • Qian Zhuang
  • Zengru Di
  • Jinshan Wu

Abstract

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs.

Suggested Citation

  • Qian Zhuang & Zengru Di & Jinshan Wu, 2014. "Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-16, August.
    • Handle: RePEc:plo:pone00:0105391
    DOI: 10.1371/journal.pone.0105391
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    References listed on IDEAS

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    3. Drew Fudenberg & David K. Levine, 2009. "Learning and Equilibrium," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 385-420, May.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    5. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, April.
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    Cited by:

    1. Benndorf, Volker & Martínez-Martínez, Ismael, 2017. "Perturbed best response dynamics in a hawk–dove game," Economics Letters, Elsevier, vol. 153(C), pages 61-64.
    2. Ivan S Menshikov & Alexsandr V Shklover & Tatiana S Babkina & Mikhail G Myagkov, 2017. "From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-17, November.
    3. Lee, Joung Hun & Kakinuma, Kaoru & Okuro, Toshiya & Iwasa, Yoh, 2015. "Coupled social and ecological dynamics of herders in Mongolian rangelands," Ecological Economics, Elsevier, vol. 114(C), pages 208-217.

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