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Reference-dependent preferences, super-dominance and stochastic stability

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  • Sawa, Ryoji
  • Wu, Jiabin

Abstract

This paper investigates stochastic stability of noisy best response dynamics with reference-dependent preferences. We define a strategy as super-dominant in a 2 × 2 coordination game if it is the maximin strategy in terms of monetary returns and the state that all players play it constitutes an equilibrium which Pareto-dominates all other equilibria. If such a strategy exists, the corresponding equilibrium, which we call the super-dominant equilibrium, is uniquely stochastically stable for the BRM choice rule (the best response choice rule with uniform random errors) given any model of reference-dependent preferences. However, for any 2 × 2 coordination game with a super-dominant strategy, there exists a model of reference-dependent preferences with which the super-dominant equilibrium fails to be stochastically stable for the logit choice rule.

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  • Sawa, Ryoji & Wu, Jiabin, 2018. "Reference-dependent preferences, super-dominance and stochastic stability," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 96-104.
    • Handle: RePEc:eee:mateco:v:78:y:2018:i:c:p:96-104
    DOI: 10.1016/j.jmateco.2018.08.002
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    3. Roberto Rozzi, 2021. "Competing Conventions with Costly Information Acquisition," Games, MDPI, vol. 12(3), pages 1-29, June.
    4. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    5. Sawa, Ryoji & Wu, Jiabin, 2018. "Prospect dynamics and loss dominance," Games and Economic Behavior, Elsevier, vol. 112(C), pages 98-124.
    6. Khan, Abhimanyu, 2022. "Expected utility versus cumulative prospect theory in an evolutionary model of bargaining," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    7. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    8. Daniel Christopher Opolot, 2022. "On the relationship between p-dominance and stochastic stability in network games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 307-351, June.
    9. Nax, Heinrich H. & Newton, Jonathan, 2019. "Risk attitudes and risk dominance in the long run," Games and Economic Behavior, Elsevier, vol. 116(C), pages 179-184.

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