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Simple Adaptive Strategies:From Regret-Matching to Uncoupled Dynamics

Author

Listed:
  • Sergiu Hart

    (The Hebrew University of Jerusalem, Israel)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Spain)

Abstract

This volume collects almost two decades of joint work of Sergiu Hart and Andreu Mas-Colell on game dynamics and equilibria. The starting point was the introduction of the adaptive strategy called regret-matching , which on the one hand is simple and natural, and on the other is shown to lead to correlated equilibria. This initial finding ¡ª boundedly rational behavior that yields fully rational outcomes in the long run ¡ª generated a large body of work on the dynamics of simple adaptive strategies. In particular, a natural condition on dynamics was identified: uncoupledness , whereby decision-makers do not know each other's payoffs and utilities (so, while chosen actions may be observable, the motivations are not). This condition turns out to severely limit the equilibria that can be reached. Interestingly, there are connections to the behavioral and neurobiological sciences and also to computer science and engineering (e.g., via notions of ¡°regret¡±). Simple Adaptive Strategies is self-contained and unified in its presentation. Together with the formal treatment of concepts, theorems, and proofs, significant space is devoted to informal explanations and illuminating examples. It may be used for advanced graduate courses ¡ª in game theory, economics, mathematics, computer science, engineering ¡ª and for further research. Contents: Correlated Equilibria: Existence of Correlated Equilibria (Sergiu Hart and David Schmeidler) Regret Matching: A Simple Adaptive Procedure Leading to Correlated Equilibrium (Sergiu Hart and Andreu Mas-Colell) A General Class of Adaptive Strategies (Sergiu Hart and Andreu Mas-Colell) A Reinforcement Procedure Leading to Correlated Equilibrium (Sergiu Hart and Andreu Mas-Colell) Regret-Based Continuous-Time Dynamics (Sergiu Hart and Andreu Mas-Colell) General Procedures Leading to Correlated Equilibria (Amotz Cahn) Uncoupled Dynamics: Uncoupled Dynamics Do Not Lead to Nash Equilibrium (Sergiu Hart and Andreu Mas-Colell) Stochastic Uncoupled Dynamics and Nash Equilibrium (Sergiu Hart and Andreu Mas-Colell) Uncoupled Automata and Pure Nash Equilibria (Yakov Babichenko) How Long to Equilibrium? The Communication Complexity of Uncoupled Equilibrium Procedures (Sergiu Hart and Yishay Mansour) Dynamics and Equilibria: Adaptive Heuristics (Sergiu Hart) Nash Equilibrium and Dynamics (Sergiu Hart) Readership: Graduate students and researchers in game theory, economic theory, econometrics, computer science and engineering. Key Features: Prominent authors (two world-leading game theorists) Significant cutting-edge body of research Novel ideas and insights that are useful and applicable in many areas

Suggested Citation

  • Sergiu Hart & Andreu Mas-Colell, 2013. "Simple Adaptive Strategies:From Regret-Matching to Uncoupled Dynamics," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8408, October.
  • Handle: RePEc:wsi:wsbook:8408
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    Citations

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    Cited by:

    1. Hart, Sergiu & Nisan, Noam, 2018. "The query complexity of correlated equilibria," Games and Economic Behavior, Elsevier, vol. 108(C), pages 401-410.
    2. Parras, Juan & Zazo, Santiago, 2020. "A distributed algorithm to obtain repeated games equilibria with discounting," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Yakov Babichenko & Siddharth Barman & Ron Peretz, 2017. "Empirical Distribution of Equilibrium Play and Its Testing Application," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 15-29, January.
    4. Foster, Dean P. & Hart, Sergiu, 2018. "Smooth calibration, leaky forecasts, finite recall, and Nash dynamics," Games and Economic Behavior, Elsevier, vol. 109(C), pages 271-293.
    5. Gregory Pavlov, 2013. "Correlated Equilibria and Communication Equilibria in All-pay Auctions," UWO Department of Economics Working Papers 20132, University of Western Ontario, Department of Economics.
    6. Li, Zifan & Tewari, Ambuj, 2018. "Sampled fictitious play is Hannan consistent," Games and Economic Behavior, Elsevier, vol. 109(C), pages 401-412.
    7. Drew Fudenberg & David K Levine, 2013. "Learning with Recency Bias," Levine's Bibliography 786969000000000846, UCLA Department of Economics.

    More about this item

    Keywords

    Game Theory; Dynamics; Equilibrium; Nash Equilibrium; Correlated Equilibrium; Adaptive Dynamics; Simple Strategies; Regret-Based Strategies; Uncoupled Dynamics; Bounded Rationality;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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