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Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment

Author

Listed:
  • P. Jean-Jacques Herings

    (Maastricht University)

  • Andrey Meshalkin

    (Maastricht University)

  • Arkadi Predtetchinski

    (Maastricht University)

Abstract

The paper considers a class of decision problems with an infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. Our results are twofold: Firstly, we demonstrate that the set of subgame optimal policies coincides with the set of subgame perfect equilibria of the decision problem. Furthermore, the set of subgame optimal policies is contained in the set of optimal policies and the set of optimal policies is contained in the set of Nash equilibria. Secondly, we show that the set of pure subgame optimal policies is the unique minimal curb set of the decision problem. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.

Suggested Citation

  • P. Jean-Jacques Herings & Andrey Meshalkin & Arkadi Predtetchinski, 2020. "Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment," Dynamic Games and Applications, Springer, vol. 10(2), pages 478-492, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00328-w
    DOI: 10.1007/s13235-019-00328-w
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    More about this item

    Keywords

    Game theory; Decision problem; Multiple selves; Subgame perfect equilibrium; Curb sets;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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