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Unpredictability of complex (pure) strategies

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  • Hu, Tai-Wei

Abstract

Unpredictable behavior is central to optimal play in many strategic situations because predictable patterns leave players vulnerable to exploitation. A theory of unpredictable behavior based on differential complexity constraints is presented in the context of repeated two-person zero-sum games. Each player's complexity constraint is represented by an endowed oracle and a strategy is feasible if it can be implemented with an oracle machine using that oracle. When one player's oracle is sufficiently more complex than the other player's, an equilibrium exists with one player fully exploiting the other. If each player has an incompressible sequence (relative to the opponent's oracle) according to Kolmogorov complexity, an equilibrium exists in which equilibrium payoffs are equal to those of the stage game and all equilibrium strategies are unpredictable. A full characterization of history-independent equilibrium strategies is also obtained.

Suggested Citation

  • Hu, Tai-Wei, 2014. "Unpredictability of complex (pure) strategies," Games and Economic Behavior, Elsevier, vol. 88(C), pages 1-15.
    • Handle: RePEc:eee:gamebe:v:88:y:2014:i:c:p:1-15
    DOI: 10.1016/j.geb.2014.08.002
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    References listed on IDEAS

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    Cited by:

    1. Bavly, Gilad & Peretz, Ron, 2015. "How to gamble against all odds," Games and Economic Behavior, Elsevier, vol. 94(C), pages 157-168.

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    More about this item

    Keywords

    Kolmogorov complexity; Objective probability; Frequency theory of probability; Mixed strategy; Zero-sum game; Algorithmic randomness;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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