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On a Class of Optimization Problems with No “Effectively Computable” Solution

Author

Listed:
  • Misha Gavrilovich

    (National Research University Higher School of Economics)

  • Victoriya Kreps

    (National Research University Higher School of Economics)

Abstract

It is well-known that large random structures may have non-random macroscopic properties. We give an example of non-random properties for a class of large optimization problems related to the computational problem MAXFLS^= of calculating the maximal number of consistent equations in a given overdetermined system of linear equations. A problem of this kind is faced by a decision maker (an Agent) choosing the means to protect a house from natural disasters. For this class we establish the following. There is no “efficiently computable” optimal strategy for the Agent. When the size of a random instance of the optimization problem goes to infinity the probability that the uniform mixed strategy of the Agent is ? optimal goes to one. Moreover, there is no “efficiently computable” strategy for the Agent which is substantially better for each instance of the optimization problem

Suggested Citation

  • Misha Gavrilovich & Victoriya Kreps, 2015. "On a Class of Optimization Problems with No “Effectively Computable” Solution," HSE Working papers WP BRP 112/EC/2015, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:112/ec/2015
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    File URL: http://www.hse.ru/data/2015/11/20/1081927635/112EC2015.pdf
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    References listed on IDEAS

    as
    1. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
    2. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
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    More about this item

    Keywords

    optimization; concentration of measure; probabilistically checkable proofs;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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