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Monotone Decision Rules and Supermodularity

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  • Gregorio Curello

Abstract

We study decision problems under uncertainty involving the choice of a rule mapping states into actions. We show that for any rule, there exists an increasing rule generating higher expected value for all payoff functions that are supermodular in action and state. We present applications to problems of taxation, betting, and price-discrimination in markets with demand externalities. We then consider rules mapping noisy signals of the state into actions. Under some conditions, optimal rules are increasing when (a) several agents are constrained to choose a single rule or (b) the relationship between signal and state is ambiguous. Moreover, standard informativeness criteria apply.

Suggested Citation

  • Gregorio Curello, 2024. "Monotone Decision Rules and Supermodularity," CRC TR 224 Discussion Paper Series crctr224_2024_567, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2024_567
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp567
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    Keywords

    monotone comparative statics; rearrangement; optimal taxation; price discrimination; uncertainty; informativeness;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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