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Implementable Mechanisms for discrete utility functions, a solution using Tropical Geometry

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  • Juli√°n Enrique Chitiva Bocanegra

Abstract

For mechanisms with two possible outcomes and a unique agent with two posible types, we state sufficient and necessary conditions over the type space that guarantees the existence of an incentive compatible mechanism. By using tropical geometry, we found that these conditions rely only on the relative valuations to be increasing over types. This result extends implementability for discrete utility functions.

Suggested Citation

  • Juli√°n Enrique Chitiva Bocanegra, 2019. "Implementable Mechanisms for discrete utility functions, a solution using Tropical Geometry," Documentos CEDE 17485, Universidad de los Andes, Facultad de Economía, CEDE.
    • Handle: RePEc:col:000089:017485
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    References listed on IDEAS

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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