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Bayesian Estimation of Linear Sum Assignment Problems

In: Essays in Honor of Cheng Hsiao

Author

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  • Yu-Wei Hsieh
  • Matthew Shum

Abstract

The authors propose an Markov Chain Monte Carlo (MCMC) method for estimating a class of linear sum assignment problems (LSAP; the discrete case of the optimal transport problems). Prominent examples include multi-item auctions and mergers in industrial organizations. This contribution is to decompose the joint likelihood of the allocation and prices by exploiting the primal and dual linear programming formulation of the underlying LSAP. Our decomposition, coupled with the data augmentation technique, leads to an MCMC sampler without a repeated model-solving phase.

Suggested Citation

  • Yu-Wei Hsieh & Matthew Shum, 2020. "Bayesian Estimation of Linear Sum Assignment Problems," Advances in Econometrics, in: Essays in Honor of Cheng Hsiao, volume 41, pages 323-339, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320200000041011
    DOI: 10.1108/S0731-905320200000041011
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    More about this item

    Keywords

    Linear sum assignment problems; two-sided matching; MCMC; position auction; optimal transport; sponsored-search auction; D44; D47; C11; C15;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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