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Constrained equilibrium in a bidding problem


  • James Falk


  • Jana Hranaiova


  • Harry Gorter



There are a number of situations where firms vie for some constrained total quantity by bidding individual quantities but where the allocation is determined on a ‘pro-rated’ basis. One such example is a licenses-on-demand method of import quota allocation. Bidders are constrained to bid at most the total quantity, and if the sum of all bids exceeds this total, the awards are granted proportional to the fractional amounts that the bidders request. In this note, we identify the (Nash) equilibrium of the model, present some examples, and do a sensitivity analysis of the bids as the total amount available changes. We also look into changes of the bids when a new participant enters the bidding process. In an economic context, such allocation methods are shown to be biased in favor of the least efficient firms. Copyright Physica-Verlag 2006

Suggested Citation

  • James Falk & Jana Hranaiova & Harry Gorter, 2006. "Constrained equilibrium in a bidding problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(3), pages 299-311, September.
  • Handle: RePEc:spr:cejnor:v:14:y:2006:i:3:p:299-311
    DOI: 10.1007/s10100-006-0006-7

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    References listed on IDEAS

    1. Skully, David W., 2001. "Economics of Tariff-Rate Quota Administration," Technical Bulletins 184332, United States Department of Agriculture, Economic Research Service.
    2. Jana Hranaiova & Harry de Gorter & James Falk, 2006. "The Economics of Administering Import Quotas with Licenses-on-Demand in Agriculture," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(2), pages 338-350.
    3. Skully, David W., 2001. "Economics Of Tariff-Rate Quota Administration," Technical Bulletins 33576, United States Department of Agriculture, Economic Research Service.
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    More about this item


    Constrained equilibrium; Quantity bidding; Prorated distribution; Nash equilibrium; Licenses-on-demand; C70;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General


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