Advanced Search
Article Contents
Article Contents

A Bayesian equilibrium for simultaneous first-price auctions for complementary goods and quasi-linear bids

  • * Corresponding author: karla.zarur@uaslp.mx

    * Corresponding author: karla.zarur@uaslp.mx 

The first author is supported by CONACyT grant 2019-000002-01NACF-06046

Abstract Full Text(HTML) Related Papers Cited by
  • This article shows a Symmetrical Bayesian Nash Equilibrium in a context of $ m $ simultaneous first-price sealed-bid auctions and $ n $ bidders for complementary goods. We consider that the individual valuations of the $ m $ goods are common knowledge and identical among bidders and if the whole set of goods is gained, a private independent extra profit is obtained by the winner. For relaxing and solving the so-many mathematical complications involved in the general case we followed a classical methodology and proposed a particular bidding function that implies linear separability. Under this assumptions we obtain a Symmetric Bayesian Nash Equilibrium which functional form implies the classic quasi-linear property for bivariate functions. On addition, we compare the seller expected revenue between auctioning the complete set in one single first-price sealed-bid auction versus auctioning each item in $ m $ simultaneous first-price sealed-bid auctions.

    Mathematics Subject Classification: Primary: 91B26.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] J. C. Harsanyi, Games with incomplete information played by bayesian players, Ⅰ–Ⅲ part Ⅰ. The basic model, Management Science, 14 (1967), 159-182.  doi: 10.1287/mnsc.14.3.159.
    [2] O. Morgenstern, A. Tucker and W. Vickrey, Auctions and bidding games, in Recent Advances in Game Theory, Princeton University Press, Princeton, 1962.
    [3] P. R. Milgrom and R. J. Weber, A theory of auctions and competitive bidding, Econometrica, 50 (1982), 1089-1122.  doi: 10.2307/1911865.
    [4] H. P. Young and Z. Shmuel, Handbook of game theory with economic applications, Elsevier, 4 (2015).
    [5] P. L. Lorentziadis, Optimal bidding in auctions from a game theory perspective, European Journal of Operational Research, 248 (2016), 347-371.  doi: 10.1016/j.ejor.2015.08.012.
    [6] V. Krishna and R. W. Rosental, Simultaneous auctions with synergies, Games and Economic Behavior, 17 (1996), 1-31.  doi: 10.1006/game.1996.0092.
    [7] R. W. Rosental and R. Wang, Simultaneous auctions with synergies and common values, Games and Economic Behavior, 17 (1996), 32-55.  doi: 10.1006/game.1996.0093.
    [8] B. Szentes and R. W. Rosenthal, Three-object two-bidder simultaneous auctions: Chopsticks and tetrahedra, Games and Economic Behavior, 44 (2003), 114-133.  doi: 10.1016/S0899-8256(02)00530-4.
    [9] B. Szentes, Two-object two-bidder simultaneous auctions, International Game Theory Review, 9 (2007), 483-493.  doi: 10.1142/S0219198907001552.
    [10] H. EtzionE. Pinker and A. Seidmann, Analyzing the simultaneous use of auctions and posted prices for online selling, Manufacturing and Service Operations Management, 8 (2006), 68-91.  doi: 10.1287/msom.1060.0101.
    [11] J. C. Harsanyi, Games with incomplete information played by bayesian players, Ⅰ–Ⅲ part Ⅱ. Bayesian equilibrium points, Management Science, 14 (1968), 320-334.  doi: 10.1287/mnsc.14.5.320.
  • 加载中

Article Metrics

HTML views(851) PDF downloads(573) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint