• Previous Article
    On the impact of the Covid-19 health crisis on GDP forecasting: An empirical approach
  • JDG Home
  • This Issue
  • Next Article
    On two-player games with pure strategies on intervals $ [a, \; b] $ and comparisons with the two-player, two-strategy matrix case
doi: 10.3934/jdg.2022007
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

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

1. 

Universidad Autónoma de San Luis Potosí, School of Science, Av. Chapultepec No. 1570, Mexico

2. 

Universidad Autónoma de San Luis Potosí, School of Economics, Av. Pintores S/N, Mexico

* Corresponding author: karla.zarur@uaslp.mx

Received  August 2021 Revised  February 2022 Early access March 2022

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

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.

Citation: Karla Flores-Zarur, William Olvera-Lopez. A Bayesian equilibrium for simultaneous first-price auctions for complementary goods and quasi-linear bids. Journal of Dynamics and Games, doi: 10.3934/jdg.2022007
References:
[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.

show all references

References:
[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.

[1]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics and Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006

[2]

Priyanjana M. N. Dharmawardane. Decay property of regularity-loss type for quasi-linear hyperbolic systems of viscoelasticity. Conference Publications, 2013, 2013 (special) : 197-206. doi: 10.3934/proc.2013.2013.197

[3]

Vasily Denisov and Andrey Muravnik. On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations. Electronic Research Announcements, 2003, 9: 88-93.

[4]

Shunfu Jin, Haixing Wu, Wuyi Yue, Yutaka Takahashi. Performance evaluation and Nash equilibrium of a cloud architecture with a sleeping mechanism and an enrollment service. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2407-2424. doi: 10.3934/jimo.2019060

[5]

Yongqin Liu, Shuichi Kawashima. Global existence and asymptotic behavior of solutions for quasi-linear dissipative plate equation. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1113-1139. doi: 10.3934/dcds.2011.29.1113

[6]

Xueqin Peng, Gao Jia. Existence and asymptotical behavior of positive solutions for the Schrödinger-Poisson system with double quasi-linear terms. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2325-2344. doi: 10.3934/dcdsb.2021134

[7]

Xiaolin Xu, Xiaoqiang Cai. Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial and Management Optimization, 2008, 4 (4) : 843-859. doi: 10.3934/jimo.2008.4.843

[8]

Vitali Liskevich, Igor I. Skrypnik. Pointwise estimates for solutions of singular quasi-linear parabolic equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1029-1042. doi: 10.3934/dcdss.2013.6.1029

[9]

Tuhin Ghosh, Karthik Iyer. Cloaking for a quasi-linear elliptic partial differential equation. Inverse Problems and Imaging, 2018, 12 (2) : 461-491. doi: 10.3934/ipi.2018020

[10]

Christopher Grumiau, Marco Squassina, Christophe Troestler. On the Mountain-Pass algorithm for the quasi-linear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1345-1360. doi: 10.3934/dcdsb.2013.18.1345

[11]

Timur Akhunov. Local well-posedness of quasi-linear systems generalizing KdV. Communications on Pure and Applied Analysis, 2013, 12 (2) : 899-921. doi: 10.3934/cpaa.2013.12.899

[12]

Boris Buffoni, Laurent Landry. Multiplicity of homoclinic orbits in quasi-linear autonomous Lagrangian systems. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 75-116. doi: 10.3934/dcds.2010.27.75

[13]

Teemu Tyni, Valery Serov. Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line. Inverse Problems and Imaging, 2019, 13 (1) : 159-175. doi: 10.3934/ipi.2019009

[14]

Markus Harju, Jaakko Kultima, Valery Serov, Teemu Tyni. Two-dimensional inverse scattering for quasi-linear biharmonic operator. Inverse Problems and Imaging, 2021, 15 (5) : 1015-1033. doi: 10.3934/ipi.2021026

[15]

Jaakko Kultima, Valery Serov. Reconstruction of singularities in two-dimensional quasi-linear biharmonic operator. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022011

[16]

Xiaohu Qian, Min Huang, Wai-Ki Ching, Loo Hay Lee, Xingwei Wang. Mechanism design in project procurement auctions with cost uncertainty and failure risk. Journal of Industrial and Management Optimization, 2019, 15 (1) : 131-157. doi: 10.3934/jimo.2018036

[17]

Yingte Sun, Xiaoping Yuan. Quasi-periodic solution of quasi-linear fifth-order KdV equation. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6241-6285. doi: 10.3934/dcds.2018268

[18]

Misha Bialy, Andrey E. Mironov. Rich quasi-linear system for integrable geodesic flows on 2-torus. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 81-90. doi: 10.3934/dcds.2011.29.81

[19]

Osama Moaaz, Omar Bazighifan. Oscillation criteria for second-order quasi-linear neutral functional differential equation. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2465-2473. doi: 10.3934/dcdss.2020136

[20]

Massimo Lanza de Cristoforis, aolo Musolino. A quasi-linear heat transmission problem in a periodic two-phase dilute composite. A functional analytic approach. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2509-2542. doi: 10.3934/cpaa.2014.13.2509

 Impact Factor: 

Metrics

  • PDF downloads (151)
  • HTML views (98)
  • Cited by (0)

Other articles
by authors

[Back to Top]