Solutions for bargaining games with incomplete information: General type space and action space

Feimin Zhong; Jinxing Xie; Jing Jiao

doi:10.3934/jimo.2017084

Article Contents

2018, Volume 14, Issue 3: 953-966. Doi: 10.3934/jimo.2017084

This issue Previous Article Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts Next Article Single-machine rescheduling problems with learning effect under disruptions

Solutions for bargaining games with incomplete information: General type space and action space

1.
School of Business Administration, Hunan University, Changsha 410082, China
2.
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
3.
School of Economics and Management, Northwest University, Xi'an 710127, China

* Corresponding author
* Corresponding author

Received: February 29, 2016

Revised: August 31, 2016

Early access: August 2017

Published: June 2018

This work has been supported by the National Natural Science Foundation of China under Projects Nos. 71210002 and 71671099. The authors are grateful to the anonymous referees for their constructive comments and suggestions.

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Abstract

A Nash bargaining solution for Bayesian collective choice problem with general type and action spaces is built in this paper. Such solution generalizes the bargaining solution proposed by Myerson who uses finite sets to characterize the type and action spaces. However, in the real economics and industries, types and actions can hardly be characterized by a finite set in some circumstances. Hence our generalization expands the applications of bargaining theory in economic and industrial models.

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Mathematics Subject Classification: Primary: 91A12, 91B26; Secondary: 91B02.

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References

[1]	X. Brusset and P. J. Agrell, Intrinsic impediments to category captainship collaboration, Journal of Industrial and Management Optimization, 13 (2017), 113-133. doi: 10.3934/jimo.2016007.
[2]	W. S. Chang, B. Chen and T. C. Salmon, An investigation of the average bid mechanism for procurement auctions, Management Science, 61 (2015), 1237-1254. doi: 10.1287/mnsc.2013.1893.
[3]	J. C. Harsanyi and R. Selten, A generalized Nash solution for two-person bargaining games with incomplete information, Management Science, 18 (1972), 80-106. doi: 10.1287/mnsc.18.5.80.
[4]	B. Holmström and R. B. Myerson, Efficient and durable decision rules with incomplete information, Econometrica, 51 (1983), 1799-1819.
[5]	M. Huang, X. Qian, S. C. Fang and X. Wang, Winner determination for risk aversion buyers in multi-attribute reverse auction, Omega, 59 (2016), 184-200. doi: 10.1016/j.omega.2015.06.007.
[6]	E. Kalai and M. Smorodinsky, Other solutions to Nash's bargaining problem, Econometrica, 43 (1975), 513-518. doi: 10.2307/1914280.
[7]	T. Kruse and P. Strack, Optimal stopping with private information, Journal of Economic Theory, 159 (2015), 702-727. doi: 10.1016/j.jet.2015.03.001.
[8]	R. B. Myerson, Incentive compatibility and the bargaining problem, Econometrica, 47 (1979), 61-73. doi: 10.2307/1912346.
[9]	R. B. Myerson, Cooperative games with imcomplete information, International Journal of Game Theory, 13 (1984), 69-96. doi: 10.1007/BF01769817.
[10]	R. B. Myerson, Two-person bargaining problems with incomplete information, Econometrica, 52 (1984), 461-487. doi: 10.2307/1911499.
[11]	J. F. Nash, The bargaining problem, Econometrica, 18 (1950), 155-162. doi: 10.2307/1907266.
[12]	Ö. Özer and W. Wei, Strategic commitments for an optimal capacity decision under asymmetric forecast information, Management Science, 52 (2006), 1238-1257.
[13]	M. A. Perles and M. Maschler, The super-additive solution for the Nash bargaining game, International Journal of Game Theory, 10 (1981), 163-193. doi: 10.1007/BF01755963.
[14]	H. L. Royden and P. Fitzpatrick, Real Analysis, 3$^{ed}$ edition, Macmillan, New York, 1988.
[15]	F. Weidner, The generalized Nash bargaining solution and incentive compatible mechanisms, International Journal of Game Theory, 21 (1992), 109-129. doi: 10.1007/BF01245455.