July  2018, 14(3): 953-966. doi: 10.3934/jimo.2017084

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

Received  March 2016 Revised  September 2016 Published  July 2018 Early access  September 2017

Fund Project: 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.

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.

Citation: Feimin Zhong, Jinxing Xie, Jing Jiao. Solutions for bargaining games with incomplete information: General type space and action space. Journal of Industrial and Management Optimization, 2018, 14 (3) : 953-966. doi: 10.3934/jimo.2017084
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. ChangB. 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. HuangX. QianS. 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.

show all references

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. ChangB. 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. HuangX. QianS. 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.

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