October  2020, 7(4): 335-350. doi: 10.3934/jdg.2020026

Pricing equilibrium of transportation systems with behavioral commuters

1. 

Department of Decision Sciences and Managerial Economics, CUHK Business School, Chinese University of Hong Kong, Hong Kong SAR, China

2. 

Saint-Petersburg State University, St. Petersburg, Russia, Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk, Russia

3. 

Department of Economics, School of Economics and Management, Tsinghua University, Beijing, China, 100084

* Corresponding author: Vladimir V. Mazalov

Received  April 2020 Published  October 2020 Early access  August 2020

We study Wardrop equilibrium in a transportation system with profit-maximizing firms and heterogeneous commuters. Standard commuters minimize the sum of monetary costs and equilibrium travel time in their route choice, while "oblivious" commuters choose the route with minimal idle time. Three possible scenarios can arise in equilibrium: A pooling scenario where all commuters make the same transport choice; A separating scenario where different types of commuters make different transport choices; A partial pooling scenario where some standard commuters make the same transport choice as the oblivious commuters. We characterize the equilibrium existence condition, derive equilibrium flows, prices and firms' profits in each scenario, and conduct comparative analyses on parameters representing route conditions and heterogeneity of commuters, respectively. The framework nests the standard model in which all commuters are standard as a special case, and also allows for the case in which all commuters are oblivious as the other extreme. Our study shows how the presence of behavioral commuters under different route conditions affects equilibrium behavior of commuters and firms, as well a the equilibrium outcome of the transportation system.

Citation: Jaimie W. Lien, Vladimir V. Mazalov, Jie Zheng. Pricing equilibrium of transportation systems with behavioral commuters. Journal of Dynamics and Games, 2020, 7 (4) : 335-350. doi: 10.3934/jdg.2020026
References:
[1]

C. F. CamererT. H. Ho and J. K.Chong, A cognitive hierarchy model of games, Quart. J. Econom., 119 (2004), 861-898. 

[2]

V. P. Crawford, Boundedly rational versus optimization-based models of strategic thinking and learning games, J. Econom. Lit., 51 (2013), 512-527. 

[3]

X. DiX. HeX. Guo and H. X. Liu, Braess paradox under the boundedly rational user equilibria, Trans. Res. Part B, 67 (2014), 86-108.  doi: 10.1016/j.trb.2014.04.005.

[4]

X. Di and H. X. Liu, Boundedly rational route choice behavior: A review of models and methodologies, Trans. Res. Part B, 85 (2016), 142-179.  doi: 10.1016/j.trb.2016.01.002.

[5]

W. FordJ. W. LienV. V. Mazalov and J. Zheng, Riding to Wall Street: Determinants of commute time using Citibike, Int. Journal of Logistics: Research and Applications, 22 (2019), 473-490. 

[6]

R. JouD. A. HensherY. Liu and C. Chiu, Urban commuters' mode-switching behaviour in Taipai, with an application of the bounded rationality principle, Urban Studies, 47 (2010), 650-665. 

[7]

G. KarakostasN. KimA. Viglas and H. Xia, On the degradation of performance for traffic networks with oblivious users, Trans. Res. Part B, 45 (2011), 364-371. 

[8]

Z. Kuang, V. V. Mazalov, X. Tang and J. Zheng, Transportation network with externalities, J. Comp. Appl. Math., (2020). doi: 10.1016/j.cam.2020.113091.

[9]

Z. Kuang, Z. Lian, J. W. Lien and J. Zheng, Serial and parallel duopoly competition in two-part transportation routes, Trans. Res. Part E, 133 (2020), 101821.

[10]

J. W. LienV. V. MazalovA. V. Melnik and J. Zheng, Wardrop equilibrium for networks with the BPR latency function, Lecture Notes in Computer Science, 9869 (2016), 37-49.  doi: 10.1007/978-3-319-44914-2_4.

[11]

J. L. Lien, H. Zhao and J. Zheng, Perception bias in Tullock contests, Working Paper, (2019).

[12]

H. S. Mahmassani and G. Chang, On boundedly rational user equilibrium in transportation systems, Trans. Sci., 21 (1987), 89-99. 

[13]

V. V. Mazalov and A. V. Melnik, Equilibrium prices and flows in the passenger traffic problem, Int. Game Theory Rev., 18 (2016). doi: 10.1142/S0219198916500018.

[14]

C. SunL. Cheng and J. Ma, Travel time reliability with boundedly rational travelers, Transportmetrica A: Transport Science, 14 (2018), 210-229. 

[15]

T. TangX. Luo and K. Liu, Impacts of the driver's bounded rationality on the traffic running cost under the car-following model, Physica A, 457 (2016), 316-321. 

[16]

J. Wardrop, Some theoretical aspects of road traffic research, Proceedings of the Institution of Civil Engineers, Part II (1952), 325–278. doi: 10.1680/ipeds.1952.11362.

[17]

H. Ye and H. Yang, Rational Behavior adjustment process with boundedly rational user equilibrium, Trans. Sci., 51 (2017), 968-980. 

[18]

C. Zhao and H. Huang, Experiment of boundedly rational route choice behavior and the model under satisficing rule, Trans. Res. Part C, 68 (2016), 22-37. 

show all references

References:
[1]

C. F. CamererT. H. Ho and J. K.Chong, A cognitive hierarchy model of games, Quart. J. Econom., 119 (2004), 861-898. 

[2]

V. P. Crawford, Boundedly rational versus optimization-based models of strategic thinking and learning games, J. Econom. Lit., 51 (2013), 512-527. 

[3]

X. DiX. HeX. Guo and H. X. Liu, Braess paradox under the boundedly rational user equilibria, Trans. Res. Part B, 67 (2014), 86-108.  doi: 10.1016/j.trb.2014.04.005.

[4]

X. Di and H. X. Liu, Boundedly rational route choice behavior: A review of models and methodologies, Trans. Res. Part B, 85 (2016), 142-179.  doi: 10.1016/j.trb.2016.01.002.

[5]

W. FordJ. W. LienV. V. Mazalov and J. Zheng, Riding to Wall Street: Determinants of commute time using Citibike, Int. Journal of Logistics: Research and Applications, 22 (2019), 473-490. 

[6]

R. JouD. A. HensherY. Liu and C. Chiu, Urban commuters' mode-switching behaviour in Taipai, with an application of the bounded rationality principle, Urban Studies, 47 (2010), 650-665. 

[7]

G. KarakostasN. KimA. Viglas and H. Xia, On the degradation of performance for traffic networks with oblivious users, Trans. Res. Part B, 45 (2011), 364-371. 

[8]

Z. Kuang, V. V. Mazalov, X. Tang and J. Zheng, Transportation network with externalities, J. Comp. Appl. Math., (2020). doi: 10.1016/j.cam.2020.113091.

[9]

Z. Kuang, Z. Lian, J. W. Lien and J. Zheng, Serial and parallel duopoly competition in two-part transportation routes, Trans. Res. Part E, 133 (2020), 101821.

[10]

J. W. LienV. V. MazalovA. V. Melnik and J. Zheng, Wardrop equilibrium for networks with the BPR latency function, Lecture Notes in Computer Science, 9869 (2016), 37-49.  doi: 10.1007/978-3-319-44914-2_4.

[11]

J. L. Lien, H. Zhao and J. Zheng, Perception bias in Tullock contests, Working Paper, (2019).

[12]

H. S. Mahmassani and G. Chang, On boundedly rational user equilibrium in transportation systems, Trans. Sci., 21 (1987), 89-99. 

[13]

V. V. Mazalov and A. V. Melnik, Equilibrium prices and flows in the passenger traffic problem, Int. Game Theory Rev., 18 (2016). doi: 10.1142/S0219198916500018.

[14]

C. SunL. Cheng and J. Ma, Travel time reliability with boundedly rational travelers, Transportmetrica A: Transport Science, 14 (2018), 210-229. 

[15]

T. TangX. Luo and K. Liu, Impacts of the driver's bounded rationality on the traffic running cost under the car-following model, Physica A, 457 (2016), 316-321. 

[16]

J. Wardrop, Some theoretical aspects of road traffic research, Proceedings of the Institution of Civil Engineers, Part II (1952), 325–278. doi: 10.1680/ipeds.1952.11362.

[17]

H. Ye and H. Yang, Rational Behavior adjustment process with boundedly rational user equilibrium, Trans. Sci., 51 (2017), 968-980. 

[18]

C. Zhao and H. Huang, Experiment of boundedly rational route choice behavior and the model under satisficing rule, Trans. Res. Part C, 68 (2016), 22-37. 

Figure 1.  2-Route Transportation System with Duopoly Firms and Heterogeneous Commuters
Figure 2.  The regions of optimal behavior of commuters and firms
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