Abstract
We consider the problem of coordination via signaling in network congestion games to improve social welfare deteriorated by incomplete information about traffic flow. Traditional studies on signaling, which focus on exogenous factors of congestion and ignore congestion externalities, fail to discuss the oscillations of traffic flow. To address this gap, we formulate a problem of designing a coordination signal on endogenous information about traffic flow and introduce a self-fulfilling characteristic of a signal that guarantees an outcome flow consistent with the signal itself without causing the unwanted oscillation. An instance of the self-fulfilling signal is shown in the case of a Gaussian signal distribution. In addition, we show simple numerical examples. The results reveal how a self-fulfilling signal suppresses the oscillation and simultaneously improves social welfare through improved network efficiency.
Similar content being viewed by others
References
Altman E, Wynter L (2004) Equilibrium, games, and pricing in transportation and telecommunication networks. Networks and Spatial Economics 4(1):7–21
Angeletos G-M, Pavan A (2005) Efficiency and welfare in economies with incomplete information. Working paper
Arthur W B (1994) Inductive reasoning and bounded rationality. Am Econ Rev 84(2):406–411
Barth D, Bournez O, Boussaton O, Cohen J (2008) Distributed learning of wardrop equilibria. In: International conference on unconventional computation, pp 19–32
Ben-Akiva M, Bierlaire M, Burton D, Koutsopoulos HN, Mishalani R (2001) Network state estimation and prediction for real-time traffic management. Networks and Spatial Economics 1(3):293–318
Bergemann D, Morris S (2013) Robust predictions in games with incomplete information. Econometrica 81(4):1251–1308
Bishop CM (2006) Pattern recognition and machine learning. Springer
Bottom JA (2000) Consistent anticipatory route guidance. PhD Thesis of Massachusetts Institute of Technology
Challet D, Zhang Y-C (1997) Emergence of cooperation and organization in an evolutionary game. Physica A: Statistical Mechanics and its Applications 246(3):407–418
Christodoulou G, Koutsoupias E, Nanavati A (2009) Coordination mechanisms. Theor Comput Sci 410(36):3327–3336
Engelson L (1997) Self-fulfilling and recursive forecasts-an analytical perspective for driver information systems Proceedings of the 8th IATBR meeting
Fabrikant A, Papadimitriou CH (2008) The complexity of game dynamics: BGP oscillations, sink equilibria, and beyond. In: Proceedings of the nineteenth annual ACM-SIAM symposium on discrete algorithms, pp 844–853
Friesz TL, Bernstein D, Kydes N (2004) Dynamic congestion pricing in disequilibrium. Networks and Spatial Economics 4(2):181–202
Fukuda T, Takefuji K, Ikemoto Y, Hasegawa Y (2002) Dynamical route-planning for vehicles based on global traffic information and communication. In: The IEEE 5th international conference on intelligent transportation systems, Proceedings. pp 538–543
Garcia M, Chatterjee A, Ruina A, Coleman M (1998) The simplest walking model: stability, complexity, and scaling. J Biomech Eng 120(2):281–288
Gentzkow M, Kamenica E (2011) Bayesian persuasion. Am Econ Rev 101(6):2590–2615
Goldman CV, Zilberstein S (2004) Decentralized control of cooperative systems: categorization and complexity analysis. J Artif Intell Res 22:143–174
Hauert C, Szabó G (2005) Game theory and physics. Am J Phys 73(5):405–414
Kaelbling LP, Littman ML, Moore AW (1996) Reinforcement learning: a survey. J Artif Intell Res 4:237–285
Kanamori R, Takahashi J, Ito T (2012) Evaluation of anticipatory stigmergy strategies for traffic management. In: Vehicular networking conference
Klein M, Metzler R, Bar-Yam Y (2005) Handling emergent resource use oscillations. IEEE Trans Syst Man Cybern Part A Syst Hum 35(3):327–336
Kremer I, Mansour Y, Perry M (2014) Implementing the “Wisdom of the crowd”. J Polit Econ 122(5):988–1012
LeBlanc LJ, Morlok EK, Pierskalla WP (1975) An efficient approach to solving the road network equilibrium traffic assignment problem. Transp Res 9(5):309–318
Littman ML (2001) Value-function reinforcement learning in Markov games. Cogn Syst Res 2(1):55–66
Nakayama S (2009) Bayesian learning, day-to-day adjustment process, and stability of Wardrop equilibrium. In: Transportation and traffic theory 2009: golden jubilee, pp 425–440
Olfati-Saber R, Fax A, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233
Paz A, Peeta S (2009) Paradigms to deploy a behavior-consistent approach for information-based real-time traffic routing. Networks and Spatial Economics 9(2):217–241
Rosenthal RW (1973) A class of games possessing pure-strategy Nash equilibria. Int J Game Theory 2(1):65–67
Roughgarden T (2005) Selfish routing and the price of anarchy. MIT Press, Cambridge
Staňková K, Olsder GJ, Bliemer MCJ (2006) Bilevel optimal toll design problem solved by the inverse Stackelberg games approach. Urban Transport 12:871–880
Tharakunnel K (2008) Leader-follower multiagent systems: incentive design with limited information. ProQuest
Wahlea J, Lúcia A, Bazzanb C, Klüglc F, Schreckenberga M (2002) The impact of real-time information in a two-route scenario using agent-based simulation. Transportation Research Part C: Emerging Technologies 10(5):399–417
Wardrop JG (1952) Some theoretical aspects of road traffic research. ICE Proceedings: Engineering Divisions 1(3):325–362
Yang H, Huang H-J (1998) Principle of marginal-cost pricing: how does it work in a general road network? Transp Res A Policy Pract 32(1):45–54
Yang H, Han D, Lo HK (2008) Efficiency of atomic splittable selfish routing with polynomial cost functions. Networks and Spatial Economics 8(4):443–451
Yang X, Ban XJ, Ma R (2016) Mixed equilibria with common constraints on transportation networks. Networks and Spatial Economics:1–33
Zhang C, Lesser V (2012) Coordinated multi-agent learning for decentralized pomdps. In: 7th annual workshop on multiagent sequential decision-making under uncertainty
Zhang W-Y, Guan W, Ma J-H, Tian J-F (2015) A nonlinear pairwise swapping dynamics to model the selfish rerouting evolutionary game. Networks and Spatial Economics 15(4):1075–1092
Author information
Authors and Affiliations
Corresponding author
Appendix: Bayesian Inference for Linear Gaussian Model
Appendix: Bayesian Inference for Linear Gaussian Model
Here, we summarize the general results of Bayesian inference for a linear Gaussian model (Bishop 2006). Let prior Gaussian distribution of x be denoted by
In linear Gaussian model, the conditional distribution of y given x has a mean that is a linear function of x, such as
The posterior distribution of x given y is denoted by
where
The marginal distribution of y is denoted by
If covariance matrices are not full rank, it is impossible to calculate their inverse matrices. In this case, there exists a linear transformation that reduces the dimension of vector x and makes its covariance Σ full rank as follows
This transformation matrix C is obtained by singular value decomposition. The calculation including inverse matrices can be processed in this reduced vector space. Let \(\tilde {\boldsymbol {x}}_{2}\) be the result. This is converted into the original vector space by the following reverse transformation
Rights and permissions
About this article
Cite this article
Iwase, T., Tadokoro, Y. & Fukuda, D. Self-Fulfilling Signal of an Endogenous State in Network Congestion Games. Netw Spat Econ 17, 889–909 (2017). https://doi.org/10.1007/s11067-017-9351-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11067-017-9351-4