Bi-level optimal toll design problem solved by the inverse Stackelberg games approach

Staňková, Kateřina; Olsder, Geert Jan; Bliemer, Michiel C.J.

doi:10.2495/ut060841

Cited by 16 publications

(12 citation statements)

References 9 publications

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“…Originally applications were found in economics, but nowadays Stackelberg problems are recognized to be present in many other areas; see e.g. [10][11][12][13].…”

Section: Example 14mentioning

confidence: 99%

Phenomena in Inverse Stackelberg Games, Part 1: Static Problems

Olsder

2009

J Optim Theory Appl

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Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers. Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower (or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse Stackelberg concept. As a side issue, expressions like "two captains on a ship" and "divide and conquer" are given a mathematical foundation.

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“…Originally applications were found in economics, but nowadays Stackelberg problems are recognized to be present in many other areas; see e.g. [10][11][12][13].…”

Section: Example 14mentioning

confidence: 99%

Phenomena in Inverse Stackelberg Games, Part 1: Static Problems

Olsder

2009

J Optim Theory Appl

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“…In many Stackelberg formulations, the upper level was for authority and the lower level for users, which meant that users would fully implement the optimal strategies set by the authority. In reality, traffic flow patterns may not follow this plan exactly, especially if traffic conditions change ( 34 , 35 ). Some exceptions existed in works published by Chiu and Mahmassani ( 36 , 37 ).…”

Section: Literature Reviewmentioning

confidence: 99%

Modified Stackelberg Games Approach for Dynamic Signal Control and Route Choice Equilibrium on Mixed Networks

Yang

Wang

Zou

et al. 2020

Transportation Research Record: Journal of the Transportation R

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The dynamic signal control and route choice equilibrium are usually integrated into a noncooperative game between the network authority and the road users. There are mainly two problems in most existing optimization methods. Firstly, the authority is often placed in the upper level in bi-level programming models, this pure system-optimization-oriented framework may increase the difficulty in obtaining an equilibrium flow distribution. Secondly, the rate of drivers’ compliance on the control strategy has not been fully investigated, which makes the problem intractable in real time, especially in a connected vehicle (CV) environment. This paper proposes a modified Stackelberg games model to change the format of the authority-user and user-authority dynamically. The direct communication between the authority and users is established, and the drivers’ compliance rate is applied as the level-change threshold index. Considering the difference between the drivers’ realized travel time and the predicted travel time on the variable message sign (VMS), a logit model is formed to calibrate the compliance rate in every time step. Based on a modified wavelet neural network algorithm, the model predictive control (MPC) fulfills the level-change procedure using the software Matlab 2018b. Six benchmarks are applied in a numerical example. The results show that the proposed model with the centralized framework obtains the minimum total travel cost compared with the benchmarks. Combined with the real-time mutual feedback between drivers’ response and control strategy, the level-change procedure potentially maintains the compliance rate within a certain level.

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“…Coordination problems with a mediator have also been examined in leader-follower games (Tharakunnel 2008) and Stackelberg games (Staňková et al 2006). In these studies, a leader makes a decision that affects followers' rewards such that followers are motivated to coordinate.…”

Section: Related Workmentioning

confidence: 99%

Self-Fulfilling Signal of an Endogenous State in Network Congestion Games

Iwase¹,

Tadokoro²,

Fukuda

2017

Netw Spat Econ

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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.

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Bi-level optimal toll design problem solved by the inverse Stackelberg games approach

Cited by 16 publications

References 9 publications

Phenomena in Inverse Stackelberg Games, Part 1: Static Problems

Phenomena in Inverse Stackelberg Games, Part 1: Static Problems

Modified Stackelberg Games Approach for Dynamic Signal Control and Route Choice Equilibrium on Mixed Networks

Self-Fulfilling Signal of an Endogenous State in Network Congestion Games

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