Network Pricing: How to Induce Optimal Flows Under Strategic Link Operators

José Correa (), Cristóbal Guzmán (), Thanasis Lianeas (), Evdokia Nikolova () and Marc Schröder
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José Correa: Department of Industrial Engineering, Universidad de Chile, Santiago, Chile
Cristóbal Guzmán: Institute for Mathematical and Computational Engineering, Facultad de Matemáticas y Escuela de Ingeniería, Pontificia Universidad Católica de Chile, Santiago, Chile
Thanasis Lianeas: School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece
Evdokia Nikolova: Department of Electrical and Computer Engineering, Cockrell School of Engineering, University of Texas at Austin, Austin, Texas 78712

Operations Research, 2022, vol. 70, issue 1, 472-489

Abstract: Network pricing games provide a framework for modeling real-world settings with two types of strategic agents: operators of a network and users of the network. Operators of the network post a price so as to attract users and maximize profit; users of the network select routes based on these prices and congestion from other users. Motivated by the fact that equilibrium in these games may not exist, may not be unique, and may induce an inefficient network performance, our main result is to observe that a simple regulation on the network owners’ market solves these three issues. Specifically, if an authority could set appropriate caps (upper bounds) on the tolls (prices) operators can charge, then the game among the link operators has a unique and strong Nash equilibrium and the users’ game results in a Wardrop equilibrium that achieves the optimal total delay. We call any price vector with these properties a great set of tolls and investigate the efficiency of great tolls with respect to the users’ surplus. We derive a bicriteria bound that compares the users’ surplus under great tolls with the users’ surplus under optimal tolls. Finally, we consider two different extensions of the model. First, we assume that operators face operating costs that depend on the amount of flow on the link, for which we prove existence of great tolls. Second, we allow operators to own more than one link. In this case, we prove that, when operators own complementary links (i.e., links for which an increase in toll value may only increase the flow on the other owned links), any toll vector that induces the optimal flow and that is upper bounded by the marginal tolls is a great set of tolls, and furthermore, we show that, when all links in the network are complementary, then the aforementioned toll vector is also a strong cap equilibrium.

Keywords: Optimization; network pricing games; competition regulation; price caps; selfish routing (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:1:p:472-489

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