A Simulation-Based Heuristic to Find Approximate Equilibria with Disaggregate Demand Models

Stefano Bortolomiol (), Virginie Lurkin () and Michel Bierlaire ()
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Stefano Bortolomiol: School of Architecture, Civil and Environmental Engineering, Transport and Mobility Laboratory, École Polytechnique Fédérale de Lausanne, Vaud, Lausanne 1015, Switzerland
Virginie Lurkin: Department of Industrial Engineering & Innovation Science, Eindhoven University of Technology, 5612 AZ Eindhoven, Netherlands; Faculty of Business and Economics, University of Lausanne, Lausanne 1015, Switzerland
Michel Bierlaire: School of Architecture, Civil and Environmental Engineering, Transport and Mobility Laboratory, École Polytechnique Fédérale de Lausanne, Vaud, Lausanne 1015, Switzerland

Transportation Science, 2021, vol. 55, issue 5, 1025-1045

Abstract: Oligopolistic competition occurs in various transportation markets. In this paper, we introduce a framework to find approximate equilibrium solutions of oligopolistic markets in which demand is modeled at the disaggregate level using discrete choice models, according to random utility theory. Compared with aggregate demand models, the added value of discrete choice models is the possibility to account for more complex and precise representations of individual behaviors. Because of the form of the resulting demand functions, there is no guarantee that an equilibrium solution for the given market exists, nor is it possible to rely on derivative-based methods to find one. Therefore, we propose a model-based algorithmic approach to find approximate equilibria, which is structured as follows. A heuristic reduction of the search space is initially performed. Then, a subgame equilibrium problem is solved using a mixed integer optimization model inspired by the fixed-point iteration algorithm. The optimal solution of the subgame is compared against the best responses of all suppliers over the strategy sets of the original game. Best response strategies are added to the restricted problem until all ε -equilibrium conditions are satisfied simultaneously. Numerical experiments show that our methodology can approximate the results of an exact method that finds a pure equilibrium in the case of a multinomial logit model of demand with a single-product offer and homogeneous demand. Furthermore, it succeeds at finding approximate equilibria for two transportation case studies featuring more complex discrete choice models, heterogeneous demand, a multiproduct offer by suppliers, and price differentiation for which no analytical approach exists.

Keywords: competition; equilibrium; disaggregate demand; discrete choice modeling (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:55:y:2021:i:5:p:1025-1045

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