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

数学优化 离散选择 启发式 子对策完全均衡 数理经济学 寡头垄断 纳什均衡 计算机科学 数学 经济 古诺竞争 计量经济学
作者
Stefano Bortolomiol,Virginie Lurkin,Michel Bierlaire
出处
期刊:Transportation Science [Institute for Operations Research and the Management Sciences]
卷期号:55 (5): 1025-1045 被引量:4
标识
DOI:10.1287/trsc.2021.1071
摘要

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.
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