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

References

• Adler N (2001) Competition in a deregulated air transportation market. Eur. J. Oper. Res. 129(2):337–345.Crossref, Google Scholar
• Adler N, Pels E, Nash C (2010) High-speed rail and air transport competition: Game engineering as tool for cost-benefit analysis. Transportation Res. Part B Methodological 44(7):812–833.Crossref, Google Scholar
• Ait Ali A, Eliasson J (2019) Railway capacity allocation: A survey of market organizations, allocation processes and track access charges. Technical report, Swedish National Road & Transport Research Institute, Stockholm, Sweden.Google Scholar
• Aksoy-Pierson M, Allon G, Federgruen A (2013) Price competition under mixed multinomial logit demand functions. Management Sci. 59(8):1817–1835.Link, Google Scholar
• Albalate D, Bel G, Fageda X (2015) Competition and cooperation between high-speed rail and air transportation services in Europe. J. Transport Geography 42:166–174.Crossref, Google Scholar
• Andersson SE (1998) Passenger choice analysis for seat capacity control: A pilot project in Scandinavian Airlines. Internat. Trans. Oper. Res. 5(6):471–486.Crossref, Google Scholar
• Anderson SP, De Palma A, Thisse JF (1992) Discrete Choice Theory of Product Differentiation (MIT Press, Cambridge, MA).Crossref, Google Scholar
• Beck A (2011) Barriers to entry in rail passenger services: Empirical evidence for tendering procedures in Germany. Eur. J. Transport Infrastructure Res. 11(1).Google Scholar
• Ben-Akiva ME, Lerman SR (1985) Discrete Choice Analysis: Theory and Application to Travel Demand (MIT Press, Cambridge, MA).Google Scholar
• Ben-Akiva ME, Cascetta E, Coppola P, Papola A, Velardi V (2010) High speed rail demand forecasting in a competitive market: The Italian case study. Proc. 12th World Conf. Transportation Res. http://www.civil.ist.utl.pt/wctr12_lisboa/proceedings.htm.Google Scholar
• Benati S, Hansen P (2002) The maximum capture problem with random utilities: Problem formulation and algorithms. Eur. J. Oper. Res. 143(3):518–530.Crossref, Google Scholar
• Bernstein F, Federgruen A (2004) Dynamic inventory and pricing models for competing retailers. Naval Res. Logist. 51(2):258–274.Crossref, Google Scholar
• Berry S, Levinsohn J, Pakes A (1995) Automobile prices in market equilibrium. Econometrica 63(4):841–890.Crossref, Google Scholar
• Bertrand J (1883) Théorie des richesses: Revue de ’Théorie mathématique de la richesse sociale’ par Léon Walras et ’Recherches sur les principes mathématiques de la richesse’ par Augustin Cournot. J. Savants, 499–508.Google Scholar
• Bertsimas D, Gupta V, Paschalidis IC (2015) Data-driven estimation in equilibrium using inverse optimization. Math. Programming 153(2):595–633.Crossref, Google Scholar
• Binder S, Maknoon Y, Bierlaire M (2017) Exogenous priority rules for the capacitated passenger assignment problem. Transportation Res. Part B Methodological 105:19–42.Crossref, Google Scholar
• Börjesson M (2014) Forecasting demand for high speed rail. Transportation Res. Part A Policy Practice 70:81–92.Crossref, Google Scholar
• Bracken J, McGill JT (1973) Mathematical programs with optimization problems in the constraints. Oper. Res. 21(1):37–44.Link, Google Scholar
• Brander JA, Zhang A (1993) Dynamic oligopoly behaviour in the airline industry. Internat. J. Indust. Organ. 11(3):407–435.Crossref, Google Scholar
• Bresnahan TF, Reiss PC (1991) Entry and competition in concentrated markets. J. Political Econom. 99(5):977–1009.Crossref, Google Scholar
• Broman E, Eliasson J (2019) Welfare effects of open access competition on railway markets. Transportation Res. Part A Policy Practice 129:72–91.Crossref, Google Scholar
• Capurso M, Hess S, Dekker T (2019) Modelling the role of consideration of alternatives in mode choice: An application on the Rome-Milan corridor. Transportation Res. Part A Policy Practice 129:170–184.Crossref, Google Scholar
• Cascetta E, Coppola P (2012) An elastic demand schedule-based multimodal assignment model for the simulation of high speed rail (HSR) systems. EURO J. Transportation Logist. 1(1–2):3–27.Crossref, Google Scholar
• Cascetta E, Coppola P (2016) Assessment of schedule-based and frequency-based assignment models for strategic and operational planning of high-speed rail services. Transportation Res. Part A Policy Practice 84:93–108.Crossref, Google Scholar
• Cascetta E, Cartenì A, Henke I, Pagliara F (2020) Economic growth, transport accessibility and regional equity impacts of high-speed railways in Italy: Ten years ex post evaluation and future perspectives. Transportation Res. Part A Policy Practice 139:412–428.Crossref, Google Scholar
• Christodoulou G, Koutsoupias E, Spirakis PG (2011) On the performance of approximate equilibria in congestion games. Algorithmica 61(1):116–140.Crossref, Google Scholar
• Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann. Oper. Res. 153(1):235–256.Crossref, Google Scholar
• Cournot AA (1838) Recherches sur les Principes Mathématiques de la Théorie des Richesses, vol. L (Hachette, Paris).Google Scholar
• Daskalakis C, Mehta A, Papadimitriou CH 2007 Progress in approximate Nash equilibria. Proc. Eighth ACM Conf. Electronic Commerce (Association for Computing Machinery, New York), 355–358.Google Scholar
• Fageda X, Sansano S (2018) Factors influencing prices and frequencies in the interurban bus market: Evidence from Europe. Transportation Res. Part A Policy Practice 111:266–276.Crossref, Google Scholar
• Fisk C (1984) Game theory and transportation systems modelling. Transportation Res. Part B Methodological 18(4–5):301–313.Crossref, Google Scholar
• Friedman JW (1971) A non-cooperative equilibrium for supergames. Rev. Econom. Stud. 38(1):1–12.Crossref, Google Scholar
• Fudenberg D, Tirole J (1991) Game Theory (MIT Press, Cambridge, MA).Google Scholar
• Gabszewicz JJ, Thisse JF (1979) Price competition, quality and income disparities. J. Econom. Theory 20(3):340–359.Crossref, Google Scholar
• Gallego G, Wang R (2014) Multiproduct price optimization and competition under the nested logit model with product-differentiated price sensitivities. Oper. Res. 62(2):450–461.Link, Google Scholar
• Grimaldi R, Augustin K, Beria P (2017) Intercity coach liberalisation. The cases of Germany and Italy. Transportation Res. Procedia 25:474–490.Crossref, Google Scholar
• Haase K (2009) Discrete location planning. Technical report, Institute of Transport and Logistics Studies, University of Sydney, Sydney.Google Scholar
• Hanson W, Martin K (1996) Optimizing multinomial logit profit functions. Management Sci. 42(7):992–1003.Link, Google Scholar
• Hensher DA, Rose JM, Greene WH (2005) Applied Choice Analysis: A Primer (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Hotelling H (1929) Stability in competition. Econom. J. (London) 39(153):41–57.Crossref, Google Scholar
• Ibeas A, Dell’Olio L, Bordagaray M, Ortúzar Jd D (2014) Modelling parking choices considering user heterogeneity. Transportation Res. Part A Policy Practice 70:41–49.Crossref, Google Scholar
• Koppelman FS (1976) Guidelines for aggregate travel prediction using disaggregate choice models. Transportation Res. Rec. 610:19–24.Google Scholar
• Levin Y, McGill J, Nediak M (2009) Dynamic pricing in the presence of strategic consumers and oligopolistic competition. Management Sci. 55(1):32–46.Link, Google Scholar
• Li H, Huh WT (2011) Pricing multiple products with the multinomial logit and nested logit models: Concavity and implications. Manufacturing Service Oper. Management 13(4):549–563.Link, Google Scholar
• Li H, Webster S, Mason N, Kempf K (2019) Product-line pricing under discrete mixed multinomial logit demand. Manufacturing Service Oper. Management 21(1):14–28.Link, Google Scholar
• Lin KY, Sibdari SY (2009) Dynamic price competition with discrete customer choices. Eur. J. Oper. Res. 197(3):969–980.Crossref, Google Scholar
• Liu TL, Chen J, Huang HJ (2011) Existence and efficiency of oligopoly equilibrium under toll and capacity competition. Transportation Res. Part E Logist. Transportation Rev. 47(6):908–919.Crossref, Google Scholar
• Manski CF (1977) The structure of random utility models. Theory Decision 8(3):229–254.Crossref, Google Scholar
• Maskin E, Tirole J (1987) A theory of dynamic oligopoly, III: Cournot competition. Eur. Econom. Rev. 31(4):947–968.Crossref, Google Scholar
• Maskin E, Tirole J (1988a) A theory of dynamic oligopoly, I: Overview and quantity competition with large fixed costs. Econometrica 56(3):549–569.Crossref, Google Scholar
• Maskin E, Tirole J (1988b) A theory of dynamic oligopoly, II: Price competition, kinked demand curves, and Edgeworth cycles. Econometrica 56(3):571–599.Crossref, Google Scholar
• McFadden D, Reid F (1975) Aggregate Travel Demand Forecasting from Disaggregated Behavioral Models (Institute of Transportation and Traffic Engineering, University of California, Berkeley, CA).Google Scholar
• McFadden D, Train K (2000) Mixed MNL models for discrete response. J. Appl. Econometrics 15(5):447–470.Crossref, Google Scholar
• Milgrom P, Roberts J (1990) Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58(6):1255–1277.Crossref, Google Scholar
• Morrow WR, Skerlos SJ (2011) Fixed-point approaches to computing Bertrand-Nash equilibrium prices under mixed-logit demand. Oper. Res. 59(2):328–345.Link, Google Scholar
• Murphy FH, Sherali HD, Soyster AL (1982) A mathematical programming approach for determining oligopolistic market equilibrium. Math. Programming 24(1):92–106.Crossref, Google Scholar
• Nash J (1951) Non-cooperative games. Ann. Math. 54(2):286–295.Crossref, Google Scholar
• Nisan N, Roughgarden T, Tardos E, Vazirani VV (2007) Algorithmic Game Theory, vol. 1 (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Nuzzolo A, Crisalli U, Gangemi F (2000) A behavioural choice model for the evaluation of railway supply and pricing policies. Transportation Res. Part A Policy Practice 34(5):395–404.Crossref, Google Scholar
• Osborne MJ, Rubinstein A (1994) A Course in Game Theory (MIT Press, Cambridge, MA).Google Scholar
• Pacheco Paneque M (2020) A general framework for the integration of complex choice models into mixed integer optimization. Unpublished PhD thesis, École Polytechnique Fédérale de Lausanne, Switzerland.Google Scholar
• Pacheco Paneque M, Bierlaire M, Gendron B, Sharif Azadeh S (2021) Integrating advanced discrete choice models in mixed integer linear optimization. Transportation Res. Part B Methodological 146:26–49.Crossref, Google Scholar
• Radner R (1980) Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives. J. Econom. Theory 22(2):136–154.Crossref, Google Scholar
• Rotemberg J, Saloner G (1986) A supergame-theoretic model of price wars during booms. Amer. Econom. Rev. 76(3):390–407.Google Scholar
• Shaked A, Sutton J (1983) Natural oligopolies. Econometrica 51(5):1469–1483.Crossref, Google Scholar
• Starkie D (2002) Airport regulation and competition. J. Air Transport Management 8(1):63–72.Crossref, Google Scholar
• Stigler GJ (1964) A theory of oligopoly. J. Political Econom. 72(1):44–61.Crossref, Google Scholar
• Talluri K, Van Ryzin G (2004) Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50(1):15–33.Link, Google Scholar
• Train KE (2009) Discrete Choice Methods with Simulation (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Valeri E (2013) Air and rail transport in the Rome-Milan corridor: Competition policy implications based on a discrete choice analysis. Unpublished PhD thesis, Università degli Studi di Trieste, Italy.Google Scholar
• von Stackelberg H (1934) Marktform und Gleichgewicht (Julius Springer, Vienna, Austria).Google Scholar
• Vulcano G, Van Ryzin G, Chaar W (2010) Choice-based revenue management: An empirical study of estimation and optimization. Manufacturing Service Oper. Management 12(3):371–392.Link, Google Scholar