Capacity, Information and Minority Games in Public Transport Paul Bouman † Leo Kroon † Gábor Maróti ‡ Peter Vervest † PBouman@rsm.nl LKroon@rsm.nl G.Maroti@vu.nl PVervest@rsm.nl † Rotterdam School of Management, Erasmus University ‡ Netherlands Railways Department of Technology & Operations Management Utrecht, The Netherlands Burgemeester Oudlaan 50, 3062 PA, Rotterdam, The Netherlands ‡ VU University, Amsterdam, The Netherlands ABSTRACT Many public transport operators are faced with high peak de- mands. Often this leads to crowded vehicles and discomfort for the passengers. The increasing use of information tech- nologies creates new opportunities for passengers to avoid crowding. However, the role of crowding in the dynamics of a public transport system is not well understood. With the definition and implementation of a model based on the minority games, a class of games that deals with crowding dynamics, we aim to provide public transport operators with insights to deal with crowded situations. We propose an extension of a minority game where multiple resources and heterogeneous agent preferences are included. We have conducted two simulation studies, aimed at inves- tigating the dynamics of crowding within public transport. In our first experiment we investigate the effect of the avail- ability of information on crowding. In a second experiment we study the dynamic optimization of capacities according to a rolling stock circulation model. We find that both the availability of information disclosed and the chosen capacity optimization mechanism have an impact on the number of agents utilizing resources and their payoffs. As such, these models will allow us to develop new operator policies to deal with crowded situations in the future. Categories and Subject Descriptors I.2.11 [Distributed Artificial Intelligence]: Miscellaneous— Coherence and coordination General Terms Experimentation, Management, Performance Keywords capacity, coordination, information, minority games, public transport, resource allocation 1. INTRODUCTION Operators in public transport are often faced with peak demands, typically during the morning and afternoon rush hours. As a result, vehicles can become very crowded, greatly reducing the comfort experienced by the passengers. As in- formation technologies enable passengers to have more direct communications with the public transport operators and have more freedom to work at different locations, passengers are gaining more opportunities to avoid crowded situations. However, the impact of crowding on passenger behavior and the interaction between railway operations and passengers is not well understood. In this paper we develop a model, based on the concept of minority games, that allows us to study the dynamics of crowding in public transport through computa- tional experiments and evaluate the impact of operational and behavioral models on a number of performance measures, most importantly the utilization of available capacities. Since the “El-Farol Bar Game” [1] was first introduced in 1994, the concept of the minority game has received a lot of attention from researchers. One of the great strengths of this model lies in the simplicity of its description: a population of agents have to decide every Thursday night whether to go to the bar or not. Once they go the bar, they have a positive payoff if less than 60% of the population goes to the bar, while they have a negative payoff if it is too crowded. As everyone makes this choice every Thursday, the El-Farol Bar Game has an iterative nature. While historic information is provided, the interesting aspect comes from the fact that there is no direct coordination between the agents. Issues related to limited availability of resources and a lack of explicit coordination occur in many real world systems. The applications of these models include car traffic [2], con- gestion in computer networks [8] and financial markets [4]. While these types of applications were considered earlier from a game theory perspective, most notably under the name of congestion games [11], the novelty from the “El-Farol Bar” study was the application of a complex systems approach enabled by simulation of a repeated game, while game theory is mostly concerned with the properties of equilibria. In this paper, we focus on minority games where the op- erator cannot control agent behavior, but has control over the disclosure of information and the system capacities. The main application domain is public transport systems, where passengers share vehicles depending on their chosen route and time of travel. If a connection is operated frequently, passengers with some flexibility in their schedule can try to avoid crowded situations by shifting time of travel. Since