Commuters route choice behaviour
Introduction
Understanding individual travel behaviour is essential for the design of Advanced Traveller Information Systems (ATIS), which provide real-time travel information, like link travel times. However, the response of road users to information is still an open question. It is not clear whether more information is beneficial. Drivers confronted with too much information may become oversaturated in the sense that information processing becomes too difficult and users develop simple heuristics to solve the situation. Drivers may also overreact to information and thereby cause additional fluctuations. Thus, the behaviour of the drivers has to be incorporated in traffic forecasts. ATIS can reduce fluctuations only if behavioural effects are correctly taken into account. However, are there general patterns of decision behaviour with respect to information available?
A number of experiments on route choice behaviour (e.g. Bonsal, 1992, Mahmassani and Liu, 1999) have already been reported. Here, we focus on the route choice in a generic two route scenario, which already has been investigated in literature (e.g. Iida et al., 1992). However, our aim is to present experiments with a large number of periods and with sufficiently many independent observations for meaningful applications of non-parametric significance tests.
The route choice game explored here has some similarities to experimental games in literature. The route choice game has a multitude of pure equilibria. In each of these equilibria, the payoff for each player is 10. Therefore, one can regard the route choice game as a coordination problem in which the players have to coordinate their route choices which they distribute among the alternatives in an equilibrium fashion. Nevertheless, the situation is very different from that of the coordination games in experimental literature (Van Huyck et al., 1990). There, the players have to coordinate on an equilibrium at which everybody chooses the same pure strategy.
Market entry games (Rapoport et al., 2002, Erev and Rapoport, 1998) are another kind of games found in experimental literature. Usually in these games, the players have the choice either to enter a market or to stay out. The payoff for entering the market is a decreasing function of the number of entrants. The payoff for staying out is a constant opportunity cost. One may say that the route choice game is similar to a market entry game with two markets instead of one. However, the players do not have the choice to stay out of both markets.
Coordination games and market entry games typically have been played over a small number of periods (e.g. Van Huyck et al., 1990). It has been shown (Berninghaus and Erhart, 2001) that in coordination games extending over 100 periods, the behaviour is very different. In the minimum effort game, it converts to the best equilibrium instead of the worst. Traffic situations are best modelled as frequently repeated games. Therefore, our experiments are run over 200 periods.
If one wants to investigate results of day-to-day route choice which can be transferred to more realistic environments, it is necessary to explore individual behaviour in an interactive experimental set-up. Does behaviour converge to equilibrium? Does more feedback reduce fluctuations? What is the structure of individual responses to recent experiences? Our experimental study tries to throw light on these questions.
Section snippets
Experimental set-up
Subjects are told that in each of the 200 periods, they have to make a choice between a main road M and a side road S for travelling from A to B (see Fig. 1).
They were told that M is faster if M and S are chosen by the same number of people. The number of subjects in each session was 18, mostly law and economic students from the University of Bonn. The time and depends on the numbers and of participants choosing M and S respectively: The period payoff was
Number of players on the side road S
It can be seen that there is no convergence to the theoretical equilibrium. There are substantial fluctuations until the end of the session. Figure 2 shows the number of participants on S in a typical session of treatment I. The same is true for all sessions of both treatments. The overall average of numbers of participants on S is very near to the equilibrium prediction. In each session the median number of players on the side road S is 6. The mean number of players on the side road S is 5.98
Response mode
A participant who had a bad payoff on the road chosen may change his road in order to travel where it is less crowded. We call this the direct response mode. A road change is the more probable the worse the payoff was.
The direct response mode is the prevailing one but there is also a contrary response mode. Under the contrary response mode, a road change is more likely the better the payoff was. The contrary participant expects that a high payoff will attract many others and that therefore the
Simulation of the laboratory experiments
In order to get a deeper insight into this theoretical significance of our result, we have run simulations based on a version of a well-known reinforcement learning model, the payoff-sum model. This model already described by Harley (1981) and later by Arthur (1991) has been used extensively by Erev and Roth (1998) in the literature on experimental economics. The algorithm could be described as is shown in the enclosed box below.
We are looking at player i who has to choose among n strategies
Conclusion
The study has shown that the mean numbers on both roads tend to be very near to the equilibrium. Nevertheless, fluctuations persist until the end of the sessions in both treatments. This is of particular interest in view of the fact that the experiments run over 200 periods which is unusually long and should be enough to show a tendency of convergence to equilibrium if there is one.
Feedback on both road times significantly reduces fluctuations in treatment II compared to treatment I. However,
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