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How do people choose their commuting mode? An evolutionary approach to travel choices

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A considerable amount of studies in the transport literature is aimed at understanding the behavioural processes underlying travel choices, like mode and destination choices. In the present work, we propose the use of evolutionary game theory as a framework to study commuter mode choice. Evolutionary game models work under the assumptions that agents are boundedly rational and imitate others’ behaviour. We examine the possible dynamics that can emerge in a homogeneous urban population where commuters can choose between two modes, private car or public transport. We obtain a different number of equilibria depending on the values of the parameters of the model. We carry out comparative-static exercises and examine possible policy measures that can be implemented in order to modify the agents’ payoff, and consequently the equilibria of the system, leading society towards more sustainable transportation patterns.

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  1. Standard evolutionary theory, as well as replicator dynamics, when applied to biology, assume that agents meet a sufficiently high number of times, either deterministically or stochastically. This interpretation is not suitable for our specific application. Therefore, we rely on the alternative “behavioral” interpretation of the theory, according to which agents hold limited information and therefore make choices by reacting to what they observe in the population (Vega-Redondo 1996).

  2. As pointed out above, the current model is a generalisation and extension of this model.

  3. In the one-dimensional context of the model, every sign preserving adoption dynamics (i.e. for which the sign of the time derivative \(\dot{x}\) and the one of the payoff differential \(\Pi _{A}-\Pi _{B}\) is the same (Weibull 1995) generates the same trajectories of replicator dynamics in the interval (0, 1).

  4. The payoff difference can be rewritten as: \(\Pi _{A-B}=(d-g)\left( x^{2}-\frac{2d }{d-g}x+\frac{f+d}{d-g}\right) .\) Being the y-coordinate of a parabola equal to \(y=- \frac{\triangle }{4a}\), in our case this value will be equal to \(y=\frac{df-dg-fg}{d-g}\). In the current case (\(d<g\)), the denominator is always negative, therefore the only condition needed for determining the sign of the whole fraction is the sign of the numerator.

  5. In fact, since the abscissa of the vertex of the parabola is equal to \(\frac{ d}{d-g}\), recalling that \(d\ge 0\) and that in the present scenario \(d>g\), we can conclude that if \(d>0\) the entire fraction is positive. Notice that if \(d=0\) (i.e. bus users are not harmed by overcrowded buses), the abscissa of the vertex is zero; if so, \(\dot{x}\in (0,1)\) is the one-dimensional analogous of the saddle-node point in a two-dimensional space.

  6. There the values of the parameters are: \(a=0.2\), \(b=0.1\), \(c=0.4\), \(d=0.3\), \(e=0.4\); and the payoff difference equation is equal to \((\Pi _{A}-\Pi _{B})=0.1-0.6x+0.6x^{2}\).

  7. Fuel taxes are generally seen as an effective measure, but some studies question their effectiveness. For example, Storchmann (2001) recognizes that an increase in fuel taxes potentially implies a “triple dividend”, i.e. a regulative, modal-shift effect, a fiscal effect and a positive effect on the public transport sector, represented by a decrease in deficit. But the author argues that the first two effects are rarely jointly achievable: in fact, if demand for car use is inelastic (i.e. people will not give up their car when the tax is imposed) the fiscal effect will prevail, while if it is elastic the regulative one will, with negative consequences for public revenue.


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Correspondence to Chiara Calastri.

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Calastri, C., Borghesi, S. & Fagiolo, G. How do people choose their commuting mode? An evolutionary approach to travel choices. Econ Polit 36, 887–912 (2019).

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