## 1 Introduction  
The behavioral mechanisms underlying the day-to-day evolution of route choices have been the object of active research within the field of transport analysis since the seminal work of [PERSON] [1] demonstrated their impact upon the attractiveness and stability of equilibrium states in traffic networks. Understanding the fundamental drivers of day-to-day route choice behavior is of utmost importance for the prediction of users' response to traffic management and information provision measures, notably the deployment of Advanced Traveler Information Systems (ATISs). The study of day-to-day route choice dynamics in traffic networks can be undertaken either from a theoretical standpoint or through an empirical approach. With regard to discrete-time deterministic process models, which are of particular interest to our study, [PERSON] and [PERSON] [2] established general theoretical results, followed by several contributions dealing with specific aspects and applications [3; 4; 5; 6; 7]. Repeated route choice behavior has also been the object of empirical research, often focusing on the effects of experiential knowledge or ATIS-supplied information on the evolutionary dynamics of traffic networks. While virtual experiments in laboratory-like settings have been extensively used as a method of investigation [8; 9; 10; 11; 12; 13; 14; 15], partially controlledon-road experiments [16; 17] and analyses of large sets of route choice data observed in real networks have also been reported in the literature [18; 19]. A connection between modeling and empirical approaches has been pursued as well [20; 21; 22]. The main purpose of the present study is to analyze how a specific feature, referred to as _contrarian route choice behavior_, may affect the day-to-day dynamics and the stability of traffic in transport networks. Generally speaking, contrarian behavior can be defined as a tendency to act \"contrary to the crowd\", and can be observed in a variety of collective systems in which individual decisions are based on the expectation of the choices that are likely to be made by others. Contrarianism is thus a kind of strategic behavior that can be framed within the wider context of cognitive hierarchy theory [23]. The emergence of contrarian behavior has been addressed by studies relating to various fields, ranging from investment strategies in financial markets [24; 25; 26] to social psychology and opinion dynamics [27; 28; 29], and has been analyzed in the framework of game theory as well [30; 31]. In order to introduce the setting of our study, we begin by presenting the basic concept through a simple example. Consider a group of travelers choosing repeatedly between two routes, denoted by \(I\) and \(2\), as in the case of individuals commuting daily from home to work. Route choices are dictated by _expected_ travel times, say \(t_{1}\) and \(t_{2}\), which may be based on experiential knowledge and/or on navigational advice supplied by an ATIS. If, on any given day, \(t_{1}<t_{2}\), subjects choosing route \(I\) are said to exhibit _direct choice behavior_, while those selecting route \(2\) are said to exhibit _contrarian choice behavior_. The latter is inspired by strategic reasoning based on the presumption that the majority of travelers will behave in a direct manner. If this is indeed the case, route \(I\) is likely to become the more crowded, and thus contrarians may end up traveling on the fastest route. Clearly, contrarian behavior can be successful only as long as it is adopted by a minority of subjects within the traveling population. Contrarian route choice behavior in traffic networks is a possible reaction of drivers to the information and recommendations supplied by route guidance systems [32], and has been investigated in several studies of day-to-day traffic dynamics adopting either experimental or agent-based simulation approaches. [PERSON] et al. [9] found that contrarian behavior was adopted by a minority of the participants confronted with a two-route scenario in a laboratory experiment.