## 1 Introduction
[PERSON] et al. [33] introduced _strategy coefficients_ in order to identify individual propensities toward direct or contrarian behavior in route choice games. In a controlled experiment on repeated route choice, [PERSON] et al. [34] detected the occurrence of strategic behavior, whereby some participants used ATIS recommendations as a means of anticipating other players' decisions. Typical behaviors of participants in a two-route repeated choice experiment were classified using cluster analysis by [PERSON] et al. [35], who studied the effect of providing full vs. partial travel time information on the fraction of contrarian responses. [PERSON] [36] analyzed day-to-day route choices in a laboratory-like setting and found a prevalence of direct behavior, with contrarians achieving lower individual travel times than subjects who reacted in a direct manner to the provided information. As shown by an experimental study reported in [37], contrarian behavior may emerge not only under conditions of selfish routing, but also in a scenario of cooperative routing promoted by means of a system-optimal oriented ATIS. Simulation-based studies have also addressed the issue of contrarianism in repeated route choice contexts. [PERSON] et al. [38] proposed to model typical commuter route choice behaviors in a multi-agent system using the notion of _personalities_. They concluded that the best performing agents were subjects making choices that are opposite to those appearing as \"good\" on the basis of the recent outcomes. [PERSON] and [PERSON] [39] applied the concept of strategic reasoning to simulate the day-to-day route choice behaviors of _first-level_ and _second-level thinkers_ in a simplified traffic system, and showed that strategic subjects could attain lower individual travel times only on the condition of being a minority within the population of network users. Motivated by the lack of analytical (as opposed to experimental or simulation-based) studies of contrarianism in day-to-day route choice, [PERSON] [40] proposed a macro scopic, closed-form model of traffic dynamics incorporating both direct and contrarian behaviors, and investigated several properties of the resulting nonlinear dynamical system. The study described in the present paper extends and generalizes the above cited work of the author by:  
* Introducing inertia into the dynamic process model representing the day-to-day evolution of the network state under mixed direct and contrarian route choices;
* Providing a more general statement of the fixed point stability conditions through the analysis of the Jacobian matrix of the resulting two-dimensional nonlinear dynamical system;
* Analyzing model behavior in the case of nonlinear link cost functions. The remainder of the paper is organized as follows. In Section 2, the proposed model is formulated as a discrete-time nonlinear dynamical system, and the related analysis of fixed point stability is carried out. Section 3 illustrates the results of numerical tests of the model on a simple network under different assumptions about the form of the travel cost functions. The significance, limitations and policy implications of the research findings are discussed in Section 4, together with concluding remarks and suggestions for possible developments of the proposed approach.