Why Does Theft Oscillate in Guadalajara? Evidence of Adaptive Behavior

This article proposes and empirically evaluates an evolutionary game model to explain cyclical patterns in the incidence of opportunistic theft in Guadalajara, Mexico. The objective is to assess whether crime fluctuations are compatible with an endogenous outcome of adaptive strategic interaction between potential victims and criminals under bounded rationality, rather than with an exogenous stochastic phenomenon, and whether this mechanism can be formalized, calibrated, and tested with data. The model integrates Routine Activity Theory (Cohen and Felson, 1979), the Economics of Crime (Becker, 1968), and proposes the Opportunistic Replicator Dynamics. The empirical analysis applies STL decomposition to 84 monthly observations (2017-2023) from the SESNSP. Using Augmented Dickey-Fuller and Ljung-Box tests, together with spectral analysis, a dominant period of 5 months is identified and used as a reference to set the SMM calibration target at 7 months. The parameters are calibrated using the Simulated Method of Moments. The out-of-sample contrast (2024-2025) is compatible with the stability of the cyclical pattern and identifies a second structural shift in the Nash equilibrium of -60%, comparable to that induced by COVID-19. The evidence establishes coherence between the model and the observed patterns, although not counterfactual causality. The results suggest the viability of evolutionary game theory for analyzing urban crime and indicate that security policies should modify the structural parameters of the game, particularly the effective probability of apprehension.