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Understanding Recurrent Crime as System-Immanent Collective Behavior

Figure 5

Robustness of crime cycles against the variation of network topology.

The social interaction networks were constructed by rewiring links of a square lattice of size with probability . For low values of , small-world properties emerge, while for we have a random regular graph. As is small and increases, the stationary fractions of the three competing strategies remain almost the same. However, due to the increasing interconnectedness of the players, the amplitude of oscillations increases. When a critical threshold value of is reached, the maxima become comparable to the system size and oscillations terminate abruptly. The winner is the strategy that mediates the evolutionary competition between the two other strategies. (A) For small inspection costs , large temptation and moderate inspection incentives , ordinary people are the winners [see the evolution in panels (A–D) in Fig. 4, in particular panel (C)]. (B) For moderate inspection costs , small temptation , and medium inspection incentives , criminals are the winners [see the evolution in panels (E–H) in Fig. 4, in particular panel (G)]. While cycles of crime are in general robust to variations of the network structure, the globalization by shortcut links adds another layer of complexity to the game that can result in the emergence of discontinuous phase transitions to absorbing states, for example, the prevalence of ordinary individuals (but not necessarily so). Note, however, that the evolutionary dynamics becomes more and more fragile as the cycles escalate [inset in (B)] shows the envelope of oscillations of ), until they eventually involve almost the whole population. A supplementary video depicting such an evolutionary process where criminals are the victors is available at youtube.com/watch?v = oGNOmLognOY. The final outcome of this dynamics may be hard to predict, especially if the population size is small and the strategies become subject to random extinction.

doi: https://doi.org/10.1371/journal.pone.0076063.g005