Traffic police faces the problem of enforcing speed limits under restricted budget. Implementing high Enforcement Thresholds (ET) will ease the workload on the police but will also intensify the problem of speeding. We model this as a game between the police, which wish that drivers obey the speed limits and the drivers who wish to speed without getting caught. For the police we construct a multi-stage strategy in which at each stage the ET is randomized between low and high values. This confuses the drivers who now need to consider the worst case of low ET. We establish analytically and by simulations that this strategy gradually reduces the ET until it converges to the desired speed limit without increasing the workload along the process. Importantly, this method works even if the strategy is known to the drivers. We study the effect of several factors on the convergence rate of the process. Interestingly, we find that increasing the frequency of randomization is more effective in expediting the process than raising the average amount of fines.
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The police may wish to avoid sanctions when the speed is too close to the speed limit. In this case b refers to the minimal value that the police consider for implementation.
Later we show that for “reasonable” (i.e. not too large) h, the process is bounded from below by b.
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Dreyfuss, M., Nowik, I. A puzzled driver is a better driver: enforcing speed limits using a randomization strategy. J Glob Optim 76, 645–660 (2020). https://doi.org/10.1007/s10898-018-0700-8