A system dynamics model for a mixed-strategy game between police and driver

Game theorists have recommended many reasonable strategies in policy problems, using, in general, the concept of equilibrium strategy for analyzing the dynamic consequences of available policy options. One of the best known recommendations is that of George Tsebelis, which contends that increasing penalties is not a viable policy tool for decreasing the law-violation tendencies of drivers. This is because the interactions between police and driver can best be represented as a mixed strategy in which the players choose their alternative actions based upon a probability, but the probability of driver's law violation cannot be decreased by increasing the penalty. Our system dynamics model for a mixed-strategy game shows that it takes a very long time for a game-theoretic equilibrium to appear. Therefore, game players cannot, and should not, depend on the equilibrium for choosing their actions. Furthermore, our mixed-game model shows that an increase in penalty can induce compliance from the people, contradictory to the game-theoretic solution, but consistent with real-world behaviors.