optimal cartel penalty regime with history dependency

in general compliance with competition law and deterrence of forming or joining any anti-competitive conducts are achieved through the deterrent effects of penalties. nevertheless, full compliance behavior is not observed from all firms. in this paper, we study dynamic enforcement of competition law in a dynamic model of an antitrust and firms and analyze via differential games how efficient is this law. we show that the current monetary penalty legislation seems not to be as efficient in the sense that full compliance behavior does not arise as the long-run steady-state equilibrium of the model. furthermore, we suggest a penalty regime that depends both on the infringement's duration and the rate of law enforcement and could totally prevent collusion. this regime is efficient from the point of view of the possibility of complete deterrence of cartel formation in long-run and there is a possibility to achieve the socially desirable outcome, i.e. the outcome with no anti-competitive conduct.