Under a countryâ??s justice system, the prosecutor is the lawyer responsible for building casesagain

Under a country’s justice system, the prosecutor is the lawyer responsible for building casesagainst criminals. In addition, the prosecutor is involved in the legal negotiations with partnersin crime to get one or both of them to “Fink” ( i n o t h e r w o r d s , t o “turn state’sevidence”) on their partner so that the prosecutor has a stronger case against both criminals,and so obtains greater prison sentences for both partners, which are the negative “payoffs”for both parties.Then, consider the following situation: if, in advance of their crimes, both partners in crimeagree not to Fink, which is to stay “Mum” (or remain silent: note that the prosecutor does nothope this to happen), then the prosecutor can only get a one-year sentence from the court forboth of them: however, if both partners in crime Fink on each other, the prosecutor can get thecourt to hand down a five-year sentence for both of them.Then, consider what the prosecutor can choose (or control), which are the rewards they canoffer a s u s p e c t w h o i s a potential Finker for their cooperation toward the prosecutor(denote this negative payoff as -a), and the harsher penalties they can i m p o s e against anon-cooperative suspect who decides to remain Mum (denote this negative payoff as -b). Thatis, the payoff matrix here is:Prisoner BMumFinkMum(-1.-1)(-b,-a)Prisoner AFink(-a,-b)(-5.-5)Note: A bundle of payoff (x, y) means that Prisoner A gets x and Prisoner B gets y.In a Nash Equilibrium sense, how should the prosecutor structure the “reward” parametera and the “punishment” parameter b so that he can induce the two prisoners to Fink on eachother, given how the court sets the sentence lengths in the (Mum, Mum) and (Fink, Fink)cases?

 

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