Batman Interrogating The Joker and Mr Freeze: Confess or Keep Quiet?

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    Assume The Joker and Mr Freeze robbed a bank together and have been caught by Batman and Gotham City’s police. Batman is interrogating The Joker and Mr Freeze in separate rooms, The Joker and Mr Freeze cannot communicate at all. Should The Joker and Mr Freeze confess or keep quiet? If both The Joker and Mr Freeze confess to robbing the bank they will both go to jail for 5 years each. If The Joker confesses and Mr Freeze keeps quiet then Gotham police will let The Joker off for cooperating with them and throw the book at Mr Freeze by jailing him for 30 years and vice versa. If both The Joker and Mr Freeze keep quiet then they will both go to jail for just 1 year each.

    If The Joker believes Mr Freeze will keep quiet then The Joker will want to confess and get away with the crime rather than keep quiet too and go to jail for 1 year. Mr Freeze will reason the same way. So both The Joker and Mr Freeze will play their dominant strategy and confess.

    Both The Joker and Mr Freeze confessing means they will go to jail for 5 years each. So the Nash equilibrium (Confess, Confess) makes The Joker and Mr Freeze worse off than if they both keep quiet. As long as The Joker and Mr Freeze cannot communicate and do not trust each other to keep quiet, they will both confess. If The Joker and Mr Freeze could collude and make an agreement or if they trust each other then they could both keep quiet.

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