A small time crook is being interrogated by a policeman. The crook committed a petty crime, but everyone knows that gathering sufficient evidence to prove it will be time consuming for the police. The policeman tells the crook that if she doesn’t confess, he’s going to spend all of his time making sure that she gets the harshest sentence possible. The crook, in light of the threat, confesses. Analyze these game strategies. Verify that this scenario represents a Nash equilibrium, provided that the policeman would actually follow through with his threat. Now verify that the subgame-perfect equilibrium is for the crook not to confess and for the policeman to go back on his threat. That is, explain why the policeman’s threat is actually not credible.
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