Domain 12
Crime and Policing
Enforcement is an inspection game; deterrence depends on detection probability far more than on penalty severity.
The comparative static is the useful part. Because each side mixes to make the other indifferent, raising the penalty reduces the equilibrium inspection rate rather than the violation rate — unless the inspection rate is held fixed from outside the game. Which means increasing sentences without increasing detection is predicted to change very little, and the empirical literature broadly agrees. Plea bargaining is an ultimatum with an enormous asymmetry in the cost of refusal, which is why guilty pleas do not straightforwardly indicate guilt.
Victims, who are frequently not parties to the prosecution at all. Also the communities where enforcement is concentrated, whose willingness to cooperate is a shared resource that heavy-handed enforcement depletes.
What to look for
- Is coverage predictable? Then it is being routed around.
- Is the policy raising the penalty or raising the chance of being caught?
- What does refusing the offer cost the defendant, versus accepting it?
- Is community cooperation being spent faster than it is being replaced?
The shapes that run this field
The Inspection Game
A strictly competitive game with no pure equilibrium: the inspector wants to match, the evader wants to miss.
Shape 10The Ultimatum
One side proposes a split; the other can only accept or destroy the whole thing.
Shape 07The Repeated Game
Repetition creates a future cost to defecting today, which can make cooperation individually rational without changing anyone's character.
Shape 06The Commons
A rival but non-excludable resource: each user's extraction imposes a cost spread across all users.
Shape 01The Prisoner's Dilemma
Mutual cooperation beats mutual defection, but defecting is the better move whatever the other side does.
In practice
The Inspection Game
Patrols on a fixed schedule, and offending that has simply moved to the gaps.
The Ultimatum
A plea offer where refusal risks many times the sentence. It is rational to accept whether or not you did it.
The Commons
Enforcement that raises short-term compliance and spends the cooperation it will need next year.