Game Theory Applied to the Death Penalty - Appunti

Game theory

Prof. Francesco Parisi

The use of death penalty does not prevent murders

Daniele Ruggiero

4743786

Summary

• Introduction.
• The game.
• Expected Loss and prospective penalties.
• Application to the three types of penalty.
• Focal Nash Equilibrium.
• Utility maximization.
• Conclusion.

Introduction

The evolution of humanity has brought into almost every single civilized community the need to have a legal system. This need was dictated by the desire of citizens to have an authoritative central organization that would take care of the community as a whole. As proved and seen in the past, anarchy did not lead to anything good.

One of the utmost achievements that the legal system has to keep in mind, besides providing services and facilities needed by the community, is the prevention of crimes. The citizens want to feel secure on the territory under the jurisdiction of the State they had given the power to reign on.

This is the reason that brought to the birth of the Criminal Law System. Prevention of crimes has to be guaranteed for an efficient functioning of the society and the possibility of the State’s growth. There are several elements and goals that the Criminal Law System has to take into consideration in deciding how to prevent crimes. Retribution, deterrence, rehabilitation, incapacitation, and restitution are some of them. But the most peculiar and difficult part is defining the penalty that has to be addressed to the committed crime.

Nowadays, the most advanced Criminal Law Systems use the theory of ‘marginal deterrence’, that is a principle stating that the most severe crimes need to be punished harder than lesser crimes and that a series of crimes should be punished harder than a single crime of the same kind, in order to avoid the criminal’s benefits from committing additional crimes. Following this rule, the worst crimes, usually involving the death of someone, have to be punished with the worst penalty that can be applied, that is the death penalty.

In the past, almost all societies had adopted the use of the death penalty for ‘capital crimes’. But, since the end of the 18^th century, the world faced a change of course: States began to remove death penalties from their criminal systems and today more than sixty percent of countries worldwide have rejected it as a way of punishment.

Why did this change of course take place? Probably because the more civilized a society becomes, the more sensible the people are when life is at stake. A long series of philosophies that arose since the 18^th century prove that the views of people have changed: the murder, executed by whomever, State included, is now considered to be inhuman and cruel. And it is the States’ duty to reflect the common opinion in their systems.

Usually penalties have two effects: punishing the delinquent for the committed crime and preventing them from committing other crimes. But when it comes to capital punishment, does the marginal deterrence rule still work? Does the death penalty actually prevent murders? Or does it, counter-intuitive as it is, increase their number? Will a lower penalty decrease the number of murders more than the ‘final penalty’?

The game

The following analysis will answer this question. In order to demonstrate that the use of death p