Legalization of drugs and strategic behaviour

ALBUQUERQUEMELLO, VINÍCIUS PHILLIPE DE; RAMOS, FRANCISCO S.

doi:10.1590/0101-31572021-3117

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Brazilian Journal of Political Economy

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Articles • Brazil. J. Polit. Econ. 41 (3) • 2021 • https://doi.org/10.1590/0101-31572021-3117 copy

Legalization of drugs and strategic behaviour

Legalização das drogas e comportamento estratégico

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The growing number of users, about 250 million, in 2016, and the sheer number of health problems, that cause 190,000 deaths per year, are just some of the data that has rekindled the debate and discussion into the efficiency of the prohibitionist drug policies concerning drug consumption throughout the world. As a result, there has been the establishment of a special branch of literature focused on the investigation into this theme. In this regard, the present article conducts an economic analysis of scenarios where there is no decriminalization of drugs and other areas where legalization has been partial (marijuana) or complete, based on Game Theory. Thus, different from other studies, this paper establishes conditions of compatibility of incentives so that the economy could become formal, after decriminalization, to avoid contraband under a legal guise. This paper also manages to show which situation (Nash equilibrium) provides the greatest well-being for society.

KEYWORDS:
Drug trafficking; smuggling; drug legalization; Game Theory

Scenario	State	Drug Dealer
I	$τ R_{L} + R_{I L} - C_{s, l, p, j} (R_{I L})$	$(1 - τ) R_{L} - C_{t r a f i c} - C_{a r m} (R_{I L}) - C_{a d v}$
II	$τ R_{L} - C_{s, l, p, j} (R_{I L})$	$(1 - τ) R_{L} + R_{I L} - C_{t r a f i c} - C_{a r m} (R_{I L}) - C_{a d v}$
III	$τ R_{L} - C_{s, l, p, j} (R_{I L})$	$(1 - τ) R_{L}$
IV	$R_{I L} - C_{s, l, p, j} (R_{I L})$	$- C_{c o n t r a b} - C_{a r m} (R_{I L}) - C_{a d v}$
V	$- C_{s, l, p, j} (R_{I L})$	$R_{I L} - C_{t r a f i c} - C_{c o n t r a b} - C_{a r m} (R_{I L})$
VI	$R_{I L} - C_{p} (R_{L})$	$- C_{c o n t r a b} - C_{a r m} (R_{I L}) - C_{a d v}$
VII	$- C_{p} (R_{L})$	$R_{I L} - C_{c o n t r a b} - C_{a r m} (R_{I L})$
VIII	$τ R_{L} - C_{p} (R_{L})$	$(1 - τ) R_{L}$
IX	$R_{I L} - C_{s, l, p, j} (R_{I L})$	$- C_{t r a f i c} - C_{a r m} (R_{I L}) - C_{a d v}$
X	$- C_{s, l, p, j} (R_{L})$	$R_{I L} - C_{t r a f i c} - C_{a r m} (R_{I L})$

		Drug Dealer
		Trafficking	Smuggling	Legal sales + Trafficking	Smuggling + Trafficking	Legal Sales
Government	Partially legalized	-	-	$pV (I) + (1 - p) V (II) pU (I) + (1 - p) U (II)$	$pV (IV) + (1 - p) V (V) pU (IV) + (1 - p) U (V)$	V(III), U(III)
	Fully legalized	-	$pV (VI) + (1 - p) V (VII) pU (VI) + (1 - p) U (VII)$	-	-	V(VIII), U(VIII)
	Not legalized	$pV (IX) + (1 - p) V (X) pU (IX) + (1 - p) U (X)$	-	-	-	-

Nash Equilibrium	Government Payoff
$\{LP, VL\}$	${τR}_{L} - C_{s, l, p, j} (R_{IL})$
$\{LP, VL + T\}$	${τR}_{L} + {pR}_{IL} - C_{s, l, p, j} (R_{IL})$
$\{LP, C + T\}$	${pR}_{IL} - C_{s, l, p, j} (R_{IL})$
$\{LT, C\}$	${pR}_{IL} - C_{p} (R_{L})$
$\{LT, VL\}$	${τR}_{L} - C_{p} (R_{L})$
$\{NL, T\}$	${pR}_{IL} - C_{s, l, p, j} (R_{IL})$

Characteristics	Drug Dealers	Source
Male	83.8%	Bureau of Justice Statistics - BJS (2019)
Female	16.2%	Bureau of Justice Statistics - BJS (2019)
Mean Age	29.38 years	Bureau of Justice Statistics - BJS (2019)
Citizenship
American	74.1%	Bureau of Justice Statistics - BJS (2019)
Foreign	25.95%	Bureau of Justice Statistics - BJS (2019)
Ethnicity
White	22.4%	Bureau of Justice Statistics - BJS (2019)
Black	24.6%	Bureau of Justice Statistics - BJS (2019)
Hispanic	49.8%	Bureau of Justice Statistics - BJS (2019)
Other	3.2%	Bureau of Justice Statistics - BJS (2019)
Schooling
Less than High School	36.6%	National Prisoner Statistics - NPS (2019)National Prisoner Statistics - NPS. 2019. Available at: <Available at: https://www.census.gov/econ/overview/go3000.html >. Acessed on: February 2019. https://www.census.gov/econ/overview/go3...
High School	52.0%	National Prisoner Statistics - NPS (2019)National Prisoner Statistics - NPS. 2019. Available at: <Available at: https://www.census.gov/econ/overview/go3000.html >. Acessed on: February 2019. https://www.census.gov/econ/overview/go3...
University Studies	11.4%	National Prisoner Statistics - NPS (2019)National Prisoner Statistics - NPS. 2019. Available at: <Available at: https://www.census.gov/econ/overview/go3000.html >. Acessed on: February 2019. https://www.census.gov/econ/overview/go3...
Mean time of imprisonment: drug trafficking	73.53 months	Calculated based on data from the United States Sentence Commission - USSC (2019)
Mean time of imprisonment: smuggling	17 months	Calculated based on data from the United States Sentence Commission - USSC (2019)
% of total inmates imprisoned for drug-related crimes	45.9%	Federal Bureau of Prisons - BOP (2019)Federal Bureau of Prisons - BOP. (2019). Available at: <Available at: https://www.bop.gov/about/statistics/statistics_inmate_offenses.jsp >. Acessed on: February 2019. https://www.bop.gov/about/statistics/sta...

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[TFN1] Source: Prepared by the authors.