Skip to main content

Main menu

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
    • Front Matter Portal
    • Journal Club
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Accessibility Statement
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian

User menu

  • Log in
  • My Cart

Search

  • Advanced search
Home
Home
  • Log in
  • My Cart

Advanced Search

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
    • Front Matter Portal
    • Journal Club
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
Research Article

The dynamics of deterrence

Mark Kleiman and Beau Kilmer
  1. aDepartment of Public Policy, University of California, 3250 Public Affairs Building, Los Angeles, CA 90095-1656; and
  2. bDrug Policy Research Center, RAND, 1776 Main Street, Santa Monica, CA 90407-2138

See allHide authors and affiliations

PNAS August 25, 2009 106 (34) 14230-14235; https://doi.org/10.1073/pnas.0905513106
Mark Kleiman
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: kleiman@ucla.edu
Beau Kilmer
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  1. Communicated by Thomas C. Schelling, University of Maryland, College Park, College Park, MD, June 15, 2009 (received for review September 7, 2007)

  • Article
  • Figures & SI
  • Info & Metrics
  • PDF
Loading

Abstract

Because punishment is scarce, costly, and painful, optimal enforcement strategies will minimize the amount of actual punishment required to effectuate deterrence. If potential offenders are sufficiently deterrable, increasing the conditional probability of punishment (given violation) can reduce the amount of punishment actually inflicted, by “tipping” a situation from its high-violation equilibrium to its low-violation equilibrium. Compared to random or “equal opportunity” enforcement, dynamically concentrated sanctions can reduce the punishment level necessary to tip the system, especially if preceded by warnings. Game theory and some simple and robust Monte Carlo simulations demonstrate these results, which, in addition to their potential for reducing crime and incarceration, may have implications for both management and regulation.

  • crime
  • enforcement
  • game theory
  • positive feedback
  • tipping

Footnotes

  • 1To whom correspondence should be addressed. E-mail: kleiman{at}ucla.edu
  • Author contributions: M.K. designed research; M.K. and B.K. performed research; B.K. analyzed data; and M.K. and B.K. wrote the paper.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.pnas.org/cgi/content/full/0905513106/DCSupplemental.

  • ↵† A randomized controlled trial of this program is underway, and the preliminary results are promising (9).

  • ↵‡ Variously attributed to Nimzowitsch, Tartakower, and Eisenbach.

  • ↵§ There are alternative explanations and differential crime rates in seemingly similar communities. See SI Text for a review of these explanations.

  • ↵¶ Previously published theoretical models suggest that focused enforcement with announcement can outperform a strategy of random enforcement (21). Using computational modeling, this paper builds on these efforts by (i) focusing on repeated game settings, (ii) relaxing the assumption that potential offenders have perfect information about the probability of being punished, (iii) allowing those subject to a rule to update their subjective probability of being punished in Bayesian fashion, and (iv) showing that dynamic concentration as a punishment-allocation strategy can reduce both offense levels and punishment levels, compared to equal-probability punishment. The same game has also been approached from the other side, focusing on the problem of political dissenters who need to coordinate the time of their dissent to minimize the punishment risk faced by each 1 of them (22). van Baal's book on computer simulations of criminal deterrence (23) does not address our main concern about how to choose who to sanction when the number of offenders exceeds the number of available sanctions.

  • ↵‖ If P < C, then violation is a dominant strategy for both players; if P > 2C, then compliance is stochastically dominant for both players, because in that case P/2, the expected value of punishment, is greater than the cost of compliance even if both players were to violate. So only the intermediate case where C is between P and 2P (more generally, between P and nP) is strategically complex.

  • ↵†† However, if there is any player who attributes to each other player a nonzero probability of defection, then that player's subjective estimate of the probability that someone else will defect, and therefore that player's incentive to defect, tends toward unity as n grows.

  • ↵†† In Fig. 2, the tipping point for random sanctioning is ≈20% higher than it is for dynamic concentration; the comparable number for Fig. S3 is ≈33%.

  • ↵§§ That adding sanctions capacity can, mathematically, reduce actual sanctions use does not imply that any actual increase in sanctions capacity, e.g., building more prisons, will lead to less punishment. That depends on circumstances and on how the additional capacity is used; using more prison cells to impose longer terms does not increase certainty and therefore will increase, rather than decrease, total punishment actually inflicted.

View Full Text
PreviousNext
Back to top
Article Alerts
Email Article

Thank you for your interest in spreading the word on PNAS.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
The dynamics of deterrence
(Your Name) has sent you a message from PNAS
(Your Name) thought you would like to see the PNAS web site.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Citation Tools
The dynamics of deterrence
Mark Kleiman, Beau Kilmer
Proceedings of the National Academy of Sciences Aug 2009, 106 (34) 14230-14235; DOI: 10.1073/pnas.0905513106

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Request Permissions
Share
The dynamics of deterrence
Mark Kleiman, Beau Kilmer
Proceedings of the National Academy of Sciences Aug 2009, 106 (34) 14230-14235; DOI: 10.1073/pnas.0905513106
del.icio.us logo Digg logo Reddit logo Twitter logo CiteULike logo Facebook logo Google logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Mendeley logo Mendeley

Article Classifications

  • Social Sciences
  • Economic Sciences
Proceedings of the National Academy of Sciences: 106 (34)
Table of Contents

Submit

Sign up for Article Alerts

Jump to section

  • Article
    • Abstract
    • Results
    • Discussion
    • Materials and Methods
    • Acknowledgments
    • Footnotes
    • References
  • Figures & SI
  • Info & Metrics
  • PDF

You May Also be Interested in

Setting sun over a sun-baked dirt landscape
Core Concept: Popular integrated assessment climate policy models have key caveats
Better explicating the strengths and shortcomings of these models will help refine projections and improve transparency in the years ahead.
Image credit: Witsawat.S.
Model of the Amazon forest
News Feature: A sea in the Amazon
Did the Caribbean sweep into the western Amazon millions of years ago, shaping the region’s rich biodiversity?
Image credit: Tacio Cordeiro Bicudo (University of São Paulo, São Paulo, Brazil), Victor Sacek (University of São Paulo, São Paulo, Brazil), and Lucy Reading-Ikkanda (artist).
Syrian archaeological site
Journal Club: In Mesopotamia, early cities may have faltered before climate-driven collapse
Settlements 4,200 years ago may have suffered from overpopulation before drought and lower temperatures ultimately made them unsustainable.
Image credit: Andrea Ricci.
Click beetle on a leaf
How click beetles jump
Marianne Alleyna, Aimy Wissa, and Ophelia Bolmin explain how the click beetle amplifies power to pull off its signature jump.
Listen
Past PodcastsSubscribe
Birds nestling on tree branches
Parent–offspring conflict in songbird fledging
Some songbird parents might improve their own fitness by manipulating their offspring into leaving the nest early, at the cost of fledgling survival, a study finds.
Image credit: Gil Eckrich (photographer).

Similar Articles

Site Logo
Powered by HighWire
  • Submit Manuscript
  • Twitter
  • Facebook
  • RSS Feeds
  • Email Alerts

Articles

  • Current Issue
  • Special Feature Articles – Most Recent
  • List of Issues

PNAS Portals

  • Anthropology
  • Chemistry
  • Classics
  • Front Matter
  • Physics
  • Sustainability Science
  • Teaching Resources

Information

  • Authors
  • Editorial Board
  • Reviewers
  • Subscribers
  • Librarians
  • Press
  • Site Map
  • PNAS Updates
  • FAQs
  • Accessibility Statement
  • Rights & Permissions
  • About
  • Contact

Feedback    Privacy/Legal

Copyright © 2021 National Academy of Sciences. Online ISSN 1091-6490