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Should private prisons be regulated at the federal level?

A project by Annika, Class of 2021, student at The Bishop’s School
for Global Online Academy’s Catalyst Conference Spring 2020 through Game Theory

Introduction

Video Part 1

Video Part 2

Video Transcript

Here is the link to the transcript for the video if connectivity issues arise! It is also for further accessibility, since not everyone on the internet can listen to audio.

Link to Google Docs

Game Theoretic Model

Player 1 is the side of the private prisons and companies who own them. Its options are to change nothing (Strategy A), improve conditions (Strategy B), or overhaul the system (Strategy C).
Player 2 is the side of the public, represented by the federal government.Its options are to ignore everything (Strategy W), make a statement (Strategy X), pass regulating legislation (Strategy Y), or pass prohibiting legislation (Strategy Z).

With three and four strategies respectively, Players 1 and 2 have 12 outcomes of their interaction. Player 1 prefers outcomes which increase profits, including not having to make severe changes without cause, and having no loss of public support. Player 2 prefers to hold the moral high ground, and improve the conditions of the prisons at any financial cost.
This is a simultaneous non-zero-sum game, and the cardinal utilities are represented in the matrix below, under 6. The utilities from Player 1’s perspective range from 10, with the prisons changing nothing and the public ignoring the problems, to -10, with the prisons overhauling the system and the public ignoring the problems. This is because the lack of the public’s notice will mean that the prisons incur additional costs without reason. The utilities from Player 2’s perspective range from -10, with the prisons changing nothing and the public ignoring the problems, to 10, with the prisons overhauling the system and the public passing prohibiting legislation. This is because the public wants to do the most good to help the prisoners, in which case having no changes creates the worst possible outcome.

The cardinal payoffs for Player 1:

Doing nothing -2 (negated if pubic ignoring)
Improving conditions 0 (standard)
Overhauling system -2
Not doing enough Ranges from -8 to 0 by severity
Accurate response 10 for public ignoring, 2 otherwise
Going too far Ranges from -8 to -1 by severity

These payoffs take into account the cost of overhauling the system in profits, and the cost of doing nothing in reputation. The accuracy of the response relative to the public’s requirements matters as well.

The cardinal payoffs for Player 2:

Ignoring problem -9
Making statement -8
Passing restrictions -5
Passing prohibitions 1
Prisons improve (not do nothing) 9
Prisons do nothing + ignore -1
Prisons do nothing + prohibit 2
Prisons overhaul (not do nothing) 14
Prisons overhaul + restrict -1
Prisons overhaul + prohibit -5

These payoffs take into account that prisons policing themselves and changing on their own, slightly further than what the public’s reaction, yields the highest payoff. The public pushing slightly past what the prisons do, however, yields lower payoffs.

The game is represented below in Model 1, with cardinal utilities. Player 1’s strategies are on the leftmost column, and Player 2’s on the first row.

Model 1.

2W

2X

2Y

2Z

1A

(10, -10)

(-2, -8)

(-4, -5)

(-8, 1)

1B

(-2, 0)

(0, 1)

(2, 4)

(-1, 8)

1C

(-10, 5)

(-5, 6)

(-2, 8)

(0, 10)

In Model 2, the pure strategy by dominance of Player 2 is shown. Strategy Z yields the highest outcomes for Player 2, no matter what Player 1 chooses to do.

Model 2.

2W

2X

2Y

2Z

1A

(10, -10)

(-2, -8)

(-4, -5)

(-8, 1)

1B

(-2, 0)

(0, 1)

(2, 4)

(-1, 8)

1C

(-10, 5)

(-5, 6)

(-2, 8)

(0, 10)

Based off of Model 2, the rationally best strategy for Player 1 in response to Strategy Z is Strategy C, because 0 is the highest remaining outcome. By dominance, the solution to this game is shown below in Model 3, with strategies C and Z leading to the outcome (0, 10).

Model 2.

2W

2X

2Y

2Z

1A

(10, -10)

(-2, -8)

(-4, -5)

(-8, 1)

1B

(-2, 0)

(0, 1)

(2, 4)

(-1, 8)

1C

(-10, 5)

(-5, 6)

(-2, 8)

(0, 10)

The Nash equilibrium outcome, as shown by dominance, is (0, 10). This outcome uses 1C and 2D.

Response

This outcome, given by the Nash equilibrium, is Pareto optimal because there is no other result for which both players have higher payoffs. That means that the solution to this game is at (0, 10). This solution represents both players effecting the maximum change possible. Player 1 will overhaul the system, and Player 2 will pass outlawing legislation. Taken in concert, all private prisons would be outlawed.

So, the solution shown by the game theoretic model is to outlaw all private prisons (on the side of the public/federal government. Is this reasonable? How could such a drastic change be implemented?

In the context of the real world, the issue with private prisons is more complicated than a simple “pass legislation” vote. Most reforms come from the states in the US and move to the federal level when proven to work. Private prisons have already been phased out in many more progressive states such as California. What is left next is to protect all of the country. As global citizens, and especially Americans, everyone can enact change at a more local level.

Feedback

Please respond in the comment section with thoughts on the private prison situation, including the depth of your knowledge prior to and after reading this page.

Resources

Sources Consulted and Cited

This page includes some links to articles that could act as further reading on this subject, including the response to California’s outlawing of private prisons.

Works Cited on Google Docs

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COMMENTS: 1
  1. April 25, 2020 by Caroline

    Hi! Wonderful job on your page, Annika! Your use of a game simulation/model was such an interesting approach to analyzing the current private prison problem. I would definitely pay attention to jargon because there were quite a few terms like “Pareto optimal” that students may not know unless they do outside searching. I would also recommend adding a bit of your own input and having solutions provided as to how we can replace the private prison infrastructure given that it would be in our best interest outlaw it. Personally speaking, I also do not believe in the efficacy of private prisons either, and your site solidified the technicalities behind that opinion. Let me know what steps you have in mind in regards to how we should go about abolishing the private prison system.

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