game theory

E183 Environment and People Zichao Yu
Institutions
Sep/26/2019

1

Today’s Topics
“Harvest the Commons Game” – Reflections

2

“Harvest the Commons Game” – Reflections
My goal was to design a game with rules under which
Individuals have an incentive to compete and pursue self interest.
Individuals will be better off if everybody cooperates than if everybody only works for him/herself.
Communication and cooperation can lead to greater collective gain and better outcomes for everyone.
Factors that complicate collective action
Number of stakeholders
Understanding of rules and payoffs
Communication and trust (strategic behavior, weak coalition)
Incentive structure (gaming the system? changing the rules?)

Individual Incentive vs Collective Gain
Individual incentive
Individuals act to maximize their own gain, most often based on anticipation of other people’s actions.
When impaired by lack of communication and/or trust, such choices are often suboptimal, though still rational.
Collective gain
With adequate communication and trust, a group of individuals can make a joint decision and reap benefits for the group – a collective gain.
Such collective gain can often be greater than the sum of benefits realized through individualized decisions.

Today’s Topics
Prisoner’s Dilemma

5

The Prisoner’s Dilemma
Two people together committed a crime and got caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see payoff table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

Allegory
The simplest human-interactive strategic game that displays the collective action problem.
Familiar with the story, terminologies, concepts.
6

The Prisoner’s Dilemma
Two people together committed a crime and get caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

The Prisoner’s Dilemma
Two people together committed a crime and get caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

The Prisoner’s Dilemma
Two people together committed a crime and get caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

The Prisoner’s Dilemma
Two people together committed a crime and get caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

The Prisoner’s Dilemma
Two people together committed a crime and get caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

“Dominant Strategy” for Suspect 1: Testify

The Prisoner’s Dilemma
Two people together committed a crime and get caught by the police.
The police have enough evidence to put each in jail for 1 year, but they want to investigate more.
Interrogation is conducted separately, not allowing the suspects to communicate with each other.
Each suspect can either testify against the other or deny the crime. They are informed of the potential outcomes (see table below) given their own choice and the choice of the other.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

“Equalibrium Outcome” of the Game

Today’s Topics
Game Theory

13

Game Theory
Definition: A form of applied mathematics used to model and predict people’s behavior in strategic situations where people’s choices are predicated on predicting the behavior of others.
John Forbes Nash, 1994 Nobel Prize in Economic Sciences.
A Beautiful Mind

Game Theory
Payoffs – people’s gain/loss given their own and others’ choices.
Strategies – people’s choices.
Dominant strategy – a choice that always maximizes individual gain regardless of other players’ choices.
Nash Equilibrium – a stable outcome in a game when no player can benefit by changing strategies while the other players keep theirs unchanged.

Years in jail (Suspect 1, Suspect 2)

Suspect 2’s Strategies

Testify
Deny

Suspect 1’s Strategies
Testify
(2 years, 2 years)
(0 year, 3 years)

Deny
(3 years, 0 year)
(1 year, 1 year)

Today’s Topics
The Tragedy of the Commons

16

The Tragedy of the Commons
The Pasture Example, told by Garret Hardin, is a frequently cited, stylized example of mismanagement of common resources.
Everyone has access to a commonly held pasture.
No rules about sustainable level of grazing.
Everyone gains a net benefit by adding more cows to the pasture.

The Tragedy of the Commons
The Pasture Example, told by Garret Hardin, is a frequently cited, stylized example of mismanagement of common resources.
Everyone has access to a commonly held pasture.
No rules about sustainable level of grazing.
Everyone gains a net benefit by adding more cows to the pasture.

The Tragedy of the Commons

The Tragedy of the Commons
The Pasture Example, told by Garret Hardin, is a frequently cited, stylized example of mismanagement of common resources.
Everyone has access to a commonly held pasture.
No rules about sustainable level of grazing.
Everyone gains a net benefit by adding more cows to the pasture.
Consequence is the pasture being overgrazed and destroyed.
How to avoid this tragedy?

The Tragedy of the Commons
Garret Hardin’s ideas
Conscience and goodwill are flimsy and unreliable. Eventually people will act in their own interest.
Two solutions are possible, theoretically.
The first is establishing state control of the commons. Decisions are made authoritatively.
Benevolent dictatorship? Who’s keeping the powerful accountable?
The second is privatization. because private owners carry the consequences of their own decisions, good or bad. They are thus incentivized to manage their property sustainably.  This is the Coase Solution!
Hardin himself prefers privatization.

The Tragedy of the Commons
Either state control or privatization involve some form of enclosure, where an “open access” resource is bounded and given over to control either by private owners or by a strong and coercive state management body.
Nature in most of its forms (fisheries, oil fields, climate systems, etc.) are commons – those difficult-to-enclose systems that invite free-riding and defection.
Hardin’s view is widely adopted – Solutions to many environmental problems often take the form of an environmental super-police state, or private property rights over environmental objects.

Today’s Topics
Hardin’s Approach in Real Life

23

Preventing the Tragedy
Hardin’s Approaches
State control of the commons. E.g. coal mining on federal land.
The Bureau of Land Management (under the Department of Interior) manages about 570 million acres of Federal mineral estate with coal development potential.

Preventing the Tragedy
Hardin’s Approaches
Privatization. E.g. oil and gas extraction on private lands.
The U.S. is one of only a few countries in the world that allow private individuals to own the minerals under their land.

Today’s Topics
An Alternative to Hardin?
An institutional approach – alter the incentive structure to make cooperation more…