Game Theory & The Public Sector

Principles of Microeconomics 2023

Boris Nikolaev

Pacal’s Wager

• Should I believe in God?

What is Game Theory?

• Games– Strategic interaction between people.– E.g. Stalin & Hitler, Kruschev & Kennedy.– Assumptions (rationality, self-interested).

• Players (actors)• Strategies (actions)• Payoffs (associated with the strategies)

Example: The Prisoner’s Dilemma Gamereview

Solving the Game

payoffs for B whenA stays “silent”

payoffs for B when A “betrays” B

Strict Dominance

Nash-Equilibrium

Weak Dominance

• Game Theory in the Dark Knight [watch here]

Split or Steal

• [watch here] and [here]

Paper, Rock, Scissors

Provision of Public Goods• 2 self-interested players that have two strategies: steal or not steal.• simultaneous game (players don’t know how the other person will act)

I II

III IV

0

5steal

steal

not

not

1

1

5

0

3

3

A / B

Results/ Implications1. Dominant Strategy

2. Nash-Equilibrium

Is it Pareto efficient?

3. Which is the efficient solution? And how do we get there?

ONE REASON TO HAVE A GOVERNMENT IS ALLOCATIVE EFFICIENCY

Results/ Implications5. System of property rights + procedures to enforce them is a type of

SAMUELSONIAN PUBLIC GOOD = is one that is non-excludable in consumption.

A PURE PUBLIC GOOD is one that is both (1) non-excludable in consumption, and (2) non rival (e.g. National Defense).

6. What happens if we repeat the game (have a SUPERGAME)? Axelrod computer (real) simulations the cooperative solution emerges.Why do we need a government then?

7. When you expand the game it becomes virtually impossible to detect the cheater. This gives incentive for FREE RIDING.

8. DEMOCRACY as an institution for collective choice is needed only in certain communities by size, impersonability.

Coordination Games• 2 drivers on a narrow dirt road are approaching each other. They have one of two options:

go right (R) or left (L).

I II

III IV

0

0R

R

L

L

1

1

0

0

1

1

A / B

Results/ Implications1. Dominant Strategy: NO DOMINANT STRATEGY.2. MULTIPLE Nash-Equilibriums (no solution of the game).3. GOVERNMENT AS A COORDINATION MECHANISM.

Class Demonstration• How does this activity demonstrate the concept of

externality? • Is this a positive or a negative externality? • Why?

Gulf of Mexico Oil Spill (2010)

The Pacific Gyre Garbage Patch[see here]

The Aral Sea

Pollution in China

[see here]

ExternalitiesDefinition: unintended side-effects from actions that are otherwise useful

(non-market exchange). Externalities could be negative or positive. For example:

• Air pollution• Overfishing• Nuclear waste

• Education • Vaccination• Pollination

positive

negative

Graphical Analysis (- externality)

Graphical Analysis (+ externality)

How to correct this market failure?

Problems with Pigovian taxes

• How do you measure the external cost/benefit?

• Political influence [money in politics]

• Can externalities solve themselves?

The Coase’s Theorem• In the absence of transaction costs, an efficient outcome

will be achieved regardless of how property rights are assigned.

• Coase’s theorem gave rise to the field Law and Economics.

• Sparks from railroad trains setting wheat fields on fire. Two ways to solve problem: (1) spark catching attachments or (2) don’t plant next to railroad. The outcome?

• Bee keepers and farmers.

The Race for Candy• 50 pieces of candy is the

sustainable population.• The population will double

every round up to its sustainable level

• The person who collects the most candy will get 5 extra credit points on their final exam.

• If you collect more than 3 pieces of candy you will get 1 point.

The Tragedy of the Commons"That which is common to the greatest number has the

least care bestowed upon it." Aristotle

The Common Pool Problem• Common pool goods are rivalrous but non-excludable (e.g. irrigation

systems, forests, fish, hunting game, water, etc…)

• If you can take as much as you want without paying anything you have the incentive to free ride.

• Common pool resources are subject to the problem of congestion, overuse, pollution, and potential destruction.

• Government as a mechanism to prevent “the tragedy of the commons.”

• Elsinore Ostrom (she won the Nobel Prize in 2009) observes that local communities come up with solutions to this problem via different institutional arrangements (i.e. there is no need for government).

Redistribution

• The diminishing marginal utility of income

• Social insurance

• Stabilize the economy

The Public Sector

Federal DebtReal time debt clock [see here] [debt clock breaks]

Where do we go from here?

• Juan Enriquez on mind boggling science [watch here]