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 Game
review
Solving the Game
payoffs for B when
A stays “silent”
payoffs for B when
A “betrays” B
Strict Dominance
Nash-Equilibrium
Economics in Dilbert & the Classroom
• Dilbert gets caught in a prisoner’s dilemma
• He mistakenly believes that his coworkers will
deviate from the dominant strategy
[watch here]
Advertising
• Advertising
– Costly
– Purpose: increase
product demand
– If both firms advertise,
expenses go up, but
demand increases; each
cancels other out
– “Arms race” of
advertising
Cigarette Advertising on TV
• In 1970, Congress enacted a law
making cigarette advertising on TV
illegal
– Reasoning: too many ads being seen by
children and teens
– Goal: reduce smoking among all ages
• Unintended consequence
– This actually increased the economic
profits of cigarette makers
– The law ended their prisoner’s dilemma
of advertising
Weak Dominance
• Game Theory in the Dark Knight [watch here]
Split or Steal
• [watch here] and [here]
Trust Games
Escaping the Prisoner’s Dilemma
• The Nash equilibrium in prisoner dilemma
games may give the best short run payoffs
• However,
– Many games are repeated
– This repetition occurs over a longer time span
– Dominant strategies may not consider long-run
benefits of cooperation
Tit-for-Tat
- A long run strategy designed to create cooperation
among participants
– Strategy: mimic the decision your opponent made
in the previous round.
– Changes the incentives and encourages
cooperation
– Useful because interactions in life occur over the
long run. Relationships between people and
businesses involve mutual trust.
Paper, Rock, Scissors
[ watch here ]
[ how to win?]
The Penny Game
•
•
•
•
•
We will simultaneously choose H or T
If I pick H and you pick H, then I win.
If I pick H and you pick T, you win.
If I pick T and you pick T, then I win.
If I pick T and you pick H, you win.
What is the solution of this game?
Mixed Strategy vs Pure Strategy
• Pure Strategy – specific action that the player
follows in every possible attainable situation of
the game (it’s not random).
• Mixed Strategy – possible moves and a
probability distribution which corresponds to
how frequently each move is to be played. (use
mixed strategy only when indifferent between
several pure strategies, and when keeping the
opponent guessing is desirable)
Practice Question
How can a pure strategy Nash equilibrium
be accurately described?
A. It is always the overall best outcome
B. It’s an outcome in which neither player
wants to change strategies
C. It can only be reached by collusion
D. One exists in all games
The Chicken Game
[watch here]
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)
steal
A/B
I
steal
1
not
II
1
III
5
5
not
0
0
IV
3
3
Results/ Implications
1. Dominant Strategy
2. Nash-Equilibrium
Is it Pareto efficient?
3. Which is the optimal solution? And how do we get
there?
ONE REASON TO HAVE A GOVERNMENT IS ALLOCATIVE EFFICIENCY
Results/ Implications
5. 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).
A/B
R
I
R
L
1
II
1
III
0
0
L
0
0
IV
1
1
Results/ Implications
1. 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]
Externalities
Definition: 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
negative
positive
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 Debt
Real time debt clock [see here] [debt clock breaks]
Where do we go from here?
• Juan Enriquez on mind boggling science [watch here]