PUP-3002 Lecture Notes - Lecture 3: Nash Equilibrium, Twice As Much, Decision Theory

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9 Feb 2017
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PUP3002
Professor Barrilleaux
Chapter 2 Lecture Notes
Florida State University
Chapter 2:
Individuals and Social Dilemmas
I. Individuals and Social Dilemmas
A. Game Theory
a. Game Theory
1. A mathematical tool to study strategic decision making.
2. Is concerned with endogenous relationships
3. Attempts to answer a basic question
a. Conditional on what actor expects others to do, what
choice will a self-interested actor make?
b. Decision Theory
1. The study of how actors make decisions.
c. Exogenous
1. Externally determined- the actor’s decisions have no impact on
exogenous factors.
d. Endogenous
1. Internally determined- the actor’s decisions have no impact on
exogenous factors.
B. Individual Action
1. Society is composed of individuals
2. Individual choice and individual preferences have implications for
group decisions.
C. Personal Utility Maximization
1. Rational Choice: “patterns of behavior in societies reflect the
choices made by individuals as they try to maximize their benefits
and minimize their costs.
2. To make a rational choice, an actor must be able to discern the
following:
a. See all possible choices
b. Weigh the costs and benefits of all choices
c. Express and pursue what they deem best
a. Comparing Alternatives: Utility Functions
1. If an actor is ‘rational’ they will select the choice that gains them
the highest utility
2. Utility of actor A = U(a)
3. Ordinal Preferences = Rank Preferences
a. Ex: A=2, B=1; B is preferred to A
4. Cardinal Preferences = Continuous Valuation
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a. Ex: A=2, B=1; A is preferred TWICE AS MUCH as B
5. Between any two items in a set, preferences can be…
a. Strictly preferred: A > B
b. Weakly preferred: A B
c. Indifferent: A=B
6. In order to be rational, preferences must be:
a. Comparable
b. Transitive: If A>B & B>C, then A>C
D. Cooperation Problems
a. Scenario
1. Two forest-people (A and B)
2. They are cutting down trees in a rainforest
b. Two choices
1. Cooperate= Sustainably cut down trees
2. Defect= Cut down a ton of trees
E. Game Set-Up
Defect
Cooperate
Defect
D, D
D, C
Cooperate
C, D
C, C
F. Actor Behavior
a. The players act alone (not together)
b. Each actor wants to maximize their utility
c. In light of what the other actor does, how can I maximize my payoffs?
d. Nash Equilibrium
1. Set of strategies such that no player can unilaterally improve
their position given the other player’s action. Essentially, the Nash
Equilibrium reveals both players’ best response given the other’s
action.
G. Assigning Payoffs
a. Situation 1
1. If both players cooperate: The forest is preserved and both
collect a good payoff.
b. Situation 2
1. If player 1 defects and the other cooperates, the defector collects
a large share of the forest profits while bearing none of the costs.
2. The other bears the costs of commitment but receives none of
the benefits. The forest is harmed.
c. Situation 3
Player A
Player B
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