Transcript Strategic Thinking, Information and Incentives

Strategic Thinking:
Applications of Game Theory
Professor Charles M. Kahn
Lecture 1
Sequential Games
The course applies
– Game Theory
– Mechanism Design
to problems in business
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Overview of Course
First Part: Game Theory
(the study of strategic decision making)
Non-Cooperative Games:
– Sequential vs. Simultaneous
– Repeated Interactions
– Strategic Moves: Threats, Promises and
Commitments
– Unpredictability
– Coordination
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Overview of Course
Second Part: Mechanism Design
(how institutions control or exploit
strategic behavior)
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Text
• Dixit and Nalebuff The Art of Strategy
– Not required (but really good!)
• Newspaper articles
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Today’s Topic:
Decision Trees
The Basic Rule
Sequential Games
Comparison to Decision Trees
The Basic Rule for Playing Sequential Games
Examples
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Decision Tree Procedure
• Work backward through the tree.
– To each chance node assign the expected
value of its branches.
– To each decision node assign the value of
the best alternative that follows.
• In doing so, you discover the optimal
decision for the decision maker.
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Tom Osborne's Decision Tree for the closing
minutes of the 1984 Orange Bowl
(from Dixit-Nalebuff, Thinking Strategically)
Osborne's team has just scored a touchdown,
making the team 8 points behind its
opponents. Osborne must decide whether to
try to kick or to run for extra points. (Kicking
gives one extra point, running gives two extra
points). After the extra point attempt, he
knows that he then has a 10% chance* of
getting one more touchdown (a touchdown
gives six points), after which he will be faced
with the same decision of whether to kick or
run for extra points.
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Tom Osborne's Decision Tree
for the closing minutes of the Orange Bowl
• Here is the relevant information: His team
has a 60% success rate in kicking for extra
points and a 30% success rate in running for
extra points.
• As far as Osborne is concerned, a win is
much better than a loss and a tie is a little
better than a loss. Say that
– winning is worth 5 utils*
– losing is worth 0 util
– a tie is worth 1 util.
*the margin of a win or a loss is irrelevant: a win is worth 5 utils whether
the team wins by a single point or by 20 points.
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Tom Osborne's Decision Tree
for the closing minutes of the Orange Bowl
Use the following information to fill in the conditional
probabilities at each chance node, and then use the
decision tree procedure to determine Osborne's best
choice.
Compare your results to the discussion in DixitNalebuff, chapter 2.
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Decision Tree vs. Game Tree
• Decision Tree
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Decision Tree vs. Game Tree
• Game Tree
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Decision Tree vs. Game Tree
A game tree is like a decision tree except:
– the terminal nodes have a payoff for each
player
– each decision node specifies which player
makes that particular decision
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Decision Tree vs. Game Tree
What makes a game special:
• In a game you must take account of
other players' goals in order to predict
their behavior
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Sequential Games
• The rule for playing: look ahead and
reason back
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Sequential Games
• Some subtleties:
– At each decision node, use THAT player’s
objective to predict behavior.
– Distinguish between outcome (what
happens at terminal node) and payoff
(what the outcome is worth to each player).
– A player’s objective is to maximize
expected payoff
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Strategy
• A player's STRATEGY in a game is a
rule that says which action he will
choose at each of his decision nodes.
• In other words, a player's STRATEGY
in a game is a complete program for
playing that game (at each point in the
game in each possible circumstance).
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Strategy
• Notation:
In describing a strategy, each decision node may be
given a unique label
OR
Each decision node may be identified by the history
of choices (branches) that lead up to it
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Examples
Ameritech vs AT&T
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Ameritech vs USNet
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Examples
Confrontation between Russia and
Ukraine over natural gas
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• Budget Battle and
Shutdown, 2013
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Game Theory
• Fundamental tension between theory
and practice:
– Real but messy examples
– Easily analyzed but stylized theoretical
constructs
• We will jump back and forth between
them
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Game Theory
The power of the game metaphor:
It forces you to be specific.
– Who are the players?
– What are their objectives?
– What are their moves (what decisions are
available to them)?
• Use this understanding to help predict
behavior
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