Introduction: What is Game Theory? Microeconomics I: Game Theory

Microeconomics I: Game Theory
Introduction:
What is Game Theory?
(see Osborne, 2009, Sect 1.1)
Dr. Michael Trost
Department of Applied Microeconomics
October 25, 2013
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
1 / 31
What is game theory?
Game theory is the scientific discipline that studies situations
in which decision-makers interact.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
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Situations of interaction
Situations of interaction are situations in which the well-being
of a decision maker depends not only on her own action, but
also on the actions of other decision-makers.
Henceforth, such situations are referred to as games.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
3 / 31
Situations of interaction
E XAMPLES of situations of interaction:
Board and card games (e.g., chess, back gammon, poker,
bridge, etc.)
Economic games (e.g., firms competing for business,
bidders competing in auctions, joint ventures)
Political games (e.g., political candidates competing for
votes, international trade agreements)
Biological games (e.g., animals fighting over preys and
territories)
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
4 / 31
What is not a game?
Two cases: Isolated or insignificant decision maker
. (Isolation) Your decisions affect only yourself
- Personal issues like whether to go jogging or not, how many
movies to watch in a week, what to build in a sand-box.
- Price-setting behavior of a monopolistic firm
. (Insignificance) Because there so many decision-makers
involved, your decision does not (really) affect others’
decisions.
- Buying foreign exchanges or stocks.
- Price-taking behavior of a firm (assumption of perfect
competition)
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
5 / 31
Let’s play a game: The Guessing Game
The rules of this game are as follows:
. Each of you secretly submits a number from interval
[0,100]. The winner is the person whose submitted number
is the closest to the two-third of the mean of all submitted
numbers.
. The winner receives a prize. If there are several winners the
prize will be divided equally among them.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
6 / 31
Interaction in the Guessing Game
As its name suggests, the G UESSING G AME induces a situation
of interaction:
The success of a player’s guess depends essentially on the
numbers guessed by the other players.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
7 / 31
Game-theoretic models
Like other sciences, game theory consists of a variety of models.
A game-theoretic model is an abstract representation of real-life
situations of interaction.
Such abstractions allow us to study a wide range of social and
biological phenomena and to improve our understanding of the
world.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
8 / 31
Rules of a game
A game is a detailed description of a situation of interaction. It
describes the rules under which this interaction takes place.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
9 / 31
Rules of a game
For example, a game specifies
the set of participants (which are referred to as players)
the set of actions available by the players
the set of outcomes resulting from the available actions
the sequence of the players’ moves
the information the players have about the past moves of
the other players
the information the players have about the goals pursued
by the other players
...
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
10 / 31
Classes of games
A class of games is a set of games which have certain rules in
common. Following classifications of games are popular in
game theory.
- Cooperative and noncooperative games
- Strategic and extensive games
- Games with complete and with incomplete information
- Games with perfect and with imperfect information
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
11 / 31
Cooperative and noncooperative games
Noncooperative games are games in which the players choose
independently their actions. The players are not able to enforce
a binding agreement on their actions.
Cooperative games (also called coalitional games) are games in
which the players can form coalitions and engage in a binding
agreement on their actions.
R EMARK : In this course, we only deal with noncooperative
games.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
12 / 31
Strategic games and extensive games
Strategic games (also known as simultaneous move games)
describe situations of interactions in which each player moves
only ones and the players’ decisions are made simultaneously
(i.e, when choosing an action each player is not informed of
actions chosen by the other players)
E XAMPLES : R OCK -PAPER -S CISSORS, M ATCHING P ENNIES,
presidential election
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
13 / 31
Strategic games and extensive games
Extensive games (also known as dynamic games) describe
situations of interactions in which the players move
sequentially.
E XAMPLE : T IC -TAC -T OE, M ARIENBAD G AME, poker, eBay
auction
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
14 / 31
Tic-Tac-Toe
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Microeconomics I: Game Theory
Introduction
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Marienbad Game
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Microeconomics I: Game Theory
Introduction
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Complete and incomplete information
A game takes place under complete information if there is
common knowledge about the preferences the players have (i.e.,
every player knows the preferences of every player, every
player knows that every player knows the preferences of every
player, and so on ad infinitum) .
A game takes place under incomplete information if some
player is uncertain about the preferences of some other player.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
17 / 31
Perfect and imperfect information
A game takes place under perfect information if each player
when she is deciding is informed about the past moves of her
opponents.
A game takes place under imperfect information if some player
is uncertain about the past moves of her opponents.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
18 / 31
Game-theoretic solution concepts
A game describes the set of actions a player can do, but does not
specify the actions that the player do take.
A solution of a game determines the set of actions that may be
realized by the players and a solution concept for a class games
determines for each game of this class the set of actions that may
be realized by the players.
Game theory aims to provide reasonable solutions for classes of
games and to examine their properties.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
19 / 31
The Nash equilibrium concept
The most prominent solution concept of game theory is the
solution concept introduced by John F. Nash (1950), which is
known nowadays as the Nash equilibrium concept.
John F. Nash (born on June 13, 1928) received,
together with John C. Harsanyi and Reinhard
Selten, the Sveriges Riksbank Prize in Economic
Sciences in Memory of Alfred Nobel in 1994 for
their “pioneering analysis of equilibria in the
theory of noncooperative games”.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
20 / 31
The Nash equilibrium concept
The actions chosen by the players constitute a Nash equilibrium
if they satisfy following property of stability: None of the
players has an incentive to deviate from her action provided
that the other players have already realized these actions.
Q UESTION : What’s the Nash equilibrium of the G UESSING
G AME? Is it reasonable?
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
21 / 31
Positive and normative game theory
Game theory is used to address
positive issues of situations of interaction.
- Why do interacting decision-maker behave as they do?
(explanation)
- How will decision-makers behave in situations of
interaction? (prediction)
normative issues of situations of interaction.
- How should interacting decision-maker behave?
(recommendation)
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Microeconomics I: Game Theory
Introduction
22 / 31
Positive applications of game theory
For example, game theory allows us to understand
- why public goods (e.g., defense or flood protection) are
often provided by state.
- why arrangements of production cartels are often broken
by their members.
- how the size of sunk costs will affect the price setting of a
monopolistic firm.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
23 / 31
Normative applications of game theory
For example, game theory helps us to figure out
- the winning (or at least non-losing) strategies for simple
recreational games (e.g., T IC -TAC -T OE, M ARIENBAD
GAME ).
- the profit-maximizing bids in auctions.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
24 / 31
Outline of this course
I The theory of rational choice
(a) Preferences and utility function
(b) Expected utility function
II Simultaneous move games with complete information
(a) Nash equilibrium in pure strategies
(b) Nash equilibrium in mixed strategies
III Simultaneous move games with incomplete information
(a) Bayesian games and Bayes-Nash equilibrium
(b) Auctions
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
25 / 31
Outline of this course
IV Dynamic games with complete information
(a) Extensive form games and subgame perfect equilibrium
(b) Bargaining games
V Dynamic games with imperfect information
(a) Repeated games and the Folk Theorems
(b) Signalling games and sequential equilibrium
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Microeconomics I: Game Theory
Introduction
26 / 31
Lectures
D ATE : The two-hour lectures game theory start on October 25
and take place on Fridays, 8:30 a.m., room LG 2/213.
A NNOUNCEMENTS : An additional two-hour lecture (instead of
a tutorial) is given on October 25, Friday, 10:15 a.m., room LG
2/213. In the last week of lectures a mock exam will be
discussed.
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Microeconomics I: Game Theory
Introduction
27 / 31
Tutorials to the lectures
In addition to the lecture tutorials are offered.
D ATE : The two-hour tutorials start on November 1 and take
place on Fridays, 10:15 a.m., room LG 2/213.
E XERCISES : Exercise sheets for tutorials will be uploaded a
week before. We advise you to go carefully through these
exercises before we will discuss them in tutorials. The formation
of learning groups is highly recommended.
R EMARK : There are no extra credits for the tutorials.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
28 / 31
Literature
Main textbook for this course:
Osborne, M. (2009), An Introduction to Game Theory, 2nd
edition, Oxford University Press, Oxford.)
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Microeconomics I: Game Theory
Introduction
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Literature
Further possible readings:
Heifetz, A. (2012), Game Theory: Interactive Strategies in
Economics and Management, Cambridge University Press,
Cambridge. (Introductory textbook)
McCarty N. and Meirowitz, A. (2007), Political Game Theory:
An Introduction, Cambridge University Press, Cambridge.
(Advanced textbook)
Osborne, M. and Rubinstein, A. (1994), A Course in Game
Theory, MIT Press, Cambridge. (Advanced textbook)
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
30 / 31
Acknowledgments
¨ ur
¨ Gurerk
¨
¨
I am indebted to Ozg
and Manfred Konigstein
for
their permission to paste parts of their teaching materials into
these lecture notes.
Dr. Michael Trost
Microeconomics I: Game Theory
Introduction
31 / 31
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