by Brandon Taylor
What do engagement rings, the Princess
Bride, steam engines, and spider battles have in common? They can all
be explained through game theory. In the second half of the twentieth
century, game theory helped make breakthroughs in various
disciplines, including economics, biology, computer science, and
philosophy. It sheds light on such fundamental notions as morality,
coordination, cooperation, signaling, and credibility.
Intuitive strategies (coming
forthwith)
Definition of game
Large numbers assumption
Definition of utility (for our
purposes)
Utility models
Self regarding vs. altruisitic
Perfect information
Components of a game
Normal form games
Dominating strategies/dominated
strategies
Strong
Weak
Nash equilibrium (yes, as in A
Beautiful Mind)
Examples
Prisoner's Dilemma (Cooperation
game)
Tragedy of the fishers
Karma
Afterlife
Societal punishments
Caveman (Coordination game)
Focal points
New York example
Steam engine example
Mixed Nash equilibrium
Soccer game
Caveman example
Extensive form game
Nature's move
Unknown move
Backwards Induction
Burning bridges
Subgames
Subgame reduction
Subgame perfect equilibrium'
Signaling games
Engagement ring
Credibility
Changing the game: strategies for
establishing credibility
Coming forthwith
Repeated games
Finitely repeated prisoner's
dilemma
Infinitely repeated games
Certain probability of ending at
each round
Decaying returns
Tit for tat
Public Choice Theory
Voting
Giving the wrong directions
Sortition
List of Interesting
Applications:
Business School
Keyboards
Steam engines vs. combustion engines
Tragedy of the fishers
Burning bridges
Alarm clock
Lemons (warranty)
Auctions
Business collusion
Biological Examples (genetic altruism)
New York example
Weight loss example
Giving/taking money (cultural
relativity)*
Engagement rings
More coming forthwith
Discussion Questions:
What the disadvantages of this kind of
utility model?
How can society achieve cooperation
and coordination?
What are the advantages of this kind
of very quantitative model of human behavior?
What are the disadvantages?
Do societies differ in their utility
models? Their game strategies?
Bonus: Wikipedia to the rescue
Game
theory has been put to several uses in philosophy.
Responding to two papers by W.V.O.
Quine (1960, 1967), Lewis
(1969)
used game theory to develop a philosophical account of convention.
In so doing, he provided the first analysis of common
knowledge and
employed it in analyzing play in coordination
games.
In addition, he first suggested that one can understand meaning in
terms of signaling
games.
This later suggestion has been pursued by several philosophers since
Lewis (Skyrms
(1996),
Grim, Kokalis, and Alai-Tafti et al. (2004)).
Following Lewis
(1969)
game-theoretic account of conventions, Edna Ullmann-Margalit (1977)
and Bicchieri (2006)
have developed theories of social
norms that
define them as Nash equilibria that result from transforming a
mixed-motive game into a coordination game.[24][25]
Game
theory has also challenged philosophers to think in terms of
interactive epistemology:
what it means for a collective to have common beliefs or knowledge,
and what are the consequences of this knowledge for the social
outcomes resulting from agents' interactions. Philosophers who have
worked in this area include Bicchieri (1989,
1993),[26] Skyrms (1990),[27] and Stalnaker (1999).[28]
In ethics,
some[who?] authors
have attempted to pursue the project, begun by Thomas
Hobbes,
of deriving morality from self-interest. Since games like
the prisoner's
dilemma present
an apparent conflict between morality and self-interest, explaining
why cooperation is required by self-interest is an important
component of this project. This general strategy is a component of
the general social
contract view
in political
philosophy (for
examples, see Gauthier
(1986)
and Kavka
(1986).[29]
Other
authors have attempted to use evolutionary
game theory in
order to explain the emergence of human attitudes about morality and
corresponding animal behaviors. These authors look at several games
including the prisoner's dilemma, stag
hunt,
and the Nash
bargaining game as
providing an explanation for the emergence of attitudes about
morality (see, e.g., Skyrms (1996, 2004)
and Sober and Wilson (1999)).
Some
assumptions used in some parts of game theory have been challenged in
philosophy; for example, psychological
egoism states
that rationality reduces to self-interest—a
claim debated among philosophers. (see Psychological
egoism#Criticisms)