Economics Department FIU
Game Theory
Notes
Prof Dacal
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Game theory
From Wikipedia [with modifications]
Game theory
is a branch of
applied mathematics
that is used in the
social sciences
, most notably
in
economics
. Game theory attempts to mathematically capture behavior in strategic situations,
or
games
, in which an individual's success in making choices depends on the choices of others.
While initially developed to analyze competitions in which one individual does better at
another's expense (
zero sum games
).
Traditional applications of game theory attempt to find equilibrium in these games. In
equilibrium, each player of the game has adopted a strategy that they are unlikely to change
(most famous the
Nash equilibrium
).
Representation of games
A game consists of a set of
players
, a set of moves (or
strategies
) available to those players, and a
specification of payoffs for each combination of strategies. Most cooperative games are
presented in the characteristic function form, while the extensive and the normal forms are used
to define noncooperative games.
Extensive form
An extensive form game
The extensive form can be used to formalize games with some important order. Games here are
often presented as
trees
(as pictured above). Here each node represents a point of choice for a
player. The player is specified by a number listed by the node. The lines out of the node
represent a possible action for that player. The payoffs are specified at the bottom of the tree.
In the game pictured here, there are two players.
Player 1
moves first and chooses either
F
or
U
.
Player 2
sees
Player 1'
s move and then chooses
A
or
R
. Suppose that
Player 1
chooses
U
and
then
Player 2
chooses
A
, then
Player 1
gets 8 and
Player 2
gets 2.
The extensive form can also capture simultaneousmove games and games with
imperfect
information
or asymmetric information. To represent it, either a dotted line connects different
vertices to represent them as being part of the same
information set
(i.e., the players do not know
at which point they are), or a closed line is drawn around them.
2
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 Fall '11
 Dacal
 Game Theory, player, Economics Department FIU

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