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Young, Simon Christopher (1989) Bayesian models and repeated games. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b1456675~S1
Abstract
A
game is
a theoretical
model of a social situation where the people
involved have individually
only partial control over the outcomes.
Game theory is then the method used
to analyse these
models.
As
a player's outcome
from
a game
depends upon the actions of
his
opponents,
there
is
some uncertainty
in
these models.
This
uncertainty
is described probabilistically,
in terms
of
a player's subjective
beliefs
about the future
play of
his
opponent.
Any
additional
information
that is
acquired
by
the player can
be incorporated into the
analysis and
these subjective
beliefs
are revised.
Hence, the
approach taken is `Bayesian'.
Each
outcome
from the
game
has
a value
to
each of
the players, and the measure of merit
from
an outcome
is
referred to
as a player's utility.
This
concept of utility
is
combined with a
player's subjective probabilities to form
an expected utility, and
it is
assumed that each player
is trying to
maximise
his
expected utility.
Bayesian
models
for
games are constructed
in
order
to determine
strategies
for the
players that
are expected utility maximising.
These
models
are guided
by the belief that the other players are also
trying to maximise
their
own expected
utilities.
It is
shown
that
a player's
beliefs
about the
other players
form
an
infinite
regress.
This
regress can
be truncated to
a
finite
number of
levels of
beliefs,
under some assumptions about
the
utility
functions
and
beliefs
of
the
other players.
It is
shown
how the
dichotomy between
prescribed good play and observed good play exists
because of the
lack
of assumptions about
the
rationality of
the
opponents
(i.
e. the
ability of the opponents
to
be
utility maximising).
It
is
shown
how
a model
for
a game can
be built
which
is both faithful to the
observed common
sense
behaviour
of
the
subjects of an experimental game, and
is
also rational
(in
a
Bayesian
sense).
It is illustrated how
the
mathematical
form
of an optimal solution
to
a game can
be found,
and
then
used with an
inductive
algorithm to determine
an explicit optimal strategy.
It is
argued that the derived form
of
the
optimal solution can
be
used
to gain more
insight into
the
game, and
to determine
whether an assumed model
is
realistic.
It is
also shown
that
under weak regularity conditions, and assuming that an opponent
is
playing a strategy
from
a
given class of strategies,
S, it is
not optimal
for the
player
to
adopt any strategy
from S, thus
compromising the chosen model.
Item Type:  Thesis or Dissertation (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Bayesian statistical decision theory, Statistical decision, Game theory, Mathematical models  
Official Date:  September 1989  
Dates: 


Institution:  University of Warwick  
Theses Department:  Department of Statistics  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Smith, J. Q., 1953  
Sponsors:  Science and Engineering Research Council (Great Britain) (SERC)  
Extent:  vi, 170 leaves  
Language:  eng 
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