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Convergence of behaviour rules in iterated matrix games Patrick, Jonathan
Abstract
This master's thesis reports on a foray into Game Theory, focusing solely on the twoperson (not necessarily zero-sum) game. Primarily, I am interested in the convergence properties of different behaviour rules and how one might proceed to introduce some form of learning into the strategies of the players involved in the game. Therefore, I begin with the introduction of some key equilibrium sets - namely the set of Nash Equilibria (NE), the set of correlated equilibria (CE) and the marginal best-response set (MBR). I briefly discuss the relationship between these three sets before moving on to describe some desirable properties of behaviour rules. From there, I introduce six behaviour rules (four from the literature, two original) that attempt to incorporate some form of learning into the game. The four from the literature are Fictitious Play, Exponential Fictitious play, Regrets 1 and Regrets 2. I have named the two original behaviour rules Past Response and Modified Regrets. I then move on to describe the convergence properties of each. This thesis was originally motivated by a talk given by Andreu Mas-Collel on the properties of the two Regrets-based behaviour rules. Thus, a fair amount of time is spent reworking the convergence proofs of both Regretsl and Regrets2 as they were developed by Mas-Collel and Sergiu Hart. I then suggest an alternative proof of the Regretsl convergence properties. I close off the paper with some numerical results from three games - a zero-sum game, a game developed by Lloyd Shapley (called the Shapley game) and a game called Battle of the Buddies. They are designed to give some numerical confirmation of the convergence theorems stated earlier in the paper as well as some indication as to where further study might be useful.
Item Metadata
Title |
Convergence of behaviour rules in iterated matrix games
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1999
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Description |
This master's thesis reports on a foray into Game Theory, focusing solely on the twoperson
(not necessarily zero-sum) game. Primarily, I am interested in the convergence
properties of different behaviour rules and how one might proceed to introduce some form
of learning into the strategies of the players involved in the game. Therefore, I begin with
the introduction of some key equilibrium sets - namely the set of Nash Equilibria (NE),
the set of correlated equilibria (CE) and the marginal best-response set (MBR). I briefly
discuss the relationship between these three sets before moving on to describe some
desirable properties of behaviour rules. From there, I introduce six behaviour rules (four
from the literature, two original) that attempt to incorporate some form of learning into
the game. The four from the literature are Fictitious Play, Exponential Fictitious play,
Regrets 1 and Regrets 2. I have named the two original behaviour rules Past Response
and Modified Regrets. I then move on to describe the convergence properties of each.
This thesis was originally motivated by a talk given by Andreu Mas-Collel on the
properties of the two Regrets-based behaviour rules. Thus, a fair amount of time is spent
reworking the convergence proofs of both Regretsl and Regrets2 as they were developed
by Mas-Collel and Sergiu Hart. I then suggest an alternative proof of the Regretsl
convergence properties. I close off the paper with some numerical results from three
games - a zero-sum game, a game developed by Lloyd Shapley (called the Shapley game)
and a game called Battle of the Buddies. They are designed to give some numerical
confirmation of the convergence theorems stated earlier in the paper as well as some
indication as to where further study might be useful.
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Extent |
6468309 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-06-26
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080029
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1999-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.