Random parameters analysis of competitive agents in an imperfect information environment
thesisposted on 2022-03-28, 13:34 authored by Alex Edward Moore
The focus in this thesis is on the mathematics underpinning the system rather than details such as how to decode on-line sites. What now follows is a summary of the thesis in more detail: Much of the research into poker has built on the concepts developed by Von Neumann  and Borel . Game Theory concepts have been developed and used in conjunction with cutting edge techniques such as Neural Networks to develop playing algorithms in a similar way to which games such as Chess or Checkers have been solved. These techniques are not necessarily gambling related, even though poker is usually played as a gambling game. The problem with the Game Theory approach is that analysis of full scale poker rapidly becomes intractable. Prominent researchers in the Game Theory approach (, , ,,, ) have recognised this and much of the subsequent research has centred around reducing the size of the problem to be solved. Derivation of a Game Tree for a reduced problem was also the approach adopted by von Neumann and Borel. This approach has been successful and can be summarised as finding an exact solution to an approximating problem. Methods seeking approximations to the full problem that retain the properties of the real problem have been developed and are ingenious. In this thesis a different approach has been used. Instead of seeking approximating problems which may be solved exactly, approximate solutions to the full problem are sought. Regression techniques have been used to find approximate solutions to the full problem. Rather than try to tune a strategy engine using Neural Networks to solve the problem in a human-like way, the population variance in preferences (as measured by coefficients) has been measured and past data for given contexts is used to estimate where on the population distribution of preferences a particular context resides. The resulting system still "learns", but in a different way to a Neural Network. The play has been reduced to a sequence of actions which are chosen to maximise profit expectation. This has much in common with financial market trading where a sequence of trades is likewise chosen to maximise profit. The Game Theory approach also maximises profit expectancy, but because that approach necessitates analysis of a computationally intractable Game Tree, the expectation actually maximised is that of an approximating problem. In a sense the approach adopted here is the opposite of the approach adopted by the authors mentioned above in that they seek exact solutions to an approximating problem whereas this research seeks approximate solutions to the exact problem.
Table of Contents1. Trading in uncertainty -- 2. Literature review -- 3. Generic opponents model -- 4. Random parameters model -- 5. Adaptive model -- 6. Tree based contextual coefficients -- 7. Deployment -- 8. Results -- 9. Conclusions -- Appendices
NotesThis thesis is presented for the degree of Doctor of Philosophy" "September 2011 (original), September 2012 (with corrections) Bibliography: leaves 153-156
Awarding InstitutionMacquarie University
Degree TypeThesis PhD
DegreePhD, Macquarie University, Faculty of Science, Department of Statistics
Department, Centre or SchoolDepartment of Statistics
Year of Award2012
Principal SupervisorPeter Petocz
Additional Supervisor 1David Bulger
RightsCopyright disclaimer: http://www.copyright.mq.edu.au Copyright Alex Moore 2012.
Extent1 online resource (xiii, 156 leaves) illustrations
Former Identifiersmq:28099 http://hdl.handle.net/1959.14/266883 2073512
Mathematical statisticsPattern recognition systemsadaptive random parametersadaptive learning algorithmGames of chance (Mathematics)game theoretic methodsStatistical decisionGame theoryProbabilities -- Mathematical modelsPrediction theoryadaptive regressionmachine learningMachine learninggamblingProbabilitiesMachine learning -- Mathematical models