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A Study of Heuristic Approaches for Solving Generalized Nash Equilibrium Problems and Related Games

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dc.contributor.advisor Cojocaru, Monica
dc.contributor.advisor Thommes, Edward
dc.contributor.author Wild, Erin
dc.date.accessioned 2017-09-01T15:17:32Z
dc.date.available 2017-09-01T15:17:32Z
dc.date.copyright 2017-08
dc.date.created 2017-08-28
dc.date.issued 2017-09-01
dc.identifier.uri http://hdl.handle.net/10214/11483
dc.description.abstract The use of various computational heuristics for solving generalized Nash equilibrium problems (GNEPs) and related games is explored. In a model of competitive helping, agent-based simulations are used as a complementary analysis tool in conjunction with replicator equations. These agent-based simulations highlight the emergence of behaviours as well as equilibrium amounts of help provided by individuals. Using a concept of Nash dominance, an evolutionary algorithm utilizing the Sierpinski representation was then developed to find representable solution sets for GNEPs in general. Following this is a comparison of two methods which attempt to find optimal strategies for playing a classic GNEP turned card game called deck-based divide-the-dollar. The first method uses evolutionary computation to evolve optimal players who are represented by binary decision automata. The second method uses Monte Carlo policy evaluation, a form of reinforcement learning, to iteratively optimize a player's strategy through experience with particular game states and eventual outcomes. The thesis concludes with some final remarks and suggestions for future work. en_US
dc.language.iso en en_US
dc.rights Attribution-NonCommercial 2.5 Canada *
dc.rights.uri http://creativecommons.org/licenses/by-nc/2.5/ca/ *
dc.subject heuristics en_US
dc.subject game theory en_US
dc.subject optimization en_US
dc.subject agent-based modelling en_US
dc.subject evolutionary computation en_US
dc.subject competitive altruism en_US
dc.subject Monte Carlo methods en_US
dc.title A Study of Heuristic Approaches for Solving Generalized Nash Equilibrium Problems and Related Games en_US
dc.type Thesis en_US
dc.degree.programme Mathematics and Statistics en_US
dc.degree.name Doctor of Philosophy en_US
dc.degree.department Department of Mathematics and Statistics en_US
dc.rights.license All items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.


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