Fluctuations and large deviationsin game theoretical models

Student thesis: Doctoral ThesisDoctor of Philosophy


This thesis uses advanced methods from statistical physics to investigate collective effects in game theoretical models with a large number of players. Specifically, I study the strategy distributions in a large game that models how agents choose among double auction markets. I provide a classification of the possible mean field Nash equilibria, which include potentially segregated states where an agent population can split into subpopulations adopting different strategies. I compare this classification with the results of Experience-Weighted Attraction (EWA) learning, which in the long run leads to Nash equilibria in the appropriate limits of large intensity of choice, low noise (long agent memory) and perfect imputation of missing scores (fictitious play). Non-trivially, depending on how the relevant limits are taken, more than one type of equilibrium can be selected. These include the standard homogeneous mixed and heterogeneous pure states, but also heterogeneous mixed states in which different agents play different strategies that are not all pure. I also investigate the influence of heterogeneity in traders’ behaviour on the emergence of segregation described previously. The theoretical machinery is then extended from the study of systems with two markets, to the analysis of multi-agent systems where traders can choose between multiple markets.

The last part of the thesis focuses on how the interaction among players in a repeated game can be represented as an evolutionary process in a “population of ideas”. I propose the interpretation of reinforcement learning as a stochastic process in a finite population of this type. The resulting birth-death dynamics has absorbing states and allows for the extinction of ideas, which marks a key difference with mutation-selection processes. I characterise the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.
Date of Award2017
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorPeter Sollich (Supervisor) & Reimer Kuhn (Supervisor)

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