Studies of complex systems and agent-based models often focus on the relationship between microscopic behaviour and phenomena on a macroscopic level. Such models have applications in sociology, biology and economics. Here we study specific models in evolutionary game theory and game learning, analysing the differences between deterministic, population-level descriptions and stochastic, individual-level descriptions. We also examine the relationships between individual actions and global features in data from a financial market. Attempts to explain the emergence of altruism commonly use evolutionary game theory. Here, stochastic models can exhibit continued oscillations when the equivalent deterministic dynamics approach a fixed point. We classify the power spectra of such stochastic oscillations using an expansion of the master equation in the inverse system size. We find that the choice of update rule can have significant effects on the frequency and amplitude of these fluctuations.In light of recent experimental setups of social dilemmas to test the applicability of evolutionary theories to human players, we show that noise-induced oscillations can also be found in models of multiplayer game learning. We again perform an expansion in the noise strength to classify these oscillations analytically. We examine the effect that the parameters of the model can have on these fluctuations in both well-mixed and networked setups. We also use financial time series from the Spanish Stock Market to quantify features of the actions of individual trading firms. Examining how trades impact prices we find that the variety of individual behaviours cannot be inferred from that of the market. We test the applicability of an existing model by Bouchaud et al for reconstructing the response of the price to trades over time and show that it does not extend to describing any particular firm.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:542765 |
| Date | January 2011 |
| Creators | Bladon, Alexander John |
| Contributors | Tobias |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/the-statistical-mechanics-of-games-and-markets(c153c397-2e9f-480a-978f-f11ec5a9e225).html |
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