Title page for ETD etd-11082011-203241

Type of Document Dissertation
Author He, Qian
Author's Email Address heq07@vt.edu
URN etd-11082011-203241
Title Spatio-Temporal Patterns, Correlations, and Disorder in Evolutionary Game Theory
Degree PhD
Department Physics
Advisory Committee
Advisor Name Title
Tauber, Uwe C. Committee Chair
Heremans, Jean J. Committee Member
Park, Kyungwha Committee Member
Pleimling, Michel J. F. Committee Member
  • evolutionary game theory
  • rock-paper-scissors game
  • correlation
  • spatial disorder
  • universal scaling in financial market
  • heterogeneity
  • Monte Carlo simulation.
Date of Defense 2011-11-07
Availability restricted
Evolutionary game theory originated from the application of mathematical game theory to biological studies.

Well-known examples in evolutionary game theory are the prisoner's dilemma, predator-prey models, the rock-paper-scissors game, etc.

Recently, such well-known models have attracted increased interest in population dynamics to understand the

emergence of biodiversity and species coexistence. Meanwhile, it has been realized that techniques from statistical

physics can aid us to gain novel insights into this interdisciplinary field. In our research, we mainly employ

individual-based Monte Carlo simulations to study emerging spatio-temporal patterns, spatial correlations,

and the influence of quenched spatial disorder in rock-paper-scissors systems either with or without conserved

total population number. In balanced rock-paper-scissors systems far away from the ``corner'' of configuration space,

it is shown that quenched spatial disorder in the reaction rates has only minor effects on the co-evolutionary dynamics.

However, in model variants with strongly asymmetric rates (i.e., ``corner'' rock-paper-scissors systems),

we find that spatial rate variability can greatly enhance the fitness of both minor species in``corner'' systems,

a phenomenon already observed in two-species Lotka-Volterra predator-prey models. Moreover, we numerically study the

influence of either pure hopping processes or exchange processes on the emergence of spiral patterns in spatial

rock-paper-scissors systems without conservation law (i.e., May-Leonard model). We also observe distinct extinction

features for small spatial May-Leonard systems when the mobility rate crosses the critical threshold which separates

the active coexistence state from an inactive absorbing state.

In addition, through Monte Carlo simulation on a heterogeneous interacting agents model,

we investigate the universal scaling properties in financial markets such as the fat-tail distributions in return and trading volume,

the volatility clustering, and the long-range correlation in volatility. It is demonstrated that the long-tail feature in trading volume distribution

results in the fat-tail distribution of asset return, and furthermore it is shown that the long tail in trading volume

distribution is caused by the heterogeneity in traders' sensitivities to market risk.

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