The influence of topology and information diffusion on networked game dynamics

Abstract

This thesis studies the influence of topology and information diffusion on the strategic interactions of agents in a population. It shows that there exists a reciprocal relationship between the topology, information diffusion and the strategic interactions of a population of players. The structure of a population of players is abstracted by the topology and the information flow of the networks of players while the dynamics are denoted by the strategic interactions of the players in the population. While topology represents a static structure, the information flows are used to model a more dynamic and volatile structure of the population. In order to evaluate the influence of topology and information flow on networked game dynamics, strategic games are simulated on populations of players where the players are distributed in a non-homogeneous spatial arrangement. Game theory, network science and information theory are the three pillars of science used to build the underlying theoretical basis in this research. A study of evolution of the coordination of strategic players is the first part of this research where the topology or the structure of the population is shown to be critical in defining the coordination among the players. Next, the effect of network topology on the evolutionary stability of strategies is studied in detail. The evolutionary stability of a strategy determines its ability to withstand potentially competitive strategies. Based on the results obtained, it is shown that network topology plays a key role in determining the evolutionary stability of a particular strategy in a population of players. Then, the effect of network topology on the optimum placement of strategies is studied. Using genetic optimisation, it is shown that the placement of strategies in a spatially distributed population of players is crucial in maximising the collective payoff of the population. This further suggests that the topology of the social structure is critical in determining its networked game dynamics. Exploring further the effect of network topology and information diffusion on networked games, the non-optimal or bounded rationality of players is modelled using topological and directed information flow of the network. While network topology defines a more static form, information flows are used to model a more volatile and dynamic form of the population. These models are then applied to demonstrate how the scale-free and small-world networks emerge in randomly connected populations of players who operate iii under bounded rationality. It is also shown that the strategic interactions with multiple equilibrium states are directly affected by network topology. Thus, the topological and information theoretic interpretations of bounded rationality suggest the topology, information diffusion and the strategic interactions of socio-economical structures are cyclically interdependent.