On Evolutionary Games and Sand Pile Models in Networks
Başlık:
On Evolutionary Games and Sand Pile Models in Networks
Yazar:
Liu, Jie, author.
ISBN:
9780438147805
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (204 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Pak Ming Hui.
Özet:
The thesis reports results on studies on evolutionary games and sand pile models in networks. In Part I (Chapter 1--5), two special classes of memory-one strategies are studied in the context of an infinitely iterated Prisoner's Dilemmas in Chapters 2 and 3 after an introduction in Chapter 1. In Chapter 2, reactive strategies and their extension to iterated 3-player games are studied. The evolution of the extended strategies is studied numerically in a three-dimensional strategy space. We identify a few special classes of strategies that play a crucial role in the dynamics towards a dominating class at long time. Zero-determinant strategies are a novel class of strategies that can set the payoff of opponents unilaterally. We introduce a class of generalized zero-determinant strategies (gZDS) that interpolates the extortionate zero-determinant strategy and the generous zero-determinant strategy. We study the dominating relationship between gZDS and a standard strategy Y, where Y is one of the commonly used strategies including AllC (always cooperative), AllD (always non-cooperative), TFT (tit-for-tat) and WSLS (win-stay loss-shift), by analyzing the ordering of their expected payoffs when they compete against each other. How gZDS competes with the standard strategies in a well-mixed population and spatially structured populations are then studied, with simulation results explained by a payoff bands theory. Chapters 4 and 5 focus on formulating analytic approaches to evolutionary games in networks systematically and their applications. In Chapter 4, we discuss a general procedure in developing the site and link approximations that could be specialized to various contexts and apply them to the problems studied in Chapter 3 as examples. The results provide insight into the meaning behind the popularly used link approximation and different ways of implementing it. In Chapter 5, we constructed a mapping between evolutionary games using a self-questioning adaptive mechanism and the Ising model. The mapping connects two research areas, with each having much to offer to the other. We illustrate that methods as well as results from one field can be applied to another and how the mapping enhances the understanding of analytic approaches developed for the games. Part II (Chapter 6) studies dissipative sand pile models on systems without a leaking boundary. On a closed loop, the distribution of cascade areas and sizes are studied numerically and analytically. The origin of the large fluctuations, which cannot be suppressed by averaging over many realizations, in the distribution of cascade sizes is identified. On an undirected random graph of uniform degree, the densities of nodes of different loadings are studied by numerical simulations and a mean field approach. In two inter-connected networks of different sizes, the benefit and the risk of a network connecting to another and the existence of an optimal interconnection are studied. In addition to studying and understanding each problem, our analytic efforts also shed light on the challenging task of setting up a systematic framework for dynamical processes that involves switching among multiple states in networks. Parts of Chapters 3, 5, and 6 have been published as journal articles.
Notlar:
School code: 1307
Tüzel Kişi Ek Girişi:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(697026.1) | 697026-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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