@phdthesis{Melnichenko2022,
  author    = {Melnichenko, Anna},
  title     = {Selfish Creation of Realistic Networks},
  doi       = {10.25932/publishup-54814},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-548141},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 175},
  year      = {2022},
  abstract  = {Complex networks like the Internet or social networks are fundamental parts of our everyday lives. It is essential to understand their structural properties and how these networks are formed. A game-theoretic approach to network design problems has become of high interest in the last decades. The reason is that many real-world networks are the outcomes of decentralized strategic behavior of independent agents without central coordination. Fabrikant, Luthra, Maneva, Papadimitriou, and Schenker proposed a game-theoretic model aiming to explain the formation of the Internet-like networks. In this model, called the Network Creation Game, agents are associated with nodes of a network. Each agent seeks to maximize her centrality by establishing costly connections to other agents. The model is relatively simple but shows a high potential in modeling complex real-world networks. In this thesis, we contribute to the line of research on variants of the Network Creation Games. Inspired by real-world networks, we propose and analyze several novel network creation models. We aim to understand the impact of certain realistic modeling assumptions on the structure of the created networks and the involved agents' behavior. The first natural additional objective that we consider is the network's robustness. We consider a game where the agents seek to maximize their centrality and, at the same time, the stability of the created network against random edge failure. Our second point of interest is a model that incorporates an underlying geometry. We consider a network creation model where the agents correspond to points in some underlying space and where edge lengths are equal to the distances between the endpoints in that space. The geometric setting captures many physical real-world networks like transport networks and fiber-optic communication networks. We focus on the formation of social networks and consider two models that incorporate particular realistic behavior observed in real-world networks. In the first model, we embed the anti-preferential attachment link formation. Namely, we assume that the cost of the connection is proportional to the popularity of the targeted agent. Our second model is based on the observation that the probability of two persons to connect is inversely proportional to the length of their shortest chain of mutual acquaintances. For each of the four models above, we provide a complete game-theoretical analysis. In particular, we focus on distinctive structural properties of the equilibria, the hardness of computing a best response, the quality of equilibria in comparison to the centrally designed socially optimal networks. We also analyze the game dynamics, i.e., the process of sequential strategic improvements by the agents, and analyze the convergence to an equilibrium state and its properties.},
  language  = {en}
}