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Essays on the Formation of and Communities in Networks /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Essays on the Formation of and Communities in Networks /Evan Connell Storms.
作者:	Storms, Evan Connell,
面頁冊數:	1 electronic resource (182 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-03, Section: A.
附註:	Advisors: Jackson, Matthew Committee members: Carroll, Gabriel; Milgrom, Paul; Bent, Stacey F.
Contained By:	Dissertations Abstracts International87-03A.
標題:	Behavior.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32149627
ISBN:	9798290650654

Essays on the Formation of and Communities in Networks /
Storms, Evan Connell,

Essays on the Formation of and Communities in Networks /Evan Connell Storms. - 1 electronic resource (182 pages)

Source: Dissertations Abstracts International, Volume: 87-03, Section: A.

This dissertation studies the formation of economic networks and how those networks influence behavior.The first chapter focuses on one of the central solution concepts in the cooperative game theoretic study of network formation, pairwise stability. Pairwise stability, roughly stated, is the condition that no pair of agents prefers to add new links between them, and no single agent prefers to remove any of his links in the network. While the restriction to single link changes makes it a relatively weak solution concept, the richness of potential preferences over networks still makes it difficult to characterize when pairwise stable networks exist in a network formation setting. In particular, the conditions known to ensure the existence of pairwise stable networks (such as strategic complements among all links and acyclicity of the defeated relation graph) have vanishingly small probability of holding in large random network formation settings. This chapter focuses on the question: how likely are pairwise stable networks to exist in those settings? We consider several different models of random preferences. For each, we prove a novel result characterizing the existence of pairwise stable networks in a purely random limiting model. We then use these benchmarks to extend the logic of our arguments to structured random preferences. Our results establish that when the noise in agents' preferences is at the level of individual networks, as long as the magnitude of the randomness is large enough that the minimum probability a network is an agent's most preferred does not vanish too quickly, then the probability that a pairwise stable network exists converges to one. If instead the randomness is directly at the level of the defeated relation, then we can derive a 1´1{e lower bound on the asymptotic probability a pairwise stable network exists under a novel sufficient degree variability condition on a probabilistic analogue of the defeated relation graph.The second chapter is based on joint work with Matthew Jackson. In it, we take up the problem of microfounding community detection in networks in the Nash equilibrium of an underlying coordination game in which agents want to adopt a behavior if and only if at least a fraction, or behavioral threshold, of their neighbors do as well. Our approach leads us to identify which sets of agents behave the same in any equilibrium, and hence form the building blocks - or atoms - of an equilibrium adopting set. We characterize how these atoms correspond to underlying community structure in the stochastic block model, showing that as networks become large the atomic structure coincides with a coarsening of the community structure with high probability, and agrees exactly with the community structure for certain choices of behavioral threshold. We then demonstrate, using a real-world network of households in Indian villages, that the atomic structure informs a performant heuristic for the combinatorially complex problem of choosing seed nodes to maximize the spread of a behavior in a network.

English

ISBN: 9798290650654Subjects--Topical Terms:

302189
Behavior.
Subjects--Index Terms:

Economic networks

Essays on the Formation of and Communities in Networks /
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520 $a This dissertation studies the formation of economic networks and how those networks influence behavior.The first chapter focuses on one of the central solution concepts in the cooperative game theoretic study of network formation, pairwise stability. Pairwise stability, roughly stated, is the condition that no pair of agents prefers to add new links between them, and no single agent prefers to remove any of his links in the network. While the restriction to single link changes makes it a relatively weak solution concept, the richness of potential preferences over networks still makes it difficult to characterize when pairwise stable networks exist in a network formation setting. In particular, the conditions known to ensure the existence of pairwise stable networks (such as strategic complements among all links and acyclicity of the defeated relation graph) have vanishingly small probability of holding in large random network formation settings. This chapter focuses on the question: how likely are pairwise stable networks to exist in those settings? We consider several different models of random preferences. For each, we prove a novel result characterizing the existence of pairwise stable networks in a purely random limiting model. We then use these benchmarks to extend the logic of our arguments to structured random preferences. Our results establish that when the noise in agents' preferences is at the level of individual networks, as long as the magnitude of the randomness is large enough that the minimum probability a network is an agent's most preferred does not vanish too quickly, then the probability that a pairwise stable network exists converges to one. If instead the randomness is directly at the level of the defeated relation, then we can derive a 1´1{e lower bound on the asymptotic probability a pairwise stable network exists under a novel sufficient degree variability condition on a probabilistic analogue of the defeated relation graph.The second chapter is based on joint work with Matthew Jackson. In it, we take up the problem of microfounding community detection in networks in the Nash equilibrium of an underlying coordination game in which agents want to adopt a behavior if and only if at least a fraction, or behavioral threshold, of their neighbors do as well. Our approach leads us to identify which sets of agents behave the same in any equilibrium, and hence form the building blocks - or atoms - of an equilibrium adopting set. We characterize how these atoms correspond to underlying community structure in the stochastic block model, showing that as networks become large the atomic structure coincides with a coarsening of the community structure with high probability, and agrees exactly with the community structure for certain choices of behavioral threshold. We then demonstrate, using a real-world network of households in Indian villages, that the atomic structure informs a performant heuristic for the combinatorially complex problem of choosing seed nodes to maximize the spread of a behavior in a network.
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