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Title: Networks, clubs and matching
Author: Ding, Sihua
ISNI:       0000 0004 7972 9661
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2019
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This PhD dissertation is a study of how social networks and clubs form in different contexts. Chapter 1 investigates the incentives of individuals to make introductions (the act of creating a link for two neighbours) in a social network. The chapter assumes that players are endowed with different ability levels and have a network among them. Given an ability endowment and a network, players undergo a matching process where one can only be matched with one of his neighbours or stay alone, and one always prefers a more capable matching partner to a less capable one to staying alone. A strict ability ranking would yield a unique stable matching for all network structures. Our research question is: If a player can create a link for a pair of his neighbours, when would he want to do so? Two results are derived to address this question. First, the matching of a player would be unchanged if he makes an introduction for two neighbours, at least one of whom is less capable than him. Second, an introduction could benefit the introducer when both neighbours involved are more capable than him, and there exists an even-length alternating path from one of the neighbours to him. The chapter also examines the stability of networks based on no profitable introductions and characterizes Pareto efficient networks. Chapter 2 studies a general model of investment in relationships. Existing research on network formation proceeds under strong assumptions on how a link between two agents can be produced: typically link investments are assumed to be unweighted and links are formed either reciprocally or unilaterally. This chapter proposes a more general approach by allowing weighted link investment and employing a constant elasticity of substitution (CES) link formation function. This formulation has two advantages other than permitting a more flexible sponsorship of links. First, it nests the two commonly employed bilateral and unilateral link formation assumptions as special cases and thus enables robustness checks on existing works. Second, it introduces a variation in link investment substitutability and hence enables the analysis of how different link formation technologies affect network formation. We illustrate this approach through two applications: a game of pure network formation and a game of network formation with assorted activities. Chapter 3, which is co-authored with Prof Sanjeev Goyal and Dr Marcin Dziubinski, explores club joining activities of individuals and member admission activities of clubs. We assume that links between clubs are formed when they share common members. The productivity of a club is determined by its number of members and how connected it is to other clubs. Individuals wish to join clubs with high productivity and clubs admit members with the aim to raise productivity. We study the efficient and the stable club membership structures and find that both efficiency and stability implies the segregation of individuals (and clubs) into two groups with very different levels of club joining (and member admission) activeness and welfare. Our results provide a simple explanation for the phenomena of the "power elite" and interlocking board of directors.
Supervisor: Goyal, Sanjeev Sponsor: Cambridge Trust
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: Networks ; Clubs ; Matching