Consumer referral in a small world network

Tackseung Jun; Jeong Yoo Kim; Beom Jun Kim; M. Y. Choi

doi:10.1016/j.socnet.2005.07.001

Consumer referral in a small world network

Tackseung Jun, Jeong Yoo Kim, Beom Jun Kim, M. Y. Choi

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

We consider a firm's profit maximization problem when the demand for the product is created by referrals between consumers connected in a small world network. We generate a small world network by applying the rewiring algorithm of Watts and Strogatz and incorporate it into the profit maximization problem. We demonstrate (i) that contrary to our anticipation, the firm's profit smoothly (not rapidly) approaches the profit in the complete network as the rewiring probability increases, but (ii) that the per consumer profit is saturated to a finite non-zero value when the rewiring probability is near zero, implying a small world transition.

Original language	English
Pages (from-to)	232-246
Number of pages	15
Journal	Social Networks
Volume	28
Issue number	3
DOIs	https://doi.org/10.1016/j.socnet.2005.07.001
Publication status	Published - Jul 2006

Bibliographical note

Funding Information:
This research was begun in 2002 when the second author visited University at Albany, SUNY and shaped very much when he delivered a seminar talk at Korea Institute for Advanced Study (KIAS). We thank Chong Kook Park, seminar participants at KIAS and audiences in the 2004 summer conference of the Korean Economic Association. The first two authors are grateful to Kyung Hee University for financial supports and the third author acknowledges the support from Korea Science and Engineering Foundation through Grant No. R14-2002-062-01000-0.

Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.

Keywords

Consumer referral
Network marketing
Referral fee
Small world network

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10.1016/j.socnet.2005.07.001

Cite this

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title = "Consumer referral in a small world network",

abstract = "We consider a firm's profit maximization problem when the demand for the product is created by referrals between consumers connected in a small world network. We generate a small world network by applying the rewiring algorithm of Watts and Strogatz and incorporate it into the profit maximization problem. We demonstrate (i) that contrary to our anticipation, the firm's profit smoothly (not rapidly) approaches the profit in the complete network as the rewiring probability increases, but (ii) that the per consumer profit is saturated to a finite non-zero value when the rewiring probability is near zero, implying a small world transition.",

keywords = "Consumer referral, Network marketing, Referral fee, Small world network",

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note = "Funding Information: This research was begun in 2002 when the second author visited University at Albany, SUNY and shaped very much when he delivered a seminar talk at Korea Institute for Advanced Study (KIAS). We thank Chong Kook Park, seminar participants at KIAS and audiences in the 2004 summer conference of the Korean Economic Association. The first two authors are grateful to Kyung Hee University for financial supports and the third author acknowledges the support from Korea Science and Engineering Foundation through Grant No. R14-2002-062-01000-0. Copyright: Copyright 2006 Elsevier B.V., All rights reserved.",

year = "2006",

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doi = "10.1016/j.socnet.2005.07.001",

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AU - Kim, Jeong Yoo

AU - Jun Kim, Beom

AU - Choi, M. Y.

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PY - 2006/7

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N2 - We consider a firm's profit maximization problem when the demand for the product is created by referrals between consumers connected in a small world network. We generate a small world network by applying the rewiring algorithm of Watts and Strogatz and incorporate it into the profit maximization problem. We demonstrate (i) that contrary to our anticipation, the firm's profit smoothly (not rapidly) approaches the profit in the complete network as the rewiring probability increases, but (ii) that the per consumer profit is saturated to a finite non-zero value when the rewiring probability is near zero, implying a small world transition.

AB - We consider a firm's profit maximization problem when the demand for the product is created by referrals between consumers connected in a small world network. We generate a small world network by applying the rewiring algorithm of Watts and Strogatz and incorporate it into the profit maximization problem. We demonstrate (i) that contrary to our anticipation, the firm's profit smoothly (not rapidly) approaches the profit in the complete network as the rewiring probability increases, but (ii) that the per consumer profit is saturated to a finite non-zero value when the rewiring probability is near zero, implying a small world transition.

KW - Consumer referral

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KW - Referral fee

KW - Small world network

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VL - 28

SP - 232

EP - 246

JO - Social Networks

JF - Social Networks

IS - 3

ER -

Consumer referral in a small world network

Abstract

Bibliographical note

Keywords

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