dorsal/arxiv
View SchemaNetwork Marketing on a Small-World Network
| Authors | Beom Jun Kim, Tackseung Jun, Jeong-Yoo Kim, M. Y. Choi |
|---|---|
| Categories | |
| ArXiv ID | physics/0506122 |
| URL | https://arxiv.org/abs/physics/0506122 |
| DOI | 10.1016/j.physa.2005.06.059 |
Abstract
We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability $\alpha$ is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price $p$ of the product and the referral fee $r$ are used as free parameters to maximize the profit of the manufacturer. It is observed that at $\alpha=0$ the maximized profit is constant independent of the network size $N$ while at $\alpha \neq 0$, it increases linearly with $N$. This is in parallel to the small-world transition. It is also revealed that while the optimal value of $p$ stays at an almost constant level in a broad range of $\alpha$, that of $r$ is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.
{
"annotation_id": "185b47af-ca18-4944-9ce7-8638a77b8b88",
"date_created": "2026-03-02T18:01:00.820000Z",
"date_modified": "2026-03-02T18:01:00.820000Z",
"file_hash": "fe6ba2b06e00b753353628265f3975c2ddabbb985a44fc9ec861078bb4d21cd7",
"private": false,
"record": {
"abstract": "We investigate a dynamic model of network marketing in a small-world network\nstructure artificially constructed similarly to the Watts-Strogatz network\nmodel. Different from the traditional marketing, consumers can also play the\nrole of the manufacturer\u0027s selling agents in network marketing, which is\nstimulated by the referral fee the manufacturer offers. As the wiring\nprobability $\\alpha$ is increased from zero to unity, the network changes from\nthe one-dimensional regular directed network to the star network where all but\none player are connected to one consumer. The price $p$ of the product and the\nreferral fee $r$ are used as free parameters to maximize the profit of the\nmanufacturer. It is observed that at $\\alpha=0$ the maximized profit is\nconstant independent of the network size $N$ while at $\\alpha \\neq 0$, it\nincreases linearly with $N$. This is in parallel to the small-world transition.\nIt is also revealed that while the optimal value of $p$ stays at an almost\nconstant level in a broad range of $\\alpha$, that of $r$ is sensitive to a\nchange in the network structure. The consumer surplus is also studied and\ndiscussed.",
"arxiv_id": "physics/0506122",
"authors": [
"Beom Jun Kim",
"Tackseung Jun",
"Jeong-Yoo Kim",
"M. Y. Choi"
],
"categories": [
"physics.soc-ph"
],
"doi": "10.1016/j.physa.2005.06.059",
"title": "Network Marketing on a Small-World Network",
"url": "https://arxiv.org/abs/physics/0506122"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7c9ea96a-c2b7-4171-a234-0beafe3adfbc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}