{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:26:05Z","timestamp":1760243165320,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2015,12,21]],"date-time":"2015-12-21T00:00:00Z","timestamp":1450656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Everyone likes Porsche but few can afford it. Budget constraints always play a critical role in a customer\u2019s decision-making. The literature disproportionally focuses on how firms can induce customer valuations toward the product, but does not address how to assess the influence of budget constraints. We study these questions in the context of a referral reward program (RRP). RRP is a prominent marketing strategy that utilizes recommendations passed from existing customers to their friends and effectively stimulates word of mouth (WoM). We build a stylized game-theoretical model with a nested Stackelberg game involving three players: a firm, an existing customer, and a potential customer who is a friend of the existing customer. The budget is the friend\u2019s private information. We show that RRPs might be optimal when the friend has either a low or a high valuation, but they work differently in each situation because of the budget. Furthermore, there are two budget thresholds, a fixed one and a variable one, which limit a firm\u2019s ability to use rewards.<\/jats:p>","DOI":"10.3390\/fi7040516","type":"journal-article","created":{"date-parts":[[2015,12,21]],"date-time":"2015-12-21T10:43:59Z","timestamp":1450694639000},"page":"516-529","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Referral Reward Considering Customer\u2019s Budget Constraint"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3860-3910","authenticated-orcid":false,"given":"Dan","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beihang University, Beijing 100080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhong","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beihang University, Beijing 100080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,21]]},"reference":[{"key":"ref_1","first-page":"435","article-title":"Seller financing of consumer durables","volume":"7","author":"Sen","year":"1998","journal-title":"Gen. 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