{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T06:09:49Z","timestamp":1760854189316,"version":"3.41.2"},"reference-count":34,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["71771179","71532015","71371139","72021002"],"award-info":[{"award-number":["71771179","71532015","71371139","72021002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p> Cash-back industry is now witnessing surging development. Prior works on cash-back sites focus mainly on the demand side, while we are also interested in the supply side. We develop a game theoretical model with a manufacturer, an online retailer, cash-back site(s), and heterogeneous consumers. We find that when the cash-back channel cannot attract new consumers, the manufacturer raises the wholesale price and the retailer raises the retail price, which may lead to the cash-back paradox where all consumers face higher prices. Therefore, when there exists a cash-back channel, the manufacturer is always worse off and the retailer is better off when low-type consumers\u2019 product valuation is intermediate, and consumer surplus and social welfare are both lower. When the retailer affiliates with two competing cash-back sites, the manufacturer contributes to the mitigation of double marginalization problem by raising the wholesale price to a lesser extent, which drives the surprising result that when there exists downstream competition, cash-back sites enjoy higher commission rate and under some circumstances, offer lower cash-back rate and enjoy higher profit. We also show that only when the cash-back channel makes the size of the low-type segment double will the manufacturer be better off with this channel. <\/jats:p>","DOI":"10.1142\/s0217595921500056","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T15:58:12Z","timestamp":1615823892000},"source":"Crossref","is-referenced-by-count":2,"title":["Strategic Manufacturers in Online Cash-Back Shopping"],"prefix":"10.1142","volume":"38","author":[{"given":"Chen","family":"Chen","sequence":"first","affiliation":[{"name":"School of Economics and Management, Tongji University, No 1239 Siping Road, Yangpu District, Shanghai, 200092, P. R. China"}]},{"given":"Yongrui","family":"Duan","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Tongji University, No 1239 Siping Road, Yangpu District, Shanghai, 200092, P. R. 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