The Incumbent Firm’s Response to Market Encroachment: Strategic Deterrence under the Reference Price Effects

The Incumbent Firm’s Response to Market Encroachment: Strategic Deterrence under the Reference Price Effects | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article The Incumbent Firm’s Response to Market Encroachment: Strategic Deterrence under the Reference Price Effects Hao Li, Yang Cui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7429710/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract In perishable goods markets, the encroachment of imitation products has complicated the competitive landscape faced by the incumbent firms. This study examines a two-period dynamic game model that incorporates vertical reference price effects into the analysis of incumbent firm’s response to imitation product encroachment in perishable goods markets. Specifically, the model analyzes the incumbent firm’s optimal pricing strategy, expected profits, and social welfare outcomes by the varing values of the reference price effects, the quality differentiation, and the consumers’ assessment costs for imitation products. The results demonstrate that the consumers’ assessment cost for the imitation products is a pivotal determinant. Lower assessment costs accommodate the imitator to encroach. When the assessment costs are in the medium range, the incumbent firm may strategically lower prices to deter the encroachment. While the assessment costs exceed certain thresholds, the firm with imitation products chooses not to encroach on the market. Under the reference price effect, consumers tend to behave more strategically: the quality differences exacerbate strategic waiting behavior; while increased price sensitivity constrains the incumbent’s pricing power, pressuring it to reduce prices. Furthermore, the presence of a potential market entrant-even when actual encroachment doesn’t occur-can improve allocative efficiency, enhancing overall social welfare. This finding offers a theoretical basis for the incumbent’s sustainable strategy: by adjusting prices and offering differentiated services to reinforce quality advantages, the incumbent firm should actively shape the competitive landscape and maintain its market position to enhance social welfare. Earth and environmental sciences/Environmental social sciences Physical sciences/Mathematics and computing market encroachment reference price effect consumer behavior dynamic pricing Full Text Additional Declarations No competing interests reported. Supplementary Files Appendix.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 30 Mar, 2026 Reviews received at journal 07 Dec, 2025 Reviewers agreed at journal 11 Nov, 2025 Reviewers agreed at journal 18 Oct, 2025 Reviewers invited by journal 16 Oct, 2025 Editor assigned by journal 13 Oct, 2025 Editor invited by journal 28 Sep, 2025 Submission checks completed at journal 18 Sep, 2025 First submitted to journal 18 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7429710","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":535355245,"identity":"f1f29e6b-ac1c-4b28-9340-d147b1590861","order_by":0,"name":"Hao Li","email":"","orcid":"","institution":"Chongqing Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Li","suffix":""},{"id":535355246,"identity":"be1c8434-a7a2-4cff-8b72-5f44ee870334","order_by":1,"name":"Yang 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This study examines a two-period dynamic game model that incorporates vertical reference price effects into the analysis of incumbent firm\u0026rsquo;s response to imitation product encroachment in perishable goods markets. Specifically, the model analyzes the incumbent firm\u0026rsquo;s optimal pricing strategy, expected profits, and social welfare outcomes by the varing values of the reference price effects, the quality differentiation, and the consumers\u0026rsquo; assessment costs for imitation products. The results demonstrate that the consumers\u0026rsquo; assessment cost for the imitation products is a pivotal determinant. Lower assessment costs accommodate the imitator to encroach. When the assessment costs are in the medium range, the incumbent firm may strategically lower prices to deter the encroachment. While the assessment costs exceed certain thresholds, the firm with imitation products chooses not to encroach on the market. Under the reference price effect, consumers tend to behave more strategically: the quality differences exacerbate strategic waiting behavior; while increased price sensitivity constrains the incumbent\u0026rsquo;s pricing power, pressuring it to reduce prices. Furthermore, the presence of a potential market entrant-even when actual encroachment doesn\u0026rsquo;t occur-can improve allocative efficiency, enhancing overall social welfare. This finding offers a theoretical basis for the incumbent\u0026rsquo;s sustainable strategy: by adjusting prices and offering differentiated services to reinforce quality advantages, the incumbent firm should actively shape the competitive landscape and maintain its market position to enhance social welfare.\u003c/p\u003e","manuscriptTitle":"The Incumbent Firm’s Response to Market Encroachment: Strategic Deterrence under the Reference Price Effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-30 04:59:37","doi":"10.21203/rs.3.rs-7429710/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-30T16:18:07+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-08T02:50:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"222602433398703786521027443726112917004","date":"2025-11-11T11:01:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"330753149633265214205063256875855346616","date":"2025-10-18T06:49:43+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-16T06:44:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-13T05:59:18+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-28T07:01:47+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-18T10:23:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Humanities and Social Sciences Communications","date":"2025-09-18T08:14:03+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0133ce89-77b9-4a35-97e9-112d3a374f74","owner":[],"postedDate":"October 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":56909788,"name":"Earth and environmental sciences/Environmental social sciences"},{"id":56909789,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-06T14:08:33+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-30 04:59:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7429710","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"identity":"rs-7429710","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}