{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:29:31Z","timestamp":1760059771830,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T00:00:00Z","timestamp":1751932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>We analyze the endogenous formation of patent pools among three patent owners and the associated welfare effects. Under a condition of synergistic three-patent combination, either a unique symmetric equilibrium or infinitely many asymmetric equilibria can arise when patents are fragmented. By using the notion of equilibrium binding agreements, we show that (1) when there is a unique symmetric equilibrium under fragmented patents, the complete pool is both stable and welfare-maximizing; (2) fragmented patents are stable in the presence of infinitely many asymmetric equilibria; and (3) when considering only a single specific asymmetric equilibrium under fragmented patents, the complete pool is welfare-maximizing if it is stable, while fragmented patents can be both stable and welfare-maximizing under certain conditions. We also discuss an alternative version of synergism and an alternative bargaining protocol for patent pool formation.<\/jats:p>","DOI":"10.3390\/g16040035","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T09:12:48Z","timestamp":1751965968000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pool Formation with Three Patent Owners"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5199-4920","authenticated-orcid":false,"given":"Hao","family":"Liu","sequence":"first","affiliation":[{"name":"Institute of International Law, School of Law, Shandong University, Qingdao 266237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7922-5813","authenticated-orcid":false,"given":"Xuewen","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Economics, University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2524-8128","authenticated-orcid":false,"given":"Chen","family":"Qu","sequence":"additional","affiliation":[{"name":"School of Economics, University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2280-171X","authenticated-orcid":false,"given":"Jingyi","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Finance and Trade, Wenzhou Business College, Wenzhou 325035, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jinteco.2006.12.003","article-title":"Negotiating free trade","volume":"73","author":"Aghion","year":"2007","journal-title":"Journal of International Economics"},{"key":"ref_2","unstructured":"Aoki, R., and Nagaoka, S. 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