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First we provide an economic theoretical foundation of the monopoly solution in this bilateral framework through a formalization of an explicit trading process inspired by Pareto (Cours d\u2019\u00e9conomie politique. F. Rouge Editeur, Lausanne, 1896) for an exchange economy with a finite number of commodities, and we give the conditions under which our monopoly solution has the geometric characterization proposed by Schydlowsky and Siamwalla (Q J Econ 80:147\u2013153, 1966). Then, we provide a game theoretical foundation of our monopoly solution through a two-stage reformulation of our model. This allows us to prove that the set of the allocations corresponding to a monopoly equilibrium and the set of the allocations corresponding to a subgame perfect equilibrium of the two-stage game coincide. Finally, we compare our model of monopoly with a bilateral exchange version of a pioneering model proposed by Forchheimer (Jahrbuch f\u00fcr Gesetzgebung, Verwaltung und Volkswirschafts im Deutschen Reich 32:1\u201312, 1908), known as a model of \u201cpartial monopoly\u201d since there a monopolist shares a market with a\u201ccompetitive fringe.\u201d <jats:italic>Journal of Economic Literature<\/jats:italic> Classification Numbers: D42, D51.<\/jats:p>","DOI":"10.1007\/s00182-023-00847-2","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T17:05:37Z","timestamp":1683824737000},"page":"1261-1290","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the foundation of monopoly in bilateral exchange"],"prefix":"10.1007","volume":"52","author":[{"given":"Francesca","family":"Busetto","sequence":"first","affiliation":[]},{"given":"Giulio","family":"Codognato","sequence":"additional","affiliation":[]},{"given":"Sayantan","family":"Ghosal","sequence":"additional","affiliation":[]},{"given":"Damiano","family":"Turchet","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,11]]},"reference":[{"key":"847_CR1","volume-title":"La D\u00e9cision","author":"RJ Aumann","year":"1969","unstructured":"Aumann RJ (1969) Measurable utility and measurable choice theory. 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