{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:57:01Z","timestamp":1762081021503,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T00:00:00Z","timestamp":1671667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004586","name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"]}],"id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004070","name":"Khalifa University of Science and Technology","doi-asserted-by":"publisher","award":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"],"award-info":[{"award-number":["PTDC\/MAT-APL\/31753\/2017","UIDB\/00144\/2020","PD\/BD\/105726\/2014","E-26\/202.927\/2017","305544\/2011-0","307873\/2013-7","FSU-2020-09"]}],"id":[{"id":"10.13039\/501100004070","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>In this work, we consider a classic international trade model with two countries and one firm in each country. The game has two stages: in the first stage, the governments of each country use their welfare functions to choose their tariffs either: (a) competitively (Nash equilibrium) or (b) cooperatively (social optimum); in the second stage, firms competitively choose (Nash) their home and export quantities under Cournot-type competition conditions. In a previous publication we compared the competitive tariffs with the cooperative tariffs and we showed that the game is one of the two following types: (i) prisoner\u2019s dilemma (when the competitive welfare outcome is dominated by the cooperative welfare outcome); or (ii) a lose\u2013win dilemma (an asymmetric situation where only one of the countries is damaged in the cooperative welfare outcome, whereas the other is benefited). In both scenarios, their aggregate cooperative welfare is larger than the aggregate competitive welfare. The lack of coincidence of competitive and cooperative tariffs is one of the main difficulties in international trade calling for the establishment of trade agreements. In this work, we propose a welfare-balanced trade agreement where: (i) the countries implement their cooperative tariffs and so increase their aggregate welfare from the competitive to the cooperative outcome; (ii) they redistribute the aggregate cooperative welfare according to their relative competitive welfare shares. We analyse the impact of such trade agreement in the relative shares of relevant economic quantities such as the firm\u2019s profits, consumer surplus, and custom revenue. This analysis allows the countries to add other conditions to the agreement to mitigate the effects of high changes in these relative shares. Finally, we introduce the trade agreement index measuring the gains in the aggregate welfare of the two countries. In general, we observe that when the gains are higher, the relative shares also exhibit higher changes. Hence, higher gains demand additional caution in the construction of the trade agreement to safeguard the interests of the countries.<\/jats:p>","DOI":"10.3390\/math11010040","type":"journal-article","created":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T03:02:15Z","timestamp":1671764535000},"page":"40","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Welfare\u2013Balanced International Trade Agreements"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7707-6906","authenticated-orcid":false,"given":"Filipe","family":"Martins","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Porto\u2014CMUP, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2953-6688","authenticated-orcid":false,"given":"Alberto A.","family":"Pinto","sequence":"additional","affiliation":[{"name":"INESC TEC\u2014Instituto de Engenharia de Sistemas e Computadores, Tecnologia e Ci\u00eancia e Departamento de Matem\u00e1tica, FCUP\u2014Faculdade de Ci\u00eancias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1581-9505","authenticated-orcid":false,"given":"Jorge P.","family":"Zubelli","sequence":"additional","affiliation":[{"name":"Mathematics Department, Khalifa University, Abu Dhabi 127788, United Arab Emirates"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,22]]},"reference":[{"key":"ref_1","unstructured":"McMillan, J. (1986). Game Theory in International Economics, Harwood Academic Publishers."},{"key":"ref_2","unstructured":"von Haberler, G. (1937). The Theory of International Trade with Its Application to Commercial Policy, Macmillan. Available online: https:\/\/mises.org\/library\/international-trade."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1016\/S1573-4404(05)80007-3","article-title":"Strategic trade policy","volume":"Volume 3","author":"Brander","year":"1995","journal-title":"Handbook of International Economics"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bewley, T. (1987). Strategic aspects of trade policy. Advances in Economic Theory, Cambridge University Press. Chapter 9.","DOI":"10.1017\/CCOL0521340446"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"707","DOI":"10.2307\/2297771","article-title":"International R&D Rivalry and Industrial Strategy","volume":"50","author":"Spencer","year":"1983","journal-title":"Rev. Econ. Stud."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0022-1996(85)90006-6","article-title":"Export subsidies and international market share rivalry","volume":"18","author":"Brander","year":"1985","journal-title":"J. Int. Econ."},{"key":"ref_7","first-page":"605","article-title":"Rivalry between exporting countries and an importing country under incomplete information","volume":"32","author":"Liao","year":"2004","journal-title":"Acad. Econ. Pap."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0022-1996(86)90038-3","article-title":"Targeted export promotion with several oligopolistic industries","volume":"21","author":"Dixit","year":"1986","journal-title":"J. Int. Econ."},{"key":"ref_9","unstructured":"Krugman, P. (2007). Strategic export promotion: A critique. Strategic Trade Policy and the New International Economics, MIT Press. Chapter 3."},{"key":"ref_10","first-page":"779","article-title":"A Theory of Managed Trade","volume":"80","author":"Bagwell","year":"1990","journal-title":"Am. Econ. Rev."},{"key":"ref_11","unstructured":"Jones, R.W., and Kenen, P.B. (1984). Increasing Returns, Imperfect Markets, and Trade Theory. Handbook of International Economics Volume I, North Holland Press. Chapter 7."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0167-7187(94)00443-6","article-title":"Price competition between two international firms facing tariffs","volume":"13","author":"Fisher","year":"1995","journal-title":"Int. J. Ind. Organ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1086\/261312","article-title":"Multimarket Oligopoly: Strategic Substitutes and Complements","volume":"93","author":"Bulow","year":"1985","journal-title":"J. Political Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.2307\/1891121","article-title":"Optimal Trade and Industrial Policy Under Oligopoly","volume":"101","author":"Eaton","year":"1986","journal-title":"Q. J. Econ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2232651","article-title":"International Trade Policy for Oligopolistic Industries","volume":"94","author":"Dixit","year":"1984","journal-title":"Econ. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-1996(81)90041-6","article-title":"Intra-industry trade in identical commodities","volume":"11","author":"Brander","year":"1981","journal-title":"J. Int. Econ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0022-1996(89)90003-2","article-title":"Trade restrictions as facilitating practices","volume":"26","author":"Krishna","year":"1989","journal-title":"J. Int. Econ."},{"key":"ref_18","unstructured":"Jones, R.W., and Kenen, P.B. (1984). International rules and institutions for trade policy. Handbook of International Economics Volume III, North Holland Press. Chapter 29."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1086\/431782","article-title":"Enforcement, Private Political Pressure, and the General Agreement on Tariffs and Trade\/World Trade Organization (GATT\/WTO) Escape Clause","volume":"34","author":"Bagwell","year":"2005","journal-title":"J. Leg. Stud."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1257\/aer.89.1.215","article-title":"An Economic Theory of GATT","volume":"89","author":"Bagwell","year":"1999","journal-title":"Am. Econ. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.jinteco.2008.03.005","article-title":"Tariff retaliation versus financial compensation in the enforcement of international trade agreements","volume":"76","author":"Saggi","year":"2008","journal-title":"J. Int. Econ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.euroecorev.2013.05.006","article-title":"Size inequality, coordination externalities and international trade agreements","volume":"63","author":"Saggi","year":"2013","journal-title":"Eur. Econ. Rev."},{"key":"ref_23","unstructured":"Kilolo, J.M.M. (2013). Country Size, Trade Liberalization and Transfers, University Library of Munich. MPRA Paper."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1111\/ecpo.12156","article-title":"Country asymmetry, trade agreements, and transfers","volume":"33","author":"Kilolo","year":"2021","journal-title":"Econ. Politics"},{"key":"ref_25","first-page":"141","article-title":"An Economical Model For Dumping by Dumping in a Cournot Model","volume":"Volume 2","author":"Peixoto","year":"2011","journal-title":"Dynamics, Games and Science II, DYNA 2008, in Honour of Maur\u00edcio Peixoto and David Rand"},{"key":"ref_26","first-page":"145","article-title":"A Repeated Strategy for Dumping","volume":"Volume 180","author":"Alseda","year":"2016","journal-title":"Discrete Dynamical Systems and Applications, ICDEA 2012"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"149","DOI":"10.3934\/jdg.2017009","article-title":"Nash and social welfare impact in an international trade Model","volume":"4","author":"Martins","year":"2017","journal-title":"J. Dyn. Games"},{"key":"ref_28","unstructured":"Gibbons, R. (1999). A Primer in Game Theory, Pearson Prentice Hall."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"175","DOI":"10.3934\/jdg.2017010","article-title":"Trade and growth: A simple model with NOT-SO-Simple implications","volume":"4","author":"Corchon","year":"2017","journal-title":"J. Dyn. Games"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Amir, R., Jin, J.Y., and Troege, M. (2022). On the limits of free trade in a Cournot world: When are restrictions on trade beneficial?. Can. J. Econ.\/Rev. Can. D\u2019\u00e9conomique, in print.","DOI":"10.1111\/caje.12619"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"119","DOI":"10.3934\/jdg.2020022","article-title":"The sensitivity of commodity markets to exchange operations such as swing","volume":"8","author":"Bobrik","year":"2021","journal-title":"J. Dyn. Games"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"405","DOI":"10.3934\/jdg.2022016","article-title":"The dynamics of fitness and wealth distributions\u2014A stochastic game-theoretic model","volume":"9","author":"Gibaud","year":"2022","journal-title":"J. Dyn. Games"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"373","DOI":"10.3934\/jdg.2022006","article-title":"Schelling redux: An evolutionary dynamic model of residential segregation","volume":"9","author":"Sandholm","year":"2022","journal-title":"J. Dyn. Games"}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/11\/1\/40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:48:12Z","timestamp":1760147292000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/11\/1\/40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,22]]},"references-count":33,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["math11010040"],"URL":"https:\/\/doi.org\/10.3390\/math11010040","relation":{},"ISSN":["2227-7390"],"issn-type":[{"type":"electronic","value":"2227-7390"}],"subject":[],"published":{"date-parts":[[2022,12,22]]}}}