{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:38:39Z","timestamp":1760146719423,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Funds through the Portuguese funding agency, FCT\u2013Fun da\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"],"award-info":[{"award-number":["UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"]}]},{"name":"Modelling, Dynamics and Games","award":["UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"],"award-info":[{"award-number":["UIDB\/50014\/2020","PTDC\/MAT-APL\/31753\/2017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>A model of Edgeworthian economies is studied, in which participants are randomly chosen at each period to exchange two goods to increase their utilities, as described by the Cobb\u2013Douglas utility function. Participants can trade deviating from their bilateral equilibrium, provided that the market and the trade follow appropriate symmetry conditions. The article aims to study the convergence to equilibrium in a situation where individuals or small groups of participants trade in a market, and prices are determined by interactions between the participants rather than by demand and supply alone. A dynamic matching and bargaining game is considered, with statistical duality imposed on the market game, ensuring that each participant has a counterpart with opposite preferences. This guaranties that there is sufficient incentive for trade. It is shown that, in each period, the expected logarithm of the trading price in the Edgeworthian economy equals the expected Walrasian price. This demonstrates that, under symmetry conditions, the trading price in the Edgeworthian economy is related to the Walrasian price, indicating convergence of the trading price in the Edgeworthian economy towards the Walrasian price. The study suggests that, under the right conditions, the decentralized trading model leads to price convergence similar to what would be expected in a more classical Walrasian economy, where prices balance demand and supply.<\/jats:p>","DOI":"10.3390\/math12233825","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T09:18:32Z","timestamp":1733217512000},"page":"3825","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bounded Rational Players in a Symmetric Random Exchange Market"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2634-295X","authenticated-orcid":false,"given":"Aliyu","family":"Yusuf","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, Wudil 064, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7710-4284","authenticated-orcid":false,"given":"Bruno","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Faculty of Science and Nutrition, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2953-6688","authenticated-orcid":false,"given":"Alberto","family":"Pinto","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Porto, 4200-465 Porto, Portugal"},{"name":"LIAAD\u2013INESC TEC, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"given":"Athanasios N.","family":"Yannacopoulos","sequence":"additional","affiliation":[{"name":"Department of Statistics, Athens University of Economics and Business, Athens 10434, Greece"},{"name":"Stochastic Modelling and Applications Laboratory, Athens University of Economics and Business, Athens 10434, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s10100-011-0208-5","article-title":"On the convergence to Walrasian prices in random matching Edgeworthian economies","volume":"20","author":"Pinto","year":"2012","journal-title":"Cent. Eur. J. Oper. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1086\/261868","article-title":"Allocative efficiency of markets with zero-intelligence traders: Market as a partial substitute for individual rationality","volume":"101","author":"Gode","year":"1993","journal-title":"J. Political Econ."},{"key":"ref_3","unstructured":"Walras, L. (1954). Elements of Pure Economics, R. D. Irwin Inc."},{"key":"ref_4","unstructured":"Edgeworth, F.Y. (1881). 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(2012). The Stability of Walrasian General Equilibrium. J. Econ. Lit., 65, Available online: https:\/\/shs.hal.science\/halshs-00748215\/."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Peixoto, M.M., Pinto, A.A., and Rand, D.A. (2011). Bargaining skills in an Edgeworthian economy. Dynamics, Games and Science I, DYNA, in Honor of Maur\u00edcio Peixoto and David Rand, Springer.","DOI":"10.1007\/978-3-642-11456-4"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1111\/jpet.12507","article-title":"Zero-intelligence versus human agents: An experimental analysis of the efficiency of Double Auctions and Over-the-Counter markets of varying sizes","volume":"23","author":"Attanasi","year":"2021","journal-title":"J. Public Econ. Theory"}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/12\/23\/3825\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:45:53Z","timestamp":1760114753000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/12\/23\/3825"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"references-count":18,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["math12233825"],"URL":"https:\/\/doi.org\/10.3390\/math12233825","relation":{},"ISSN":["2227-7390"],"issn-type":[{"type":"electronic","value":"2227-7390"}],"subject":[],"published":{"date-parts":[[2024,12,3]]}}}