{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:40:34Z","timestamp":1760244034613,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2009,12,2]],"date-time":"2009-12-02T00:00:00Z","timestamp":1259712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A set of many identical interacting agents obeying a global additive constraint is considered. Under the hypothesis of equiprobability in the high-dimensional volume delimited in phase space by the constraint, the statistical behavior of a generic agent over the ensemble is worked out. The asymptotic distribution of that statistical behavior is derived from geometrical arguments. This distribution is related with the Gamma distributions found in several multi-agent economy models. The parallelism with all these systems is established. Also, as a collateral result, a formula for the volume of high-dimensional symmetrical bodies is proposed.<\/jats:p>","DOI":"10.3390\/e11040959","type":"journal-article","created":{"date-parts":[[2009,12,2]],"date-time":"2009-12-02T11:40:11Z","timestamp":1259754011000},"page":"959-971","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems"],"prefix":"10.3390","volume":"11","author":[{"given":"Ricardo","family":"L\u00f3pez-Ruiz","sequence":"first","affiliation":[{"name":"Department of Computer Science, Universidad de Zaragoza, Pedro Cerbuna 12, Zaragoza 50009, Spain"},{"name":"BIFI, Universidad de Zaragoza, Corona de Arag\u00f3n 42, Zaragoza 50009, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaime","family":"Sa\u00f1udo","sequence":"additional","affiliation":[{"name":"Department of Physics, Universidad de Extremadura, Avda. de Elvas s\/n, Badajoz 06071, Spain"},{"name":"BIFI, Universidad de Zaragoza, Corona de Arag\u00f3n 42, Zaragoza 50009, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xavier","family":"Calbet","sequence":"additional","affiliation":[{"name":"BIFI, Universidad de Zaragoza, Corona de Arag\u00f3n 42, Zaragoza 50009, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2009,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mantegna, R., and Stanley, H.E. (1999). An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press.","DOI":"10.1017\/CBO9780511755767"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Meyers, R.A. (2009). Encyclopedia of Complexity and System Science, Springer.","DOI":"10.1007\/978-0-387-30440-3"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1007\/s100510070114","article-title":"Statistical mechanics of money","volume":"B17","author":"Dragulescu","year":"2000","journal-title":"Eur. Phys. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s100510070173","article-title":"Statistical mechanics of money: How saving propensity affects its distribution","volume":"17","author":"Chakraborti","year":"2000","journal-title":"Eur. Phys. J. 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