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Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems
Department of Computer Science, Universidad de Zaragoza, Pedro Cerbuna 12, Zaragoza 50009, Spain
Department of Physics, Universidad de Extremadura, Avda. de Elvas s/n, Badajoz 06071, Spain
BIFI, Universidad de Zaragoza, Corona de Aragón 42, Zaragoza 50009, Spain
* Author to whom correspondence should be addressed.
Received: 3 November 2009; Accepted: 30 November 2009 / Published: 2 December 2009
Abstract: 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.
Keywords: multi-agent systems; equiprobability; economic models; Gamma distributions
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MDPI and ACS Style
López-Ruiz, R.; Sañudo, J.; Calbet, X. Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems. Entropy 2009, 11, 959-971.
López-Ruiz R, Sañudo J, Calbet X. Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems. Entropy. 2009; 11(4):959-971.
López-Ruiz, Ricardo; Sañudo, Jaime; Calbet, Xavier. 2009. "Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems." Entropy 11, no. 4: 959-971.