Istituto dei materiali per l'elettronica ed il magnetismo     
Garibaldi U., Scalas E. Tolstoy's dream and the quest for statistical equilibrium in economics and the social sciences. Naldi, Giovanni; Pareschi, Lorenzo; Toscani, Giuseppe (Eds.) (eds.). Birkhäuser Boston: Springer, 2010.
The meaning of the notion of statistical equilibrium in economics is discussed as well as its relevance for economic theory. A simple agent-based model of taxation and redistribution is presented. Its invariant equilibrium distribution is the generalized Pólya sampling distribution. It turns out that the expected wealth distribution is the dichotomous Pólya whose continuous limit is the Beta distribution and whose appropriate thermodynamic limit is the Gamma distribution, often found in describing empirical data. The shape parameter of the Gamma distribution is the inverse of the wealth preferential attachment α−1.
DOI: 10.1007/978-0-8176-4946-3_5
Subject Markov Chains
Statistical Equilibrium
Complex Systems
Probabilistic Dynamics

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