Journal of Dynamics & Games
January 2021 , Volume 8 , Issue 1
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Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [
Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the Expectation-Maximization algorithm. We propose an alternative approach based on the theory of Mean Field Games, a class of differential games with an infinite number of agents. We show that the solution of a finite state space multi-population Mean Field Games system characterizes the critical points of the log-likelihood functional for a Bernoulli mixture. The approach is then generalized to mixture models of categorical distributions. Hence, the Mean Field Games approach provides a method to compute the parameters of the mixture model, and we show its application to some standard examples in cluster analysis.
Given two stable matchings in a many-to-one matching market with
In this article, we extend to private ownership production economies, the results presented by Bergstrom, Shimomura, and Yamato (2009) on the multiplicity of equilibria for the special kind of pure-exchanges economies called Shapley-Shubik economies. Furthermore, a dynamic system that represents the changes in the distribution of the firms on the production branches is introduced. For the first purpose, we introduce a particular, but large enough, production sector to the Shapley-Shubik economies, for which a simple technique to build private-ownership economies with a multiplicity of equilibria is developed. In this context, we analyze the repercussions on the behavior of the economy when the number of possible equilibria changes due to rational decisions on the production side. For the second purpose, we assume that the rational decisions on the production side provoke a change in the distribution of the firms over the set of branches of production.
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