Interplay of simple stochastic games as models for the economy. (English) Zbl 1340.91029

Garibaldi, Ubaldo; Radivojević, Tijana; Scalas, Enrico

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 77-87 (2013).

Summary: Using the interplay among three simple exchange games, one may give a satisfactory representation of a conservative economic system where total wealth and number of agents do not change in time. With these games it is possible to investigate the emergence of statistical equilibrium in a simple pure-exchange environment. The exchange dynamics is composed of three mechanisms: a decentralized interaction, which mimics the pair-wise exchange of wealth between two economic agents, a failure mechanism, which takes into account occasional failures of agents and includes wealth redistribution favoring richer agents, and a centralized mechanism, which describes the result of a redistributive effort. According to the interplay between these three mechanisms, their relative strength, as well as the details of redistribution, different outcomes are possible.
For the entire collection see [Zbl 1277.00032].

MSC:

91B02	Fundamental topics (basic mathematics, methodology; applicable to economics in general)
60J20	Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
91A15	Stochastic games, stochastic differential games
91A80	Applications of game theory
91B80	Applications of statistical and quantum mechanics to economics (econophysics)

Keywords:

stochastic matrix; Monte Carlo step; Markov dynamics