Evolution of wealth in a nonconservative economy driven by local Nash equilibria
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants (GCIs) is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function.
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- Silver, Jonathan & Slud, Eric & Takamoto, Keiji, 2002. "Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences," Journal of Economic Theory, Elsevier, vol. 106(2), pages 417-435, October.
- Chaim Fershtman & Yoram Weiss, 1991.
"Social Status, Culture and Economic Performance,"
1007, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Yoram Weiss & Chaim Fershtman, 1997.
"Social Status and Economic Performance: A Survey,"
University of Chicago - George G. Stigler Center for Study of Economy and State
139, Chicago - Center for Study of Economy and State.
- Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
- Düring, B. & Toscani, G., 2007.
"Hydrodynamics from kinetic models of conservative economies,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 384(2), pages 493-506.
- B. Düring & G. Toscani, 2007. "Hydrodynamics from kinetic models of conservative economies," CoFE Discussion Paper 07-06, Center of Finance and Econometrics, University of Konstanz.
- Maldarella, Dario & Pareschi, Lorenzo, 2012. "Kinetic models for socio-economic dynamics of speculative markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 715-730.
- Adrien BLANCHET & Pascal MOSSAY & Filippo SANTAMBROGIO, 2013.
"Existence and Uniqueness of Equilibrium for a Spatial Model of Social Interactions,"
13055, Research Institute of Economy, Trade and Industry (RIETI).
- Blanchet, Adrien & Mossay, Pascal & Santambrogio, Filippo, 2014. "Existence and uniqueness of equilibrium for a spatial model of social interactions," TSE Working Papers 14-489, Toulouse School of Economics (TSE).
- Oded Galor & Joseph Zeira, 2013.
"Income Distribution and Macroeconomics,"
2013-12, Brown University, Department of Economics.
- Corneo, Giacomo & Jeanne, Olivier, 2001. " Status, the Distribution of Wealth, and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 103(2), pages 283-93, June.
- Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-57, July.
- Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
- Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
- David Mckenzie & Hillel Rapoport, 2004.
"Network Effects and the Dynamics of Migration and Inequality: Theory and Evidence from Mexico,"
2004-3, Bar-Ilan University, Department of Economics.
- Mckenzie, David & Rapoport, Hillel, 2007. "Network effects and the dynamics of migration and inequality: Theory and evidence from Mexico," Journal of Development Economics, Elsevier, vol. 84(1), pages 1-24, September.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- Adrien Blanchet & Guillaume Carlier, 2012.
"Optimal transport and Cournot-Nash equilibria,"
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