Taken from the movie “Beautiful Mind”

John Nash’s death on May 23, 2015 on the New Jersey Turnpike was a tragedy. However, his contribution to mathematics and economics is everlasting. His contribution to game theory led to his sharing the 1994 Nobel Memorial Prize for Economical Sciences.

Coincidentally, three weeks before his accidental death, there was an econophysics paper that employed his ideas of Nash equilibrium. Econophysics has been an inter-disciplinary quantitative field since 1990s. Victor Yakovenko, a physics professor in University of Maryland, applied the techniques of classical statistical mechanics, and concluded that the wealth of bottom 95% population follows Boltzmann-Gibbs exponential distribution, while the top a Pareto distribution. [Dragulescu & Yakovenko 2000] This approach assumes agents to have nearly “zero intelligence,” and behave randomly with no intent and purpose, contrary to the conventional assumption in economics that agents are perfectly rational, with purpose to maximize utility or profit.

This paper, written by Venkat Venkatasubramanian, described an approach aiming at reconciling econophysics and conventional economics, using the ideas in game theory. [Venkatasubramanian, Luo & Sethuraman 2015] Like statistical mechanics, it assumes the agents to be particles. Money plays the role of energy, just like other econophysics theory. The equilibrium state is the state with maximum entropy. However, it employed the idea of game theory, adding that the agents are intelligent and in a game, unlike molecules in traditional statistical mechanics. The equilibrium state is not simply the maximum entropic state, but also the Nash equilibrium. This reconciles econophysics and conventional economics. And it even further argues that, unlike equilibrium in thermodynamics being probabilistic in nature, this economical equilibrium is deterministic. And the expected distribution is log-normal distribution. (This log-normal distribution is hard to fit, which is another obstacles for economists to accept physical approach to economics.)

With this framework, Venkatasubramanian discussed about income inequality. Income inequality has aroused debates in the recent few years, especially after the detrimental financial crisis in 2008. Is capitalism not working now? Does capitalism produce unfairness? He connected entropy with the concept of fairness, or fairest inequality. And the state with maximum entropy is the fairest state. And, of course, the wealth distribution is the log-normal distribution. His study showed that:[http://phys.org/news/2015-05-fair-theory-income-inequality.html]

“Scandinavian countries and, to a lesser extent, Switzerland, Netherlands, and Australia have managed, in practice, to get close to the ideal distribution for the bottom 99% of the population, while the U.S. and U.K. remain less fair at the other extreme. Other European countries such as France and Germany, and Japan and Canada, are in the middle.”

See the figure at the end of this post about the discrepancy of the economies of a few countries to the maximum entropic state, or ideality. And [Venkatasubramanian, Luo & Sethuraman 2015]

“Even the US economy operated a lot closer to ideality, during ∼1945–75, than it does now. It is important to emphasize that in those three decades US performed extremely well economically, dominating the global economy in almost every sector.”

They even argued that these insights in economics might shed light to traditional statistical thermodynamics.

I have to say that I love this work because not only it explains real-world problem, but also links physics and economics in a beautiful way.

Take from http://phys.org/news/2015-05-fair-theory-income-inequality.html

- 1994 Nobel Memorial Prize for Economical Sciences
- John Nash’s death [http://planetprinceton.com/2015/05/24/mathematician-john-nash-and-wife-alicia-die-in-crash-on-nj-turnpike/]
- A. Dragulescu, V.M. Yakovenko, “Statistical Mechanics of Money”,
*Eur Phys. J. B.***17**(4), pp. 723-729 (2000). [arXiv:cond-mat/0001432] - Ian Wright, “Statistical Mechanics of Money”, Wolfram Demonstration.
- V. Venkatasubramanian, Y. Luo, J. Sethuraman, “How much inequality in income is fair? A microeconomic game theoretic perspective”,
*Physica A***435**, pp. 120-138 (2015). - “What’s fair?: New theory on income inequality”, Phys.org (May 27, 2015).

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