Math @ Duke

Publications [#246846] of JianGuo Liu
Papers Published
 Degond, P; Liu, JG; Ringhofer, C, Evolution of wealth in a nonconservative economy driven by local Nash equilibria.,
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028
(November, 2014),
pp. 2013039420130394, The Royal Society, ISSN 1364503X [doi]
(last updated on 2021/11/28)
Abstract: We develop a model for the evolution of wealth in a nonconservative economic environment, extending a theory developed in Degond et al. (2014 J. Stat. Phys. 154, 751780 (doi:10.1007/s1095501308884)). The model considers a system of rational agents interacting in a gametheoretical framework. This evolution drives the dynamics of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a riskaverse 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 largescale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants is developed to overcome the difficulty of the nonconservative property in the hydrodynamic closure derivation of the largescale dynamics for the evolution of wealth distribution. The result is a system of gas dynamicstype 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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