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We develop a model for the evolution of wealth in a non-conservative economicenvironment, extending a theory developed earlier by the authors. The modelconsiders a system of rational agents interacting in a game theoreticalframework. This evolution drives the dynamic of the agents in both wealth andeconomic configuration variables. The cost function is chosen to represent arisk averse strategy of each agent. That is, the agent is more likely tointeract with the market, the more predictable the market, and therefore thesmaller its individual risk. This yields a kinetic equation for an effectivesingle particle agent density with a Nash equilibrium serving as the localthermodynamic equilibrium. We consider a regime of scale separation where thelarge scale dynamics is given by a hydrodynamic closure with this localequilibrium. A class of generalized collision invariants (GCIs) is developed toovercome the difficulty of the non-conservative property in the hydrodynamicclosure derivation of the large scale dynamics for the evolution of wealthdistribution. The result is a system of gas dynamics-type equations for thedensity and average wealth of the agents on large scales. We recover theinverse Gamma distribution, which has been previously considered in theliterature, as a local equilibrium for particular choices of the cost function.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Evolution of wealth in a nonconservative economy driven by local Nash equilibria