  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.
