Collective Behavior: Macroscopic versus Kinetic Descriptions

Wealth evolution in spatially structured economies driven by local Nash equilibria with risk averse trading strategies

Christian Ringhofer

Arizona State University


We model the evolution of wealth in a spatially structured economy via a kinetic equation in a game theoretical framework and a risk averse regime. Individual agents interact with the ensemble (the market) and move incrementally towards a Nash equilibrium, with a frequency that is inverse proportional to the risk (the variance) in the market. The cases of conservative as well as non - conservative economies are considered. In the non - conservative case (when the total wealth in the economy is not a constant) we derive macroscopic balance laws for the spatial structure of the wealth via the concept of generalized collision invariants. (joint work with P. Degond and J.G. Liu)