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
[SLIDES]

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)