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

Abstract

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.

References in corpus (9)

• Colloquium: Statistical mechanics of money, wealth, and income
• A new model for self-organized dynamics and its flocking behavior
• Continuum limit of self-driven particles with orientation interaction
• On a kinetic model for a simple market economy
• Kinetic models for the trading of goods
• Self-similarity and power-like tails in nonconservative kinetic models
• Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria
• Evolution of wealth in a nonconservative economy driven by local Nash equilibria
• On the emergence of an "intention field" for socially cohesive agents

Cited by in corpus (12)

• Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation
• Evolution of wealth in a nonconservative economy driven by local Nash equilibria
• Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation
• Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects
• A continuum model for nematic alignment of self-propelled particles
• Traveling waves in a mean field learning model
• Quaternions in collective dynamics
• Meanfield games and model predictive control
• On a Boltzmann mean field model for knowledge growth
• Continuum dynamics of the intention field under weakly cohesive social interactions
• An age-structured continuum model for myxobacteria
• Reduced fluid models for self-propelled particles interacting through alignment