An operatorial view of competition and cooperation in a network of economic agents

Abstract

A network of agents interacting both with competitive and/or cooperative mechanisms is modeled by using fermionic ladder operators. The time evolution of the network is assumed to be governed by a Hermitian time-independent Hamiltonian operator, and the mean values of the number operators are interpreted as a measure of the wealth status of the agents. Besides classical Heisenberg, we use the recently introduced $(H,\rho)$-induced dynamics approach to account for some actions able to provide a self-adjustment of the network according to its time evolution. Some numerical simulations are presented and discussed. Remarkably, we show that, in a network where cooperation may emerge, the average wealth of the agents is higher, and there is a very low level of inequality.