Emerging collective behavior and local properties of financial dynamics in a public investment game

In this paper we consider a simple model of a society of economic agents, namely a variation of the well known “public investment game”, where each agent can contribute with a discrete quantity, i.e., cooperate to increase the benefits of the group. Interactions take place among nearest neighbors and depend on the motivation level (insider information, economy prospects). The profit is used to update individual motivations. We first explore a deterministic scenario and the existence of fixed points and attractors. We also consider the presence of noise, where profits fluctuate stochastically. In this scenario we analyze the global persistence as a function of time—a measure of the probability that the amount of money of the entire group remains at least equal to its initial value. Our simulations show that this quantity has a power law behavior. We have also performed simulations with a population of heterogeneous agents, including deceivers and conservatives. We show that, although there is no regular pattern regarding the average wealth, robust power laws for persistence do exist and argue that this can be used to characterize the emerging collective behavior. The influence of the motivation updating and the presence of conservatives and deceivers on persistence is also studied. Simulations for the local   persistence exploring two different versions of this concept: the probability of a particular agent not going bankrupt (i.e., remaining wealth ⩾0⩾0 up to time t) and the probability of a particular agent making more money than he initially had. Different power law behaviors are also observed in these situations.