Hedge Behavior: Statistical Equivalence of Different Systems
In Chaps. 5 and 6, we have identified a class of phase transitions in the market-directed resource-allocation game, and found that there exists a critical point at which the phase transitions occur. The critical point is given by a certain resource ratio. Here, by performing computer simulations and theoretical analysis, we report that the critical point is robust against various kinds of human hedge behavior where the numbers of herds and contrarians can be varied widely. This means that the critical point can be independent of the total number of participants composed of normal agents, herds, and contrarians, under some conditions. This finding means that the critical points we identified in this complex adaptive system (with adaptive agents) is also an intensive quantity, similar to those revealed in traditional physical systems (with non-adaptive units).