Agent inactivity in the Evolutionary Minority Game

Michael D. Mitton
In this work I have developed a model, based on the Evolutionary Minority Game (EMG), to examine the effect of agent inactivity within a group of agents competing for a limited resource, but governed by both supply-and-demand and a minority rule. The structure of the inactivity mechanism has been modeled after the strategy preference parameter, p, of the EMG. A parameter has also been introduced that models, in a very simple way, the effect of inflation on the system in order to motivate the
more » ... to motivate the agents to play the game. The behaviour of the model has been examined with the use of numerical simulations over its entire phase space. The results focus on two aspects of the model: 1. how an agent's performance depends on his activity level; and 2. how the properties of the EMG are affected when agents are given the option of not playing the game. Results of these simulations demonstrate that an agent's performance is strongly dependent on his level of activity. Specifically, it has been shown that an agent's optimal level of activity is dependent on his strategy preference and, moreover, that this optimal activity level undergoes a first-order transition from a phase of optimal inactivity to a phase of optimal activity as the inflationary force is increased. Even though an agent's activity decision has been modeled as a process independent of his decision to "buy" or "sell" during a given round, results of simulations indicate that correlations between the two decisions have emerged from the collective dynamics of the group. A theory of the model has also been developed. The formulation of the theory is based on a mean-field approach in which the actions of a single agent are considered within a background field produced by the remainder of the group. It has been found that the results of the theory agree with those of the numerical simulations very well and appear to become exact in the thermodynamic limit. Furthermore, the discrepancy between theory and simulation at finite N indicate a possib [...]
doi:10.14288/1.0085186 fatcat:chebz72fnvhrhifxo2dhasftda