Universality of Tsallis q-exponential of interoccurrence times within the microscopic model of cunning agents

We proposed the agent-based model of financial markets where agents (or traders) are represented by three-state spins located on the plane lattice or social network. The spin variable represents only the individual opinion (advice) that each trader gives to his nearest neighbors. In the model the agents can be considered as cunning. For instance, although agent having currently a maximal value of the spin advises his nearest neighbors to buy some stocks he, perfidiously, will sell some stocks in the next Monte Carlo step or will occupy a neutral position. In general, the trader has three possibilities: he can buy some stocks if his opinion change within a single time step is positive, sell some stocks if this change is negative, or remain inactive if his opinion is unchanged. The predictions of our model, found by simulations, well agree with the empirical universal distribution of interoccurrence times between daily losses below negative thresholds following the Tsallis q-exponential.