Local and global optimization in Parallel Minority Games

Abstract: The Parallel Minority Game (PMG) refers to a set of Minority Games (MG), played in parallel, where each agent only has two choices to pick from, but each choice can host agents of many kind i.e., their other alternative can be from any other choices. While the pay-off function remains the same as that in the MG -- agents picking the less crowded of their two choices win positive pay-off -- the optimization of resource allocation is significantly harder in the PMG. While a global optimization demands a uniform population in all choices, a local optimization attempts to balance the population in the two choices for a given agent. In the MG these two objectives coincides, but generally in the PMG these are competing. We study several non-dictated, stochastic strategies and compare their efficiencies in attaining the local and global optimization objectives. Counterintuitively, a strategy with partial information of populations perform the best in terms of population fluctuation and overall payoff maximization.