Local and global optimization in Parallel Minority Games

TL;DR

This paper investigates how different stochastic strategies perform in optimizing resource allocation in Parallel Minority Games, highlighting the effectiveness of strategies with partial information.

Contribution

It introduces and compares various stochastic strategies for local and global optimization in the complex setting of Parallel Minority Games.

Findings

Strategies with partial information outperform others in population fluctuation control.

Global optimization requires uniform population distribution across choices.

Local optimization balances populations for individual agents effectively.

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.