"Illusion of control" in Minority and Parrondo Games

TL;DR

This paper analytically and numerically shows that in Minority and Parrondo Games, agents who optimize based on past info perform worse than random strategies, illustrating the 'illusion of control' phenomenon.

Contribution

It provides a theoretical and simulation-based analysis demonstrating that optimization can lead to worse outcomes than randomness in specific game settings.

Findings

Optimizing agents perform worse than non-optimizing agents.

Low-entropy strategies under-perform high-entropy strategies.

Analytical and numerical evidence of the 'illusion of control'.

Abstract

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Minority game and the Parrondo Games, that agents who optimize their strategy based on past information actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the "illusion of control" in set-ups a priori defined to emphasize the importance of optimization.