Optimal strategies in collective Parrondo games

TL;DR

This paper explores a modified Parrondo's paradox where selecting the highest immediate gain leads to losses, while periodic or random choices increase capital, explained through control theory and dynamic programming.

Contribution

It introduces a modified game selection strategy in Parrondo's games and analyzes its counterintuitive outcomes using control theory methods.

Findings

Choosing the highest immediate gain causes systematic losses.

Periodic or random strategies lead to capital increase.

Continuous model analysis supports the discrete game results.

Abstract

We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic loses, whereas a periodic or random sequence of choices yields a steadily increase of the capital. An explanation of this behavior is given by noting that the short-range maximization of the returns is "killing the goose that laid the golden eggs". A continuous model displaying similar features is analyzed using dynamic programming techniques from control theory.