Multi player Parrondo games with rigid coupling

TL;DR

This paper explores how strong coupling between multiple players in Parrondo games affects their collective gains, showing that coupling can enhance and even change the underlying winning mechanisms.

Contribution

It introduces and analyzes two types of rigid coupling in multiplayer Parrondo games, demonstrating their impact on collective gains and game dynamics.

Findings

Coupling increases the average gain per player.

Coupling can dominate the original game mechanisms.

Different couplings lead to different dominant behaviors.

Abstract

In the original Parrondo game, a single player combines two losing strategies to a winning strategy. In this paper we investigate the question what happens, if two or more players play Parrondo games in a coordinated way. We introduce a strong coupling between the player such that the gain or loss of all players in one round is the same. We investigate two possible realizations of such a coupling. For both we show that the coupling increases the gain per player. The dependency of the gain on the various parameters of the games is determined. The coupling can not only lead to a larger gain, but it can also dominate the driving mechanism of the uncoupled games. Which driving mechanism dominates, depends on the type of coupling. Both couplings are set side by side and the main similarities and differences are emphasised.