Synchronous Cooperative Parrondo's Games

TL;DR

This paper introduces two new synchronous cooperative Parrondo's games where all players play simultaneously, either the same game or their own choice, revealing paradoxical outcomes dependent on the number of players.

Contribution

The paper presents novel synchronous game models and provides analytical results and algorithms for their probability distributions, extending previous asynchronous Parrondo's game research.

Findings

Paradoxical outcomes depend on the number of players

Analytical probability distribution derived for the new games

Algorithms developed for game analysis

Abstract

Inspired by asynchronous cooperative Parrondo's games we introduce two new types of games in which all players simultaneously play game A or game B or a combination of these two games. These two types of games differ in the way a combination of games A and B is played. In the first type of synchronous games, all players simultaneously play the same game (either A or B), while in the second type players simultaneously play the game of their choice, i.e. A or B. We show that for these games, as in the case of asynchronous games, occurrence of the paradox depends on the number of players. An analytical result and an algorithm are derived for the probability distribution of these games.