Effects of group interactions on the network Parrondo’s games

Abstract

A minimalistic multi-agent Parrondo’s game structure with network evolution (Game A) and branching dependent on the number of wins and losses of neighbors (Game B) was previously introduced, indicating that Parrondo’s paradox occurs, in which a losing strategy and a neutral strategy combine to yield a winning one. Using a similar Game B’s structure and introducing a new Game A’s structure with competition and cooperation behaviors, we further analyze the influences of network evolution, cooperation and competition behaviors as different group interactions on the network Parrondo’s games. Based on the multi-agent Parrondo’s game, the discrete Markov chain method is used. Theoretical analysis reveals that losing configurations of Game B, when stochastically mixed with neutral Game A with competition and cooperation behaviors, can result in paradoxical winning scenarios like network evolution and can even produce larger parameter space. Simulation results indicate that under different network topology structures stochastically mixing Game A with different group interactions and Game B can produce different enhanced winning outcomes, despite Game B being individually losing. The underlying paradoxical mechanisms where the ratcheting mechanism of Game B and the agitating mechanism of Game A with different group interactions are analyzed. It is also elucidated that agitation from Game A with different group interactions improves the capital exchange between individuals.