Influence analysis of network evolution on Parrondo effect

Parrondo's paradox is a scheme used to describe an interesting paradoxical situation that a losing Game A and a losing Game B played randomly or periodically will produce a winning result. Here, a dynamic process of network evolution of Link A + Game B is proposed to yield the Parrondo effect. Game B with two asymmetric branches depends on the relative comparison between the capital of the network node and the average capital of all its neighbors. Simulation results demonstrate that network structure evolution make the losing Game B produce a paradoxical effect of winning and would be advantageous to the development of the "ratcheting" mechanism in Game B. Furthermore, the underlying paradoxical mechanism is analyzed to illustrate the parameter space where the "strong" Parrondo effect occurs. Then influence of two types of network connection is analyzed, indicating that the "agitating" effect of the network is basically the same when a node connects to a neighbor's neighbor or randomly chooses a node other than its neighbors. Further, a higher frequency of network evolution yields a larger parameter region where the "strong" Parrondo effect emerges.