P2P soft security: On evolutionary dynamics of P2P incentive mechanism

Abstract

This paper thoroughly investigates the evolutionary dynamics of soft security mechanism, namely, reciprocity-based incentive mechanism, in P2P systems based on Evolutionary Game Theory (EGT). By soft security mechanism, it means social control mechanisms to overcome peers’ selfish (rational) behaviors, and encourage cooperation in P2P systems. Specifically, there exist three strategies in P2P systems: always cooperative (ALLC), always defect (ALLD) and reciprocator (R). Instead of existing work which take it for granted that, like ALLC users, R users did not bear any information-seeking cost, we assume small reciprocation cost, and study generalized mutation-selection dynamics. Our contributions are threefold: firstly, we prove and illustrate that, in a well-mixed P2P structure, ALLD is the only strict Nash equilibrium; secondly, we infer the specific condition under which evolution dynamics exhibits rock-scissors-paper oscillation in a structured P2P population. That is, the population cycles from ALLD to R to ALLC and back to ALLD; finally, we theoretically illustrate that the intensity of selection plays an important role in the evolutionary dynamics of P2P incentive mechanism. That is, when the intensity of selection is relatively weak and reciprocation cost limits to zero, the time average can be mostly concentrated on reciprocator. In brief, considering the existence of reciprocation cost and the small mutation in P2P incentive mechanisms, unlike existing work, it is impossible to simply achieve the “absolute cooperative” in P2P incentive mechanisms. On the other hand, stochastic evolution in P2P incentive mechanism with finite population and network structure still favor reciprocation.