Analytical Scheduling for Selfishness Detection in OppNets Based on Differential Game

Selfishness detection offers an effective way to mitigate the routing performance degradation caused by selfish behaviors in Opportunistic Networks but leads to extra network traffic and computational burden. Most existing efforts focus on designing the selfishness detection scheme by exploiting the behavioral records of nodes. In this paper, we investigate the scheduling strategy of selfishness detection during the message lifespan with the game theory. Specifically, the Long-term Selfishness Detection Game (LSDG) is proposed based on the differential game and the payoff in the integral form. LSDG formulates the selfishness detection and the node’s selfishness with the Ordinary Differential Equations (ODEs). Then, we prove the existence of the Nash equilibrium in LSDG and deduce the necessary conditions of the equilibrium strategy based on Pontryagin’s maximum principle. The recursion-based algorithm is designed in this paper to compute the numerical solution of the equilibrium strategy via Euler’s method. Both the soundness of our modeling approach and solution properties are verified by extensive experiments. The simulations also show that the obtained solution can achieve the Nash equilibrium, where neither the source node nor relay nodes can benefit more by solely changing their own strategies.