Incentive Mechanisms based on Minority Games in Heterogeneous Delay Tolerant Networks

In this paper we design an incentive mechanism for heterogeneous Delay Tolerant Networks (DTNs). The proposed mechanism tackles a core problem of such systems: how to induce coordination of DTN relays in order to achieve a target performance figure, e.g., delivery probability or end-to-end delay, under a given constraint in term of network resources, e.g., number of active nodes or energy consumption. Also, we account for the realistic case when the cost for taking part in the forwarding process varies with the devices' technology or the users' habits. Finally, the scheme is truly applicable to DTNs since it works with no need for end-to-end connectivity. In this context, we first introduce the basic coordination mechanism leveraging the notion of a Minority Game. In this game, relays compete to be in the population minority and their utility is defined in combination with a rewarding mechanism. The rewards in turn configure as a control by which the network operator controls the desired operating point for the DTN. To this aim, we provide a full characterization of the equilibria of the game in the case of heterogeneous DTNs. Finally, a learning algorithm based on stochastic approximations provably drives the system to the equilibrium solution without requiring perfect state information at relay nodes or at the source node and without using end-to-end communications to implement the rewarding scheme. We provide extensive numerical results to validate the proposed scheme.