Game theoretic analysis for resource allocation in dynamic multi-hop networks with arbitration

A connection through a mobile node may not be available because of the greediness of selfish nodes. In this paper, we address the issue of dynamic packet forwarding by a set of wireless autonomous ad hoc nodes. Wireless nodes acting in a selfish manner try to use the resources of other nodes without their own participation. We model the dynamic packet forwarding problem as a negotiation game with an arbitrator. In our model, a group of mobile nodes requesting to forward packets negotiates with a mobile arbitrator until an agreement at least by simple majority is reached on a resource allocation. The mobile arbitrator submits offers to each mobile device in the group, and the mobile nodes decide to agree or disagree on the offer. The ultimate decision is made by simple majority. We investigate and solve the negotiation by finding the optimal Nash Equilibrium strategies of the game. We consider offers generated from Dirichlet's distribution for an ensemble of mobile devices over a finite and sporadic time limitation. The solution obtained from negotiation ensures that a mobile device always finds a peer or arbitrator to help forward packets and keep the network flowing. Mathematical proofs and MATLAB simulations support our model.