Indirect Reciprocity Game Modelling for Cooperation Stimulation in Cognitive Networks

In cognitive networks, since nodes generally belong to different authorities and pursue different goals, they will not cooperate with others unless cooperation can improve their own performance. Thus, how to stimulate cooperation among nodes in cognitive networks is very important. However, most of existing game-theoretic cooperation stimulation approaches rely on the assumption that the interactions between any pair of players are long-lasting. When this assumption is not true, according to the well-known Prisoner\´s Dilemma and the backward induction principle, the unique Nash equilibrium (NE) is to always play non-cooperatively. In this paper, we propose a cooperation stimulation scheme for the scenario where the number of interactions between any pair of players are finite. The proposed algorithm is based on indirect reciprocity game modelling where the key concept is "I help you not because you have helped me but because you have helped others". We formulate the problem of finding the optimal action rule as a Markov Decision Process (MDP) and propose a modified value iteration algorithm to find the optimal action rule. Using the packet forwarding game as an example, we show that with an appropriate cost-to-gain ratio, the strategy of forwarding the number of packets that is equal to the reputation level of the receiver is an evolutionarily stable strategy (ESS). Finally, simulations are shown to verify the efficiency and effectiveness of the proposed algorithm.