Users in a social network are usually confronted with decision-making under uncertain network states. While there are some works in the social learning literature on how to construct belief in an uncertain network state, few studies have focused on integrating learning with decision-making for the scenario in which users are uncertain about the network state and their decisions influence each other. Moreover, the population in a social network can be dynamic since users may arrive at or leave the network at any time, which makes the problem even more challenging. In this chapter, we introduce a dynamic Chinese restaurant game to study how a user in a dynamic social network learns about the uncertain network state and makes optimal decisions by taking into account not only the immediate utility, but also subsequent users’ influence. We introduce a Bayesian learning-based method for users to learn the network state and discuss a multidimensional Markov decision process-based approach for users to make optimal decisions. Finally, we apply the dynamic Chinese restaurant game to cognitive radio networks and use simulations to verify the effectiveness of the scheme.

While peer-to-peer (P2P) video streaming systems have achieved promising results, they introduce a large number of unnecessary traverse links, leading to substantial network inefficiency. To address this problem, we discuss how to enable cooperation among“group peers,” which are geographically neighboring peers with large intragroup upload and download bandwidths. Considering the peers’ selfish nature, we formulate the cooperative streaming problem as an evolutionary game and introduce, for every peer, the evolutionarily stable strategy (ESS). Moreover, we discuss a simple and distributed learning algorithm for the peers to converge to the ESSs. With the discussed algorithm, each peer decides whether to be an agent who downloads data from the peers outside the group or a free-rider who downloads data from the agents by simply tossing a coin, where the probability of the coin showing a head is learned from the peer’s own past payoff history. Simulation results show that compared to the traditional noncooperative P2P schemes, the discussed cooperative scheme achieves much better performance in terms of social welfare, probability of real-time streaming, and video quality.

In cognitive networks, how to stimulate cooperation among nodes is very important. However, most 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, such as in the well-known Prisoner’s dilemma and the backward induction principle, the unique Nash equilibrium is to always play noncooperatively. In this chapter, we discuss a cooperation stimulation scheme for the scenario in which the number of interactions is finite. This scheme is based on indirect reciprocity game modeling where the key concept is “I help you not because you have helped me but because you have helped others.” The problem of finding the optimal action rule is formulated as a Markov decision process, and a modified value-iteration algorithm is utilized to find the optimal action rule. Using the packet forwarding game as an example, it is shown 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.