In this paper we study the problem of social learning under multiple true hypotheses andself-interestedagents that exchange information over a graph. In this setup, each agent receives data that might be generated from a different hypothesis (or state) than the data received by the other agents. In contrast to the related literature on social learning, which focuses on showing that the network achieves consensus, here we study the case where every agent is self-interested and wishes to find the hypothesis that generates its own observations. Moreover, agents do not know which other agents among their peers want to discover the same state as theirs. As a result they do not know which agents they should cooperate with. To enable learning under these conditions, we propose a strategy withadaptivecombination weights and study the consistency of the agents’ learning process. The method allows each agent to identify and collaborate with neighbors that observe the same hypothesis, while excluding others, thus resulting in improved performance compared to both non-cooperative learning and cooperative social learning solutions. We analyze the asymptotic behavior of agents’ beliefs and provide conditions that enable all agents to correctly identify their true hypotheses. The theoretical analysis is corroborated by numerical simulations.

A common assumption in the social learning literature is that agents exchange information in an unselfish manner. In this work, we consider the scenario where a subset of agents aims at driving the network beliefs to the wrong hypothesis. The adversaries are unaware of the true hypothesis. However, they will "blend in" by behaving similarly to the other agents and will manipulate the likelihood functions used in the belief update process to launch inferential attacks. We will characterize the conditions under which the network is misled. Then, we will explain that it is possible for such attacks to succeed by showing that strategies exist that can be adopted by the malicious agents for this purpose. We examine both situations in which the agents have minimal or no information about the network model.

In cognitive radio networks, secondary users (SUs) can access the spectrum licensed by primary users (PUs) in an opportunistic fashion provided they cause no harmful interference to primary transmissions. Assuming that selfish and malicious but rational types of SUs are present in the network, we consider a setting where the PUs can also benefit from the cooperation with the SUs. The SUs are autonomous agents, have disparate interests and aim at maximizing their own type-dependent interests. Since misbehaving users can impede the PUs' communications by malicious or selfish actions, we develop a trust management scheme employed by the PUs that rewards cooperative SUs and punishes non-cooperative ones. We study the impact of trust on both types of misbehaving SUs' optimal decision-making process, by utilizing the Markov Decision Process framework, and we derive conditions that provably thwart malicious and selfish behavior for certain model parameters.