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We study a social learning model in which agents iteratively update their beliefs about the true state of the world using private signals and the beliefs of other agents in a non-Bayesian manner. Some agents are stubborn, meaning they attempt to convince others of an erroneous true state (modeling fake news). We show that while agents learn the true state on short timescales, they "forget" it and believe the erroneous state to be true on longer timescales. Using these results, we devise strategies for seeding stubborn agents so as to disrupt learning, which outperform intuitive heuristics and give novel insights regarding vulnerabilities in social learning. 

We analyze a class of stochastic dynamic games among teams with asymmetric information, where members of a team share their observations internally with a delay of d. Each team is associated with a controlled Markov Chain, whose dynamics are coupled through the players’ actions. These games exhibit challenges in both theory and practice due to the presence of signaling and the increasing domain of information over time. We develop a general approach to characterize a subset of Nash equilibria where the agents can use a compressed version of their information, instead of the full information, to choose their actions. We identify two subclasses of strategies: sufficient private information-Based (SPIB) strategies, which only compress private information, and compressed information-based (CIB) strategies, which compress both common and private information. We show that SPIB-strategy-based equilibria exist and the set of payoff profiles of such equilibria is the same as that of all Nash equilibria. On the other hand, we show that CIB-strategy-based equilibria may not exist. We develop a backward inductive sequential procedure, whose solution (if it exists) provides a CIB strategy-based equilibrium. We identify some instances where we can guarantee the existence of a solution to the above procedure. Our results highlight the tension among compression of information, ability of compression-based strategies to sustain all or some of the equilibrium payoff profiles, and backward inductive sequential computation of equilibria in stochastic dynamic games with asymmetric information.