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Consider public health officials aiming to spread awareness about a new vaccine in a community interconnected by a social network. How can they distribute information with minimal resources, so as to avoid polarization and ensure community-wide convergence of opinion? To tackle such challenges, we initiate the study of sample complexity of opinion formation in networks. Our framework is built on the recognized opinion formation game, where we regard each agent’s opinion as a data-derived model, unlike previous works that treat opinions as data-independent scalars. The opinion model for every agent is initially learned from its local samples and evolves game-theoretically as all agents communicate with neighbors and revise their models towards an equilibrium. Our focus is on the sample complexity needed to ensure that the opinions converge to an equilibrium such that every agent’s final model has low generalization error. Our paper has two main technical results. First, we present a novel polynomial time optimization framework to quantify the total sample complexity for arbitrary networks, when the underlying learning problem is (generalized) linear regression. Second, we leverage this optimization to study the network gain which measures the improvement of sample complexity when learning over a network compared to that in isolation. Towards this end, we derive network gain bounds for various network classes including cliques, star graphs, and random regular graphs. Additionally, our framework provides a method to study sample distribution within the network, suggesting that it is sufficient to allocate samples inversely to the degree. Empirical results on both synthetic and real-world networks strongly support our theoretical findings. 

How Can Platforms Learn to Make Persuasive Recommendations? Many online platforms make recommendations to users on content from creators or products from sellers. The motivation underlying such recommendations is to persuade users into taking actions that also serve system-wide goals. To do this effectively, a platform needs to know the underlying distribution of payoff-relevant variables (such as content or product quality). However, this distributional information is often lacking—for example, when new content creators or sellers join a platform. In “Learning to Persuade on the Fly: Robustness Against Ignorance,” Zu, Iyer, and Xu study how a platform can make persuasive recommendations over time in the absence of distributional knowledge using a learning-based approach. They first propose and motivate a robust-persuasiveness criterion for settings with incomplete information. They then design an efficient recommendation algorithm that satisfies this criterion and achieves low regret compared with the benchmark of complete distributional knowledge. Overall, by relaxing the strong assumption of complete distributional knowledge, this research extends the applicability of information design to more practical settings. 

We study a variant of the principal-agent problem in which the principal does not directly observe the outcomes; rather, she gets a signal related to the agent’s action, according to a variable information structure. We provide simple necessary and sufficient conditions for implementability of an action and a utility profile by some information structure and the corresponding optimal contract — for a riskneutral or risk-averse agent, with or without the limited liability assumption. It turns out that the set of implementable utility profiles is characterized by simple thresholds on the utilities. 

The literature on strategic communication originated with the influential cheap talk model, which precedes the Bayesian persuasion model by three decades. This model describes an interaction between two agents: sender and receiver. The sender knows some state of the world which the receiver does not know, and tries to influence the receiver’s action by communicating a cheap talk message to the receiver. This paper initiates the algorithmic study of cheap talk in a finite environment (i.e., a finite number of states and receiver’s possible actions). We first prove that approximating the sender-optimal or the welfare-maximizing cheap talk equilibrium up to a certain additive constant or multiplicative factor is NP-hard. Fortunately, we identify three naturally-restricted cases that admit efficient algorithms for finding a sender-optimal equilibrium. These include a state-independent sender’s utility structure, a constant number of states or a receiver having only two actions.