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We consider a Bayesian persuasion problem where the sender tries to persuade the receiver to take a particular action via a sequence of signals. This we model by considering multi-phase trials with different experiments conducted based on the outcomes of prior experiments. In contrast to most of the literature, we consider the problem with constraints on signals imposed on the sender. This we achieve by fixing some of the experiments in an exogenous manner; these are called determined experiments. This modeling helps us understand real-world situations where this occurs: e.g., multi-phase drug trials where the FDA determines some of the experiments, start-up acquisition by big firms where late-stage assessments are determined by the potential acquirer, multi-round job interviews where the candidates signal initially by presenting their qualifications but the rest of the screening procedures are determined by the interviewer. The non-determined experiments (signals) in the multi-phase trial are to be chosen by the sender in order to persuade the receiver best. With a binary state of the world, we start by deriving the optimal signaling policy in the only non-trivial configuration of a two-phase trial with binary-outcome experiments. We then generalize to multi-phase trials with binary-outcome experiments where the determined experiments can be placed at arbitrary nodes in the trial tree. Here we present a dynamic programming algorithm to derive the optimal signaling policy that uses the two-phase trial solution’s structural insights. We also contrast the optimal signaling policy structure with classical Bayesian persuasion strategies to highlight the impact of the signaling constraints on the sender. 

Information flow measures, over the duration of a game, the audience’s belief of who will win, and thus can reflect the amount of surprise in a game. To quantify the relationship between information flow and audiences' perceived quality, we conduct a case study where subjects watch one of the world’s biggest esports events, LOL S10. In addition to eliciting information flow, we also ask subjects to report their rating for each game. We find that the amount of surprise in the end of the game plays a dominant role in predicting the rating. This suggests the importance of incorporating when the surprise occurs, in addition to the amount of surprise, in perceived quality models. For content providers, it implies that everything else being equal, it is better for twists to be more likely to happen toward the end of a show rather than uniformly throughout. 

Prediction markets are powerful tools to elicit and aggregate beliefs from strategic agents. However, in current prediction markets, agents may exhaust the social welfare by competing to be the first to update the market. We initiate the study of the trade-off between how quickly information is aggregated by the market, and how much this information costs. We design markets to aggregate timely information from strategic agents to maximize social welfare. To this end, the market must incentivize agents to invest the correct amount of effort to acquire information: quickly enough to be useful, but not faster (and more expensively) than necessary. The market also must ensure that agents report their information truthfully and on time. We consider two settings: in the first, information is only valuable before a deadline; in the second, the value of information decreases as time passes. We use both theorems and simulations to demonstrate the mechanisms. 

We initiate the study of information elicitation mechanisms for a crowd containing both self-interested agents, who respond to incentives, and adversarial agents, who may collude to disrupt the system. Our mechanisms work in the peer prediction setting where ground truth need not be accessible to the mechanism or even exist. We provide a meta-mechanism that reduces the design of peer prediction mechanisms to a related robust learning problem. The resulting mechanisms are ϵ-informed truthful, which means truth-telling is the highest paid ϵ-Bayesian Nash equilibrium (up to ϵ-error) and pays strictly more than uninformative equilibria. The value of ϵ depends on the properties of robust learning algorithm, and typically limits to 0 as the number of tasks and agents increase. We show how to use our meta-mechanism to design mechanisms with provable guarantees in two important crowdsourcing settings even when some agents are self-interested and others are adversarial. 

Peer prediction mechanisms incentivize agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with those of their peers. In the detail-free multi-task setting, agents are asked to respond to multiple independent and identically distributed tasks, and the mechanism does not know the prior distribution of agents’ signals. The goal is to provide an epsilon-strongly truthful mechanism where truth-telling rewards agents “strictly” more than any other strategy profile (with epsilon additive error) even for heterogeneous agents, and to do so while requiring as few tasks as possible. We design a family of mechanisms with a scoring function that maps a pair of reports to a score. The mechanism is strongly truthful if the scoring function is “prior ideal”. Moreover, the mechanism is epsilon-strongly truthful as long as the scoring function used is sufficiently close to the ideal scoring function. This reduces the above mechanism design problem to a learning problem – specifically learning an ideal scoring function. Because learning the prior distribution is sufficient (but not necessary) to learn the scoring function, we can apply standard learning theory techniques that leverage side information about the prior (e.g., that it is close to some parametric model). Furthermore, we derive a variational representation of an ideal scoring function and reduce the learning problem into an empirical risk minimization. We leverage this reduction to obtain very general results for peer prediction in the multi-task setting. Specifically, Sample Complexity. We show how to derive good bounds on the number of tasks required for different types of priors–in some cases exponentially improving previous results. In particular, we can upper bound the required number of tasks for parametric models with bounded learning complexity. Furthermore, our reduction applies to myriad continuous signal space settings. To the best of our knowledge, this is the first peer-prediction mechanism on continuous signals designed for the multi-task setting. Connection to Machine Learning. We show how to turn a soft-predictor of an agent’s signals (given the other agents’ signals) into a mechanism. This allows the practical use of machine learning algorithms that give good results even when many agents provide noisy information. Stronger Properties. In the finite setting, we obtain -strongly truthful mechanisms for any stochastically relevant prior. Prior works either only apply to more restrictive settings, or achieve a weaker notion of truthfulness (informed truthfulness). 

We consider two-alternative elections where voters' preferences depend on a state variable that is not directly observable. Each voter receives a private signal that is correlated to the state variable. As a special case, our model captures the common scenario where voters can be categorized into three types: those who always prefer one alternative, those who always prefer the other, and those contingent voters whose preferences depends on the state. In this setting, even if every voter is a contingent voter, agents voting according to their private information need not result in the adoption of the universally preferred alternative, because the signals can be systematically biased.We present a mechanism that elicits and aggregates the private signals from the voters, and outputs the alternative that is favored by the majority. In particular, voters truthfully reporting their signals forms a strong Bayes Nash equilibrium (where no coalition of voters can deviate and receive a better outcome).