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1. Two Strongly Truthful Mechanisms for Three Heterogeneous Agents Answering One Question

   https://doi.org/10.1145/3565560  

   Schoenebeck, Grant; Yu, Fang-Yi (December 2022, ACM Transactions on Economics and Computation)

   Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents’ reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting. Our Differential Peer Prediction mechanisms are strongly truthful: Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for asymmetric priors among agents, which the mechanisms need not know (detail-free) in the single question setting. Moreover, they only require three agents, each of which submits a single item report: two report their signals (answers), and the other reports her forecast (prediction of one of the other agent’s reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule’s special properties. Moreover, we can recast the Bayesian Truth Serum mechanism into our framework. We can also extend our results to the setting of continuous signals with a slightly weaker guarantee on the optimality of the truthful equilibrium. 

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2. Learning and Strongly Truthful Multi-Task Peer Prediction: A Variational Approach

   Schoenebeck, Grant; Yu, Fang-Yi (January 2021, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021))

   null (Ed.)

   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). 

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3. Information Elicitation from Rowdy Crowds

   https://doi.org/10.1145/3442381.3449840  

   Schoenebeck, Grant; Yu, Fang-Yi; Zhang, Yichi (April 2021, Proceedings of the Web Conference (WWW '21))

   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. 

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4. A Truthful Cardinal Mechanism for One-Sided Matching

   https://doi.org/10.1137/1.9781611975994.129  

   Abebe, Rediet; Cole, Richard; Gkatzelis, Vasilis; Hartline, Jason D. (January 2020, ACM-SIAM Symposium on Discrete Algorithms)

   We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of n agents needs to be matched to a set of n heterogeneous items. Each agent i has a value vij for each item j, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the ordinal preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full cardinal preferences of the agents, i.e., all of the vij values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest. 

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5. Incentive-Compatible Kidney Exchange in a Slightly Semi-Random Model

   https://doi.org/10.1145/3465456.3467622  

   Blum, Avrim; Gölz, Paul (January 2021, ACM Conference on Economics and Computation)

   null (Ed.)

   Motivated by kidney exchange, we study the following mechanism-design problem: On a directed graph (of transplant compatibilities among patient--donor pairs), the mechanism must select a simple path (a chain of transplantations) starting at a distinguished vertex (an altruistic donor) such that the total length of this path is as large as possible (a maximum number of patients receive a kidney). However, the mechanism does not have direct access to the graph. Instead, the vertices are partitioned over multiple players (hospitals), and each player reports a subset of her vertices to the mechanism. In particular, a player may strategically omit vertices to increase how many of her vertices lie on the path returned by the mechanism. Our objective is to find mechanisms that limit incentives for such manipulation while producing long paths. Unfortunately, in worst-case instances, competing with the overall longest path is impossible while incentivizing (approximate) truthfulness, i.e., requiring that hiding nodes cannot increase a player's utility by more than a factor of 1 + o(1). We therefore adopt a semi-random model where o(n) random edges are added to worst-case instances. While it remains impossible for truthful mechanisms to compete with the overall longest path, we give a truthful mechanism that competes with a weaker but non-trivial benchmark: the length of any path whose subpaths within each player have a minimum average length. In fact, our mechanism satisfies even a stronger notion of truthfulness, which we call matching-time incentive compatibility. This notion of truthfulness requires that each player not only reports her nodes truthfully but also does not stop the returned path at any of her nodes in order to divert it to a continuation inside her own subgraph. 

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