Forecast aggregation aims to combine information from multiple Bayesian experts' forecasts into an aggregate forecast. In much of this literature, however, the aggregate forecast is optimized for a particular loss or robustness criterion and need not itself be calibrated with respect to the outcome. We introduce and study expert aggregation, where the goal is instead to aggregate Bayesian experts into a new expert that continues to provide calibrated forecasts. In particular, we consider a setting where each input expert reports calibrated predictions, and the aggregator observes the prior distribution over states, and the input experts, but not the underlying Bayes probabilities of the states. We ask whether one can (i) construct a calibrated output expert that Blackwell refines a target expert and cannot be further Blackwell improved using the available information; and (ii) when a proper loss is specified, compute a nearly loss-optimal expert among all such refinements. We formulate calibrated experts as reduced-form information structures and measure refinement by Blackwell dominance of the induced prediction distributions. We characterize the constructible output experts through observable linear information: the input experts generate a linear system whose row space determines which calibrated output predictions are identifiable, and a new expert is constructible exactly when its predictions lie in the associated observable nonnegative cone. We establish a sharp algorithmic picture. When randomized output experts are allowed, both questions above admit efficient algorithms. In contrast, deterministic output experts are computationally intractable: deciding whether a deterministic calibrated refinement exists is 𝖭𝖯-hard, and deterministic proper-loss optimization admits no multiplicative PTAS unless 𝖯=𝖭𝖯.

We study mechanism design when agents may have hidden secondary goals which will manifest as non-trivial preferences among outcomes for which their primary utility is the same. We show that in such cases, a mechanism is robust against strategic manipulation if and only if it is not only incentive-compatible, but also nonbossy -- a well-studied property in the context of matching and allocation mechanisms. We give complete characterizations of incentive-compatible and nonbossy mechanisms in various settings, including auctions with single-parameter agents and public decision settings where all agents share a common outcome. In particular, we show that in the single-item setting, a mechanism is incentive-compatible, individually rational, and nonbossy if and only if it is a sequential posted-price mechanism. In contrast, we show that in more general single-parameter environments, there exist mechanisms satisfying our characterization that significantly outperform sequential posted-price mechanisms in terms of revenue or efficiency (sometimes by an exponential factor).

We study the limits of third-degree price discrimination when the production cost is Bayesian and private to the seller, generalizing the seminal work of Bergemann, Brooks and Morris (2015). The rough setup is the following: A monopoly seller sets different prices for buyers in different "segments" of the market so as to maximize seller surplus. Different ways in which the aggregate market is decomposed into segments lead to different welfare outcomes, i.e., (seller surplus, buyer surplus) pairs. When the production cost is Bayesian, the region of achievable welfare outcomes can exhibit complex shapes beyond the clean characterization by Bergemann, Brooks and Morris for the case with a fixed cost. We show that with a Bayesian cost, this region coincides with a proper projection of a polytope defined by a polynomial number of linear constraints, the essential ones of which correspond to flow conservation in a "discounted" flow network. As a result, we give a polynomial-time algorithm that computes optimal market segmentations in terms of any linear combination of the seller surplus and the buyer surplus. En route, we establish the following structural property: Any market can be written as a convex combination of "extremal markets" in a way preserving the seller surplus and the buyer surplus. These extremal markets are piecewise equal-surplus with respect to different possible costs, generalizing a similar notion introduced by Bergemann, Brooks and Morris when the cost is fixed.

Automated bidding to optimize online advertising with various constraints, e.g. ROI constraints and budget constraints, is widely adopted by advertisers. A key challenge lies in designing algorithms for non-truthful mechanisms with ROI constraints. While prior work has addressed truthful auctions or non-truthful auctions with weaker benchmarks, this paper provides a significant improvement: We develop online bidding algorithms for repeated first-price auctions with ROI constraints, benchmarking against the optimal randomized strategy in hindsight. In the full feedback setting, where the maximum competing bid is observed, our algorithm achieves a near-optimal $\tilde O(\sqrt{T})$ regret bound, and in the bandit feedback setting (where the bidder only observes whether the bidder wins each auction), our algorithm attains $\tilde O(T^{3/4})$ regret bound.

The recent increasing adoption of autobidding has inspired the growing interest in analyzing the performance of classic mechanism with value-maximizing autobidders both theoretically and empirically. It is known that optimal welfare can be obtained in first-price auctions if autobidders are restricted to uniform bid-scaling and the price of anarchy is $2$ when non-uniform bid-scaling strategies are allowed. In this paper, we provide a fine-grained price of anarchy analysis for non-uniform bid-scaling strategies in first-price auctions, demonstrating the reason why more powerful (individual) non-uniform bid-scaling strategies may lead to worse (aggregated) performance in social welfare. Our theoretical results match recent empirical findings that a higher level of non-uniform bid-scaling leads to lower welfare performance in first-price auctions.

Quantitative Relative Judgment Aggregation (QRJA) is a new research topic in (computational) social choice. In the QRJA model, agents provide judgments on the relative quality of different candidates, and the goal is to aggregate these judgments across all agents. In this work, our main conceptual contribution is to explore the interplay between QRJA in a social choice context and its application to ranking prediction. We observe that in QRJA, judges do not have to be people with subjective opinions; for example, a race can be viewed as a "judgment" on the contestants' relative abilities. This allows us to aggregate results from multiple races to evaluate the contestants' true qualities. At a technical level, we introduce new aggregation rules for QRJA and study their structural and computational properties. We evaluate the proposed methods on data from various real races and show that QRJA-based methods offer effective and interpretable ranking predictions.

In this survey, we summarize recent developments in research fueled by the growing adoption of automated bidding strategies in online advertising. We explore the challenges and opportunities that have arisen as markets embrace this autobidding and cover a range of topics in this area, including bidding algorithms, equilibrium analysis and efficiency of common auction formats, and optimal auction design.

We study the price of anarchy of the generalized second-price auction where bidders are value maximizers (i.e., autobidders). We show that in general the price of anarchy can be as bad as $0$. For comparison, the price of anarchy of running VCG is $1/2$ in the autobidding world. We further show a fined-grained price of anarchy with respect to the discount factors (i.e., the ratios of click probabilities between lower slots and the highest slot in each auction) in the generalized second-price auction, which highlights the qualitative relation between the smoothness of the discount factors and the efficiency of the generalized second-price auction.

We study the price of anarchy of the first-price auction in the autobidding world, where bidders can be either utility maximizers (i.e., traditional bidders) or value maximizers (i.e., autobidders). We show that with autobidders only, the price of anarchy of the first-price auction is 1/2, and with both kinds of bidders, the price of anarchy degrades to about 0.457 (the precise number is given by an optimization). These results complement the recent result by Jin and Lu [2022] showing that the price of anarchy of the first-price auction with traditional bidders only is 1 - 1/e^2. We further investigate a setting where the seller can utilize machine-learned advice to improve the efficiency of the auctions. There, we show that as the accuracy of the advice increases, the price of anarchy improves smoothly from about 0.457 to 1.

We study Bayesian persuasion under approximate best response, where the receiver may choose any action that is not too much suboptimal given their posterior belief upon receiving the signal. We focus on the computational aspects of the problem, aiming to design algorithms that efficiently compute (almost) optimal strategies for the sender. Despite the absence of the revelation principle -- which has been one of the most powerful tools in Bayesian persuasion -- we design polynomial-time exact algorithms for the problem when either the state space or the action space is small, as well as a quasi-polynomial-time approximation scheme (QPTAS) for the general problem. On the negative side, we show there is no polynomial-time exact algorithm for the general problem unless $\mathsf{P} = \mathsf{NP}$. Our results build on several new algorithmic ideas, which might be useful in other principal-agent problems where robustness is desired.

We study the problem of online binary classification in settings where strategic agents can modify their observable features to receive a positive classification. We model the set of feasible manipulations by a directed graph over the feature space, and assume the learner only observes the manipulated features instead of the original ones. We introduce the Strategic Littlestone Dimension, a new combinatorial measure that captures the joint complexity of the hypothesis class and the manipulation graph. We demonstrate that it characterizes the instance-optimal mistake bounds for deterministic learning algorithms in the realizable setting. We also achieve improved regret in the agnostic setting by a refined agnostic-to-realizable reduction that accounts for the additional challenge of not observing agents' original features. Finally, we relax the assumption that the learner knows the manipulation graph, instead assuming their knowledge is captured by a family of graphs. We derive regret bounds in both the realizable setting where all agents manipulate according to the same graph within the graph family, and the agnostic setting where the manipulation graphs are chosen adversarially and not consistently modeled by a single graph in the family.

Bilateral trade is one of the most natural and important forms of economic interaction: A seller has a single, indivisible item for sale, and a buyer is potentially interested. The two parties typically have different, privately known valuations for the item, and ideally, they would like to trade if the buyer values the item more than the seller. The celebrated impossibility result by Myerson and Satterthwaite shows that any mechanism for this setting must violate at least one important desideratum. In this paper, we investigate a richer paradigm of bilateral trade, with many self-interested buyers and sellers on both sides of a single trade who cannot be excluded from the trade. We show that this allows for more positive results. In fact, we establish a dichotomy in the possibility of trading efficiently. If in expectation, the buyers value the item more, we can achieve efficiency in the limit. If this is not the case, then efficiency cannot be achieved in general. En route, we characterize trading mechanisms that encourage truth-telling, which may be of independent interest. We also evaluate our trading mechanisms experimentally, and the experiments align with our theoretical results.

The design of internet advertisement systems is both an auction design problem and an information retrieval (IR) problem. As an auction, the designer needs to take the participants incentives into account. As an information retrieval problem, it needs to identify the ad that it is the most relevant to a user out of an enormous set of ad candidates. Those aspects are combined by first having an IR system narrow down the initial set of ad candidates to a manageable size followed by an auction that ranks and prices those candidates. If the IR system uses information about bids, agents could in principle manipulate the system by manipulating the IR stage even when the subsequent auction is truthful. In this paper we investigate the design of truthful IR mechanisms, which we term eligibility mechanisms. We model it as a truthful version of the stochastic probing problem. We show that there is a constant gap between the truthful and non-truthful versions of the stochastic probing problem and exhibit a constant approximation algorithm. En route, we also characterize the set of eligibility mechanisms, which provides necessary and sufficient conditions for an IR system to be truthful.

We study autobidding ad auctions with user costs, where each bidder is value-maximizing subject to a return-over-investment (ROI) constraint, and the seller aims to maximize the social welfare taking into consideration the user's cost of viewing an ad. We show that in the worst case, the approximation ratio of social welfare by running the vanilla VCG auctions with user costs could as bad as 0. To improve the performance of VCG, We propose a new variant of VCG based on properly chosen cost multipliers, and prove that there exist auction-dependent and bidder-dependent cost multipliers that guarantee approximation ratios of 1/2 and 1/4 respectively in terms of the social welfare.

We study equilibrium computation with extensive-form correlation in two-player turn-taking stochastic games. Our main results are two-fold: (1) We give an algorithm for computing a Stackelberg extensive-form correlated equilibrium (SEFCE), which runs in time polynomial in the size of the game, as well as the number of bits required to encode each input number. (2) We give an efficient algorithm for approximately computing an optimal extensive-form correlated equilibrium (EFCE) up to machine precision, i.e., the algorithm achieves approximation error ε in time polynomial in the size of the game, as well as log(1 / ε). Our algorithm for SEFCE is the first polynomial-time algorithm for equilibrium computation with commitment in such a general class of stochastic games. Existing algorithms for SEFCE typically make stronger assumptions such as no chance moves, and are designed for extensive-form games in the less succinct tree form. Our algorithm for approximately optimal EFCE is, to our knowledge, the first algorithm that achieves 3 desiderata simultaneously: approximate optimality, polylogarithmic dependency on the approximation error, and compatibility with stochastic games in the more succinct graph form. Existing algorithms achieve at most 2 of these desiderata, often also relying on additional technical assumptions.

Many scientific conferences employ a two-phase paper review process, where some papers are assigned additional reviewers after the initial reviews are submitted. Many conferences also design and run experiments on their paper review process, where some papers are assigned reviewers who provide reviews under an experimental condition. In this paper, we consider the question: how should reviewers be divided between phases or conditions in order to maximize total assignment similarity? We make several contributions towards answering this question. First, we prove that when the set of papers requiring additional review is unknown, a simplified variant of this problem is NP-hard. Second, we empirically show that across several datasets pertaining to real conference data, dividing reviewers between phases/conditions uniformly at random allows an assignment that is nearly as good as the oracle optimal assignment. This uniformly random choice is practical for both the two-phase and conference experiment design settings. Third, we provide explanations of this phenomenon by providing theoretical bounds on the suboptimality of this random strategy under certain natural conditions. From these easily-interpretable conditions, we provide actionable insights to conference program chairs about whether a random reviewer split is suitable for their conference.

We pose and study the problem of planning in Markov decision processes (MDPs), subject to participation constraints as studied in mechanism design. In this problem, a planner must work with a self-interested agent on a given MDP. Each action in the MDP provides an immediate reward to the planner and a (possibly different) reward to the agent. The agent has no control in choosing the actions, but has the option to end the entire process at any time. The goal of the planner is to find a policy that maximizes her cumulative reward, taking into consideration the agent's ability to terminate. We give a fully polynomial-time approximation scheme for this problem. En route, we present polynomial-time algorithms for computing (exact) optimal policies for important special cases of this problem, including when the time horizon is constant, or when the MDP exhibits a "definitive decisions" property. We illustrate our algorithms with two different game-theoretic applications: the problem of assigning rides in ride-sharing and the problem of designing screening policies. Our results imply efficient algorithms for computing (approximately) optimal policies in both applications.

We study the problem of learning influence adoption in networks. In this problem, a communicable entity (such as an infectious disease, a computer virus, or a social media meme) propagates through a network, and the goal is to learn the state of each individual node by sampling only a small number of nodes and observing/testing their states. We study this problem in heterogeneous networks, in which each individual node has a set of distinct features that determine how it is affected by the propagating entity. We give an efficient algorithm with nearly optimal sample complexity for two variants of this learning problem, corresponding to symptomatic and asymptomatic spread. In each case, the optimal sample complexity naturally generalizes the complexity of learning how nodes are affected in isolation, and the complexity of learning influence adoption in a homogeneous network.

We consider the problem of planning with participation constraints introduced in[24]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the agent. However, the agent can and will choose to end the process whenever his expected onward utility becomes negative. The principal seeks to compute and commit to a policy that maximizes her expected utility, under the constraint that the agent should always want to continue participating. We provide the first polynomial-time exact algorithm for this problem for finite-horizon settings, where previously only an additive ε-approximation algorithm was known. Our approach can also be extended to the (discounted) infinite-horizon case, for which we give an algorithm that runs in time polynomial in the size of the input and log(1/ε), and returns a policy that is optimal up to an additive error of ε.