In the setting of conference peer review, the conference aims to accept high-quality papers and reject low-quality papers based on noisy review scores. A recent work proposes the isotonic mechanism, which can elicit the ranking of paper qualities from an author with multiple submissions to help improve the conference's decisions. However, the isotonic mechanism relies on the assumption that the author's utility is both an increasing and a convex function with respect to the review score, which is often violated in realistic settings (e.g.~when authors aim to maximize the number of accepted papers). In this paper, we propose a sequential review mechanism that can truthfully elicit the ranking information from authors while only assuming the agent's utility is increasing with respect to the true quality of her accepted papers. The key idea is to review the papers of an author in a sequence based on the provided ranking and conditioning the review of the next paper on the review scores of the previous papers. Advantages of the sequential review mechanism include: 1) eliciting truthful ranking information in a more realistic setting than prior work; 2) reducing the reviewing workload and increasing the average quality of papers being reviewed; 3) incentivizing authors to write fewer papers of higher quality.
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We investigate two notions of correlated equilibrium for extensive-form games: the extensive-form correlated equilibrium (EFCE) and the behavioral correlated equilibrium (BCE). We show that the two are outcome-equivalent, in the sense that every outcome distribution achievable under one notion is achievable under the other. Our result implies, to our knowledge, the first polynomial-time algorithm for computing a BCE.
Greedy-Based Online Fair Allocation with Adversarial Input: Enabling Best-of-Many-Worlds Guarantees
PDF ↗We study an online allocation problem with sequentially arriving items and adversarially chosen agent values, with the goal of balancing fairness and efficiency. Our goal is to study the performance of algorithms that achieve strong guarantees under other input models such as stochastic inputs, in order to achieve robust guarantees against a variety of inputs. To that end, we study the PACE (Pacing According to Current Estimated utility) algorithm, an existing algorithm designed for stochastic input. We show that in the equal-budgets case, PACE is equivalent to an integral greedy algorithm. We go on to show that with natural restrictions on the adversarial input model, both the greedy allocation and PACE have asymptotically bounded multiplicative envy as well as competitive ratio for Nash welfare, with the multiplicative factors either constant or with optimal order dependence on the number of agents. This completes a "best-of-many-worlds" guarantee for PACE, since past work showed that PACE achieves guarantees for stationary and stochastic-but-non-stationary input models.
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.
Coalitions naturally exist in many real-world systems involving multiple decision makers such as ridesharing, security, and online ad auctions, but the coalition structure among the agents is often unknown. We propose and study an important yet previously overseen problem -- Coalition Structure Learning (CSL), where we aim to carefully design a series of games for the agents and infer the underlying coalition structure by observing their interactions in those games. We establish a lower bound on the sample complexity -- defined as the number of games needed to learn the structure -- of any algorithms for CSL and propose the Iterative Grouping (IG) algorithm for designing normal-form games to achieve the lower bound. We show that IG can be extended to other succinct games such as congestion games and graphical games. Moreover, we solve CSL in a more restrictive and practical setting: auctions. We show a variant of IG to solve CSL in the auction setting even if we cannot design the bidder valuations. Finally, we conduct experiments to evaluate IG in the auction setting and the results align with our theoretical analysis.
Online advertising has been one of the most important sources for industry's growth, where the demand-side platforms (DSP) play an important role via bidding to the ad exchanges on behalf of their advertiser clients. Since more and more ad exchanges have shifted from second to first price auctions, it is challenging for DSPs to adjust bidding strategy in the volatile environment. Recent studies on bid shading in first-price auctions may have limited performance due to relatively strong hypotheses about winning probability distribution. Moreover, these studies do not consider the incentive of advertiser clients, which can be crucial for a reliable advertising platform. In this work, we consider both the optimization of bid shading technique and the design of internal auction which is ex-post incentive compatible (IC) for the management of a DSP. Firstly, we prove that the joint design of bid shading and ex-post IC auction can be reduced to choosing one monotone bid function for each advertiser without loss of optimality. Then we propose a parameterized neural network to implement the monotone bid functions. With well-designed surrogate loss, the objective can be optimized in an end-to-end manner. Finally, our experimental results demonstrate the effectiveness and superiority of our algorithm.
Game theory and machine learning are two widely used techniques for predicting the outcomes of strategic interactions among humans. However, the game theory-based approach often relies on strong rationality and informational assumptions, while the machine learning-based approach typically requires the testing data to come from the same distribution as the training data. Our work studies how to integrate the two techniques to address these weaknesses. We focus on the interactions among real bidders in penny auctions, and develop a three-stage framework to predict the distributions of auction durations, which indicate the numbers of bids and auctioneer revenues. Specifically, we first leverage a pre-trained neural network to encode the descriptions of products in auctions into embeddings. Second, we apply game theory models to make preliminary predictions of auction durations. In particular, we tackle the challenge of accurately inferring parameters in game theory models. Third, we develop a Multi-Branch Mixture Density Network to learn the mapping from product embeddings and game-theoretic predictions to the distributions of actual auction durations. Experiments on real-world penny auction data demonstrate that our framework outperforms both game theory-based and machine learning-based prediction approaches.
We consider binary group decision-making under a rich model of liquid democracy: agents submit ranked delegation options, where each option may be a function of multiple agents' votes; e.g., "I vote yes if a majority of my friends vote yes." Such ballots are unravelled into a profile of direct votes by selecting one entry from each ballot so as not to introduce cyclic dependencies. We study delegation via monotonic Boolean functions, and two unravelling procedures: MinSum, which minimises the sum of the ranks of the chosen entries, and its egalitarian counterpart, MinMax. We provide complete computational dichotomies: MinSum is hard to compute (and approximate) as soon as any non-trivial functions are permitted, and polynomial otherwise; for MinMax the easiness results extend to arbitrary-arity logical ORs and ANDs taken in isolation, but not beyond. For the classic model of delegating to individual agents, we give asymptotically near-tight algorithms for carrying out the two procedures and efficient algorithms for finding optimal unravellings with the highest vote count for a given alternative. These algorithms inspire novel tie-breaking rules for the setup of voting to change a status quo. We then introduce a new axiom, which can be viewed as a variant of the participation axiom, and use algorithmic techniques developed earlier in the paper to show that it is satisfied by MinSum and a lexicographic refinement of MinMax (but not MinMax itself).
Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.
We here address the problem of fairly allocating indivisible goods or chores to n agents with weights that define their entitlement to the set of indivisible resources. Stemming from well-studied fairness concepts such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) for agents with equal entitlements, we present, in this study, the first set of impossibility results alongside algorithmic guarantees for fairness among agents with unequal entitlements. Within this paper, we expand the concept of envy-freeness up to any good or chore to the weighted context (WEFX and XWEF respectively), demonstrating that these allocations are not guaranteed to exist for two or three agents. Despite these negative results, we develop a WEFX procedure for two agents with integer weights, and furthermore, we devise an approximate WEFX procedure for two agents with normalized weights. We further present a polynomial-time algorithm that guarantees a weighted envy-free allocation up to one chore (1WEF) for any number of agents with additive cost functions. Our work underscores the heightened complexity of the weighted fair division problem when compared to its unweighted counterpart.
We study the design of iterative combinatorial auctions (ICAs). The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, several papers have recently proposed machine learning (ML)-based preference elicitation algorithms that aim to elicit only the most important information from bidders. However, from a practical point of view, the main shortcoming of this prior work is that those designs elicit bidders' preferences via value queries (i.e., “What is your value for the bundle {A, B}?''). In most real-world ICA domains, value queries are considered impractical, since they impose an unrealistically high cognitive burden on bidders, which is why they are not used in practice. In this paper, we address this shortcoming by designing an ML-powered combinatorial clock auction that elicits information from the bidders only via demand queries (i.e., “At prices p, what is your most preferred bundle of items?''). We make two key technical contributions: First, we present a novel method for training an ML model on demand queries. Second, based on those trained ML models, we introduce an efficient method for determining the demand query with the highest clearing potential, for which we also provide a theoretical foundation. We experimentally evaluate our ML-based demand query mechanism in several spectrum auction domains and compare it against the most established real-world ICA: the combinatorial clock auction (CCA). Our mechanism significantly outperforms the CCA in terms of efficiency in all domains, it achieves higher efficiency in a significantly reduced number of rounds, and, using linear prices, it exhibits vastly higher clearing potential. Thus, with this paper we bridge the gap between research and practice and propose the first practical ML-powered ICA.
Peer prediction incentive mechanisms for crowdsourcing are generally limited to eliciting samples from categorical distributions. Prior work on extending peer prediction to arbitrary distributions has largely relied on assumptions on the structures of the distributions or known properties of the data providers. We introduce a novel class of incentive mechanisms that extend peer prediction mechanisms to arbitrary distributions by replacing the notion of an exact match with a concept of neighborhood matching. We present conditions on the belief updates of the data providers that guarantee incentive-compatibility for rational data providers, and admit a broad class of possible reasonable updates.
We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network congestion games where individual drivers adhere to personal budget and fuel limitations. Despite the plethora of algorithms that efficiently compute Nash equilibria (NE) in potential games, the domain of constrained potential games remains largely unexplored. We introduce an algorithm that leverages the Lagrangian formulation of NE. The algorithm is implemented independently by each player and runs in polynomial time with respect to the approximation error, the sum of the size of the action-spaces, and the game's inherit parameters.
We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be extended to the case where agents have matroid-rank (i.e., binary submodular) valuations. We propose two families of envy-based notions for matroid-rank and general submodular valuations, one based on the idea of transferability and the other on marginal values. We show that our notions can be satisfied via generalizations of rules such as picking sequences and maximum weighted Nash welfare. In addition, we introduce welfare measures based on harmonic numbers, and show that variants of maximum weighted harmonic welfare offer stronger fairness guarantees than maximum weighted Nash welfare under matroid-rank valuations.
Mobile gaming is a rapidly growing and incredibly profitable sector; having grown seven-fold over the past 10 years, it now grosses over $100 billion annually. This growth was due in large part to a shift in monetization strategies: rather than charging players an upfront cost ("pay-to-play"), games often request optional microtransactions throughout gameplay ("free-to-play"). We focus on a common scenario in which games include wait times---gating either items or game progression---that players can pay to skip. Game designers typically say that they optimize for player happiness rather than revenue; however, prices for skips are typically set at levels that few players are willing to pay, leading to low purchase rates. Under a traditional analysis, it would seem that game designers fail at their stated goal if few players buy what they are selling. We argue that an alternate model can better explain this dynamic: players value tasks more highly as they are perceived to be more difficult. While skips can increase players' utilities by providing instant gratification, pricing skips too cheaply can lower players' utilities by decreasing the perceived amount of work needed to complete a task. We show that high revenue, high player utility, and low purchase rates can all coexist under this model, particularly under a realistic distribution of players having few buyers but a few big-spending "whales." We also investigate how a game designer should optimize prices under our model. An appendix of the paper with proofs, more comprehensive results and visualizations can be found at https://arxiv.org/abs/2312.10205.
Mechanism design on social networks has attracted extensive attention recently. The goal is to design mechanisms to incentivize participants to invite more participants via their social networks, and the challenge is that the participants are competitors. Various mechanisms have been proposed for single-/multiple-unit auctions, but it has been shown that it is challenging to design such mechanisms for more complex settings. We move this forward to investigate a double auction on a network where each trader (a buyer or a seller) can link to other buyers and sellers. Incentiving invitation is more difficult than in multi-unit one-sided auctions, because there are two different roles and a buyer (seller) seems happy to invite a seller (buyer), but again the invited seller (buyer) may invite another buyer (seller) to compete with the original buyer (seller). To combat this, we propose a solution called dynamic trade reduction (DTR), which also guarantees a non-negative revenue for the market owner. Interestingly, our solution is also applicable to the multi-unit one-sided auction when there is only one seller linking to only buyers on the network. We believe that the principle of our solution has the potential to be extended to design the multi-item one-sided auction.
Games with incomplete information are games that model situations where players do not have common knowledge about the game they play, e.g. card games such as poker or bridge. Opponent models can be of crucial importance for decision-making in such games. We propose algorithms for computing optimal and/or robust strategies in games with incomplete information, given various types of knowledge about opponent models. As an application, we describe a framework for reasoning about an opponent's reasoning in such games, where opponent models arise naturally.
We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.
We study the fair division of indivisible items with subsidies among n agents, where the absolute marginal valuation of each item is at most one. Under monotone valuations (where each item is a good), it is known that a maximum subsidy of 2(n-1) and a total subsidy of 2(n-1)² are sufficient to guarantee the existence of an envy-freeable allocation. In this paper, we improve upon these bounds, even in a wider model. Namely, we show that, given an EF1 allocation, we can compute in polynomial time an envy-free allocation with a subsidy of at most n-1 per agent and a total subsidy of at most n(n-1)/2. Moreover, we present further improved bounds for monotone valuations.
We introduce a novel definition for a small set R of k points being "representative" of a larger set in a metric space. Given a set V (e.g., documents or voters) to represent, and a set C of possible representatives, our criterion requires that for any subset S comprising a theta fraction of V, the average distance of S to their best theta*k points in R should not be more than a factor gamma compared to their average distance to the best theta*k points among all of C. This definition is a strengthening of proportional fairness and core fairness, but - different from those notions - requires that large cohesive clusters be represented proportionally to their size. Since there are instances for which - unless gamma is polynomially large - no solutions exist, we study this notion in a resource augmentation framework, implicitly stating the constraints for a set R of size k as though its size were only k/alpha, for alpha > 1. Furthermore, motivated by the application to elections, we mostly focus on the "ordinal" model, where the algorithm does not learn the actual distances; instead, it learns only for each point v in V and each candidate pairs c, c' which of c, c' is closer to v. Our main result is that the Expanding Approvals Rule (EAR) of Aziz and Lee is (alpha, gamma) representative with gamma