OpenRaiser/Intern-Atlas huggingface dataset:
Randomized Learning-Augmented Auctions with Revenue Guarantees
Venue: Conference IJCAI 2024
Year: 2024

We consider the fundamental problem of designing a truthful single-item auction with the challenging objective of extracting a large fraction of the highest agent valuation as revenue. Following a recent trend in algorithm design, we assume that the agent valuations belong to a known interval, and a (possibly erroneous) prediction for the highest valuation is available. Then, auction design aims for high consistency and robustness, meaning that, for appropriate pairs of values $γ$ and $ρ$, the extracted revenue should be at least a $γ$- or $ρ$-fraction of the highest valuation when the prediction is correct for the input instance or not. We characterize all pairs of parameters $γ$ and $ρ$ so that a randomized $γ$-consistent and $ρ$-robust auction exists. Furthermore, for the setting in which robustness can be a function of the prediction error, we give sufficient and necessary conditions for the existence of robust auctions and present randomized auctions that extract a revenue that is only a polylogarithmic (in terms of the prediction error) factor away from the highest agent valuation.
Layered Graph Security Games
Venue: Conference IJCAI 2024
Year: 2024

Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given graph). In this paper, we represent each player's strategy space using a layered graph whose paths represent an exponentially large strategy space. Our formulation entails not only classic pursuit-evasion games, but also other security games, such as those modeling anti-terrorism and logistical interdiction. We study two-player zero-sum games under two distinct utility models: linear and binary utilities. We show that under linear utilities, Nash equilibrium can be computed in polynomial time, while binary utilities may lead to situations where even computing a best-response is computationally intractable. To this end, we propose a practical algorithm based on incremental strategy generation and mixed integer linear programs. We show through extensive experiments that our algorithm efficiently computes $ε$-equilibrium for many games of interest. We find that target values and graph structure often have a larger influence on running times as compared to the size of the graph per se.
Parameterized Analysis of Bribery in Challenge the Champ Tournaments
Venue: Conference IJCAI 2024
Year: 2024

Challenge the champ tournaments are one of the simplest forms of competition, where a (initially selected) champ is repeatedly challenged by other players. If a player beats the champ, then that player is considered the new (current) champ. Each player in the competition challenges the current champ once in a fixed order. The champ of the last round is considered the winner of the tournament. We investigate a setting where players can be bribed to lower their winning probability against the initial champ. The goal is to maximize the probability of the initial champ winning the tournament by bribing the other players, while not exceeding a given budget for the bribes. Mattei et al. [Journal of Applied Logic, 2015] showed that the problem can be solved in pseudo-polynomial time, and that it is in XP when parameterized by the number of players. We show that the problem is weakly NP-hard and W[1]-hard when parameterized by the number of players. On the algorithmic side, we show that the problem is fixed-parameter tractable when parameterized either by the number of different bribe values or the number of different probability values. To this end, we establish several results that are of independent interest. In particular, we show that the product knapsack problem is W[1]-hard when parameterized by the number of items in the knapsack, and that constructive bribery for cup tournaments is W[1]-hard when parameterized by the number of players. Furthermore, we present a novel way of designing mixed integer linear programs, ensuring optimal solutions where all variables are integers.
On the Pursuit of EFX for Chores: Non-existence and Approximations
Venue: Conference IJCAI 2024
Year: 2024

We study the problem of fairly allocating a set of chores to a group of agents. The existence of envy-free up to any item (EFX) allocations is a long-standing open question for both goods and chores. We resolve this question by providing a negative answer for the latter, presenting a simple construction that admits no EFX solutions for allocating six items to three agents equipped with superadditive cost functions, thus proving a separation result between goods and bads. In fact, we uncover a deeper insight, showing that the instance has unbounded approximation ratio. Moreover, we show that deciding whether an EFX allocation exists is NP-complete. On the positive side, we establish the existence of EFX allocations under general monotone cost functions when the number of items is at most $n+2$. We then shift our attention to additive cost functions. We employ a general framework in order to improve the approximation guarantees in the well-studied case of three additive agents, and provide several conditional approximation bounds that leverage ordinal information.
Couples Can Be Tractable: New Algorithms and Hardness Results for the Hospitals/Residents Problem with Couples
Venue: Conference IJCAI 2024
Year: 2024

In this paper, we study the Hospitals / Residents problem with Couples (HRC), where a solution is a stable matching or a report that none exists. We present a novel polynomial-time algorithm that can find a near-feasible stable matching (adjusting the hospitals' capacities by at most 1) in an HRC instance where the couples' preferences are sub-responsive (i.e., if one member switches to a better hospital, then the couple also improves) and sub-complete (i.e., each pair of hospitals that are individually acceptable to both members are jointly acceptable for the couple) by reducing it to an instance of the Stable Fixtures problem. We also present a polynomial-time algorithm for HRC in a sub-responsive, sub-complete instance that is a Dual Market, or where all couples are one of several possible types. We show that our algorithm also implies the polynomial-time solvability of a stable b-matching problem, where the underlying graph is a multigraph with loops. We complement our algorithms with several hardness results. We show that HRC with sub-responsive and sub-complete couples is NP-hard, even with other strong restrictions. We also show that HRC with a Dual Market is NP-hard under several simultaneous restrictions. Finally, we show that the problem of finding a matching with the minimum number of blocking pairs in HRC is not approximable within $m^{1-\varepsilon}$, for any $\varepsilon>0$, where $m$ is the total length of the hospitals' preference lists, unless P=NP, even if each couple applies to only one pair of hospitals. Our polynomial-time solvability results greatly expand the class of known tractable instances of HRC and provide a useful tool for designing better and more efficient mechanisms in the future.
Comparing Ways of Obtaining Candidate Orderings from Approval Ballots
Venue: Conference IJCAI 2024
Year: 2024

To understand and summarize approval preferences and other binary evaluation data, it is useful to order the items on an axis which explains the data. In a political election using approval voting, this could be an ideological left-right axis such that each voter approves adjacent candidates, an analogue of single-peakedness. In a perfect axis, every approval set would be an interval, which is usually not possible, and so we need to choose an axis that gets closest to this ideal. The literature has developed algorithms for optimizing several objective functions (e.g., minimize the number of added approvals needed to get a perfect axis), but provides little help with choosing among different objectives. In this paper, we take a social choice approach and compare 5 different axis selection rules axiomatically, by studying the properties they satisfy. We establish some impossibility theorems, and characterize (within the class of scoring rules) the rule that chooses the axes that maximize the number of votes that form intervals, using the axioms of ballot monotonicity and resistance to cloning. Finally, we study the behavior of the rules on data from French election surveys, on the votes of justices of the US Supreme Court, and on synthetic data.
Selecting the Most Conflicting Pair of Candidates
Venue: Conference IJCAI 2024
Year: 2024

We study committee elections from a perspective of finding the most conflicting candidates, that is, candidates that imply the largest amount of conflict, as per voter preferences. By proposing basic axioms to capture this objective, we show that none of the prominent multiwinner voting rules meet them. Consequently, we design committee voting rules compliant with our desiderata, introducing conflictual voting rules. A subsequent deepened analysis sheds more light on how they operate. Our investigation identifies various aspects of conflict, for which we come up with relevant axioms and quantitative measures, which may be of independent interest. We support our theoretical study with experiments on both real-life and synthetic data.
Individual Rationality in Topological Distance Games Is Surprisingly Hard
Venue: Conference IJCAI 2024
Year: 2024

In the recently introduced topological distance games, strategic agents need to be assigned to a subset of vertices of a topology. In the assignment, the utility of an agent depends on both the agent's inherent utilities for other agents and its distance from them on the topology. We study the computational complexity of finding individually rational outcomes; this notion is widely assumed to be the very minimal stability requirement and requires that the utility of every agent in a solution is non-negative. We perform a comprehensive study of the problem's complexity, and we prove that even in very basic cases, deciding whether an individually rational solution exists is intractable. To reach at least some tractability, one needs to combine multiple restrictions of the input instance, including the number of agents and the topology and the influence of distant agents on the utility.
Weighted EF1 and PO Allocations with Few Types of Agents or Chores
Venue: Conference IJCAI 2024
Year: 2024

We investigate the existence of fair and efficient allocations of indivisible chores to asymmetric agents who have unequal entitlements or weights. We consider the fairness notion of weighted envy-freeness up to one chore (wEF1) and the efficiency notion of Pareto-optimality (PO). The existence of EF1 and PO allocations of chores to symmetric agents is a major open problem in discrete fair division, and positive results are known only for certain structured instances. In this paper, we study this problem for a more general setting of asymmetric agents and show that an allocation that is wEF1 and PO exists and can be computed in polynomial time for instances with: - Three types of agents, where agents with the same type have identical preferences but can have different weights. - Two types of chores, where the chores can be partitioned into two sets, each containing copies of the same chore. For symmetric agents, our results establish that EF1 and PO allocations exist for three types of agents and also generalize known results for three agents, two types of agents, and two types of chores. Our algorithms use a weighted picking sequence algorithm as a subroutine; we expect this idea and our analysis to be of independent interest.
Getting More by Knowing Less: Bayesian Incentive Compatible Mechanisms for Fair Division
Venue: Conference IJCAI 2024
Year: 2024

We study fair resource allocation with strategic agents. It is well-known that, across multiple fundamental problems in this domain, truthfulness and fairness are incompatible. For example, when allocating indivisible goods, no truthful and deterministic mechanism can guarantee envy-freeness up to one item (EF1), even for two agents with additive valuations. Or, in cake-cutting, no truthful and deterministic mechanism always outputs a proportional allocation, even for two agents with piecewise constant valuations. Our work stems from the observation that, in the context of fair division, truthfulness is used as a synonym for Dominant Strategy Incentive Compatibility (DSIC), requiring that an agent prefers reporting the truth, no matter what other agents report. In this paper, we instead focus on Bayesian Incentive Compatible (BIC) mechanisms, requiring that agents are better off reporting the truth in expectation over other agents' reports. We prove that, when agents know a bit less about each other, a lot more is possible: BIC mechanisms can guarantee fairness notions that are unattainable by DSIC mechanisms in both the fundamental problems of allocation of indivisible goods and cake-cutting. We prove that this is the case even for an arbitrary number of agents, as long as the agents' priors about each others' types satisfy a neutrality condition. Notably, for the case of indivisible goods, we significantly strengthen the state-of-the-art negative result for efficient DSIC mechanisms, while also highlighting the limitations of BIC mechanisms, by showing that a very general class of welfare objectives is incompatible with Bayesian Incentive Compatibility. Combined these results give a near-complete picture of the power and limitations of BIC and DSIC mechanisms for the problem of allocating indivisible goods.
Equilibria in Two-Stage Facility Location with Atomic Clients
Venue: Conference IJCAI 2024
Year: 2024

We consider competitive facility location as a two-stage multi-agent system with two types of clients. For a given host graph with weighted clients on the vertices, first facility agents strategically select vertices for opening their facilities. Then, the clients strategically select which of the opened facilities in their neighborhood to patronize. Facilities want to attract as much client weight as possible, clients want to minimize congestion on the chosen facility. All recently studied versions of this model assume that clients can split their weight strategically. We consider clients with unsplittable weights but allow mixed strategies. So clients may randomize over which facility to patronize. Besides modeling a natural client behavior, this subtle change yields drastic changes, e.g., for a given facility placement, qualitatively different client equilibria are possible. As our main result, we show that pure subgame perfect equilibria always exist if all client weights are identical. For this, we use a novel potential function argument, employing a hierarchical classification of the clients and sophisticated rounding in each step. In contrast, for non-identical clients, we show that deciding the existence of even approximately stable states is computationally intractable. On the positive side, we give a tight bound of $2$ on the price of anarchy which implies high social welfare of equilibria, if they exist.
The Distortion of Threshold Approval Matching
Venue: Conference IJCAI 2024
Year: 2024

We study matching settings in which a set of agents have private utilities over a set of items. Each agent reports a partition of the items into approval sets of different threshold utility levels. Given this limited information on input, the goal is to compute an assignment of the items to the agents (subject to cardinality constraints depending on the application) that (approximately) maximizes the social welfare (the total utility of the agents for their assigned items). We first consider the well-known, simple one-sided matching problem in which each of $n$ agents is to be assigned exactly one of $n$ items. We show that with $t$ threshold utility levels, the distortion of deterministic matching algorithms is $Θ(\sqrt[t]{n})$ while that of randomized algorithms is $Θ(\sqrt[t+1]{n})$. We then show that our distortion bounds extend to a more general setting in which there are multiple copies of the items, each agent can be assigned a number of items (even copies of the same one) up to a capacity, and the utility of an agent for an item depends on the number of its copies that the agent is given.
Allocating Mixed Goods with Customized Fairness and Indivisibility Ratio
Venue: Conference IJCAI 2024
Year: 2024

We consider the problem of fairly allocating a combination of divisible and indivisible goods. While fairness criteria like envy-freeness (EF) and proportionality (PROP) can always be achieved for divisible goods, only their relaxed versions, such as the ''up to one'' relaxations EF1 and PROP1, can be satisfied when the goods are indivisible. The ''up to one'' relaxations require the fairness conditions to be satisfied provided that one good can be completely eliminated or added in the comparison. In this work, we bridge the gap between the two extremes and propose ''up to a fraction'' relaxations for the allocation of mixed divisible and indivisible goods. The fraction is determined based on the proportion of indivisible goods, which we call the indivisibility ratio. The new concepts also introduce asymmetric conditions that are customized for individuals with varying indivisibility ratios. We provide both upper and lower bounds on the fractions of the modified item in order to satisfy the fairness criterion. Our results are tight up to a constant for EF and asymptotically tight for PROP.
Public Event Scheduling with Busy Agents
Venue: Conference IJCAI 2024
Year: 2024

We study a public event scheduling problem, where multiple public events are scheduled to coordinate the availability of multiple agents. The availability of each agent is determined by solving a separate flexible interval job scheduling problem, where the jobs are required to be preemptively processed. The agents want to attend as many events as possible, and their agreements are considered to be the total length of time during which they can attend these events. The goal is to find a schedule for events as well as the job schedule for each agent such that the total agreement is maximized. We first show that the problem is NP-hard, and then prove that a simple greedy algorithm achieves $\frac{1}{2}$-approximation when the whole timeline is polynomially bounded. Our method also implies a $(1-\frac{1}{e})$-approximate algorithm for this case. Subsequently, for the general timeline case, we present an algorithmic framework that extends a $\frac{1}α$-approximate algorithm for the one-event instance to the general case that achieves $\frac{1}{α+1}$-approximation. Finally, we give a polynomial time algorithm that solves the one-event instance, and this implies a $\frac{1}{2}$-approximate algorithm for the general case.
Vulnerabilities of Single-Round Incentive Compatibility in Auto-bidding: Theory and Evidence from ROI-Constrained Online Advertising Markets
Venue: Conference IJCAI 2024
Year: 2024

Most of the work in the auction design literature assumes that bidders behave rationally based on the information available for every individual auction, and the revelation principle enables designers to restrict their efforts to incentive compatible (IC) mechanisms. However, in today's online advertising markets, one of the most important real-life applications of auction design, the data and computational power required to bid optimally are only available to the platform, and an advertiser can only participate by setting performance objectives and constraints for its proxy auto-bidder provided by the platform. The prevalence of auto-bidding necessitates a review of auction theory. In this paper, we examine the markets through the lens of ROI-constrained value-maximizing campaigns. We show that second price auction exhibits many undesirable properties (computational hardness, non-monotonicity, instability of bidders' utilities, and interference in A/B testing) and loses its dominant theoretical advantages in single-item scenarios. In addition, we make it clear how IC and its runner-up-winner interdependence contribute to each property. We hope that our work could bring new perspectives to the community and benefit practitioners to attain a better grasp of real-world markets.
Ordinal Maximin Guarantees for Group Fair Division
Venue: Conference IJCAI 2024
Year: 2024

We investigate fairness in the allocation of indivisible items among groups of agents using the notion of maximin share (MMS). While previous work has shown that no nontrivial multiplicative MMS approximation can be guaranteed in this setting for general group sizes, we demonstrate that ordinal relaxations are much more useful. For example, we show that if $n$ agents are distributed equally across $g$ groups, there exists a $1$-out-of-$k$ MMS allocation for $k = O(g\log(n/g))$, while if all but a constant number of agents are in the same group, we obtain $k = O(\log n/\log \log n)$. We also establish the tightness of these bounds and provide non-asymptotic results for the case of two groups.
Toward Completing the Picture of Control in Schulze and Ranked Pairs Elections
Venue: Conference IJCAI 2024
Year: 2024

Both Schulze and ranked pairs are voting rules that satisfy many natural, desirable axioms. Many standard types of electoral control (with a chair seeking to change the outcome of an election by interfering with the election structure) have already been studied. However, for control by replacing candidates or voters and for (exact) multimode control that combines multiple standard attacks, many questions remain open. We solve a number of these open cases for Schulze and ranked pairs. In addition, we fix a flaw in the reduction of Menton and Singh [IJCAI 2013] showing that Schulze is resistant to constructive control by deleting candidates and re-establish a vulnerability result for destructive control by deleting candidates. In some of our proofs, we study variants of s-t vertex cuts in graphs that are related to our control problems.
What Is Best for Students, Numerical Scores or Letter Grades?
Venue: Conference IJCAI 2024
Year: 2024

We study letter grading schemes, which are routinely employed for evaluating student performance. Typically, a numerical score obtained via one or more evaluations is converted into a letter grade (e.g., A+, B-, etc.) by associating a disjoint interval of numerical scores to each letter grade. We propose the first model for studying the (de)motivational effects of such grading on the students and, consequently, on their performance in future evaluations. We use the model to compare uniform letter grading schemes, in which the range of scores is divided into equal-length parts that are mapped to the letter grades, to numerical scoring, in which the score is not converted to any letter grade (equivalently, every score is its own letter grade). Theoretically, we identify realistic conditions under which numerical scoring is better than any uniform letter grading scheme. Our experiments confirm that this holds under even weaker conditions, but also find cases where the converse occurs.