OpenRaiser/Intern-Atlas huggingface dataset:
Mixed Strategies for Security Games with General Defending Requirements
Venue: Conference IJCAI 2022
Year: 2022

The Stackelberg security game is played between a defender and an attacker, where the defender needs to allocate a limited amount of resources to multiple targets in order to minimize the loss due to adversarial attack by the attacker. While allowing targets to have different values, classic settings often assume uniform requirements to defend the targets. This enables existing results that study mixed strategies (randomized allocation algorithms) to adopt a compact representation of the mixed strategies. In this work, we initiate the study of mixed strategies for the security games in which the targets can have different defending requirements. In contrast to the case of uniform defending requirement, for which an optimal mixed strategy can be computed efficiently, we show that computing the optimal mixed strategy is NP-hard for the general defending requirements setting. However, we show that strong upper and lower bounds for the optimal mixed strategy defending result can be derived. We propose an efficient close-to-optimal Patching algorithm that computes mixed strategies that use only few pure strategies. We also study the setting when the game is played on a network and resource sharing is enabled between neighboring targets. Our experimental results demonstrate the effectiveness of our algorithm in several large real-world datasets.
Envy-Free and Pareto-Optimal Allocations for Agents with Asymmetric Random Valuations
Venue: Conference IJCAI 2022
Year: 2022

We study the problem of allocating $m$ indivisible items to $n$ agents with additive utilities. It is desirable for the allocation to be both fair and efficient, which we formalize through the notions of envy-freeness and Pareto-optimality. While envy-free and Pareto-optimal allocations may not exist for arbitrary utility profiles, previous work has shown that such allocations exist with high probability assuming that all agents' values for all items are independently drawn from a common distribution. In this paper, we consider a generalization of this model where each agent's utilities are drawn independently from a distribution specific to the agent. We show that envy-free and Pareto-optimal allocations are likely to exist in this asymmetric model when $m=Ω\left(n\log n\right)$, which is tight up to a log log gap that also remains open in the symmetric subsetting. Furthermore, these guarantees can be achieved by a polynomial-time algorithm.
Achieving Envy-Freeness with Limited Subsidies under Dichotomous Valuations
Venue: Conference IJCAI 2022
Year: 2022

We study the problem of allocating indivisible goods among agents in a fair manner. While envy-free allocations of indivisible goods are not guaranteed to exist, envy-freeness can be achieved by additionally providing some subsidy to the agents. These subsidies can be alternatively viewed as a divisible good (money) that is fractionally assigned among the agents to realize an envy-free outcome. In this setup, we bound the subsidy required to attain envy-freeness among agents with dichotomous valuations, i.e., among agents whose marginal value for any good is either zero or one. We prove that, under dichotomous valuations, there exists an allocation that achieves envy-freeness with a per-agent subsidy of either $0$ or $1$. Furthermore, such an envy-free solution can be computed efficiently in the standard value-oracle model. Notably, our results hold for general dichotomous valuations and, in particular, do not require the (dichotomous) valuations to be additive, submodular, or even subadditive. Also, our subsidy bounds are tight and provide a linear (in the number of agents) factor improvement over the bounds known for general monotone valuations.
Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games
Venue: Conference IJCAI 2022
Year: 2022

Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. To address this, we study Swap Schelling Games with single-peaked utility functions. Our main finding is that tolerance, i.e., agents favoring fifty-fifty neighborhoods or being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. Regarding the quality of equilibria, we derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs.
Fair Equilibria in Sponsored Search Auctions: The Advertisers’ Perspective
Venue: Conference IJCAI 2022
Year: 2022

In this work we introduce a new class of mechanisms composed of a traditional Generalized Second Price (GSP) auction and a fair division scheme, in order to achieve some desired level of fairness between groups of Bayesian strategic advertisers. We propose two mechanisms, $β$-Fair GSP and GSP-EFX, that compose GSP with, respectively, an envy-free up to one item, and an envy-free up to any item fair division scheme. The payments of GSP are adjusted in order to compensate advertisers that suffer a loss of efficiency due the fair division stage. We investigate the strategic learning implications of the deployment of sponsored search auction mechanisms that obey to such fairness criteria. We prove that, for both mechanisms, if bidders play so as to minimize their external regret they are guaranteed to reach an equilibrium with good social welfare. We also prove that the mechanisms are budget balanced, so that the payments charged by the traditional GSP mechanism are a good proxy of the total compensation offered to the advertisers. Finally, we evaluate the quality of the allocations through experiments on real-world data.
Understanding Distance Measures Among Elections
Venue: Conference IJCAI 2022
Year: 2022

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance used to form the so-called map of elections. Among the six, the latter seems to strike the best balance between its computational complexity and expressiveness.
Toward Policy Explanations for Multi-Agent Reinforcement Learning
Venue: Conference IJCAI 2022
Year: 2022

Advances in multi-agent reinforcement learning (MARL) enable sequential decision making for a range of exciting multi-agent applications such as cooperative AI and autonomous driving. Explaining agent decisions is crucial for improving system transparency, increasing user satisfaction, and facilitating human-agent collaboration. However, existing works on explainable reinforcement learning mostly focus on the single-agent setting and are not suitable for addressing challenges posed by multi-agent environments. We present novel methods to generate two types of policy explanations for MARL: (i) policy summarization about the agent cooperation and task sequence, and (ii) language explanations to answer queries about agent behavior. Experimental results on three MARL domains demonstrate the scalability of our methods. A user study shows that the generated explanations significantly improve user performance and increase subjective ratings on metrics such as user satisfaction.
Let’s Agree to Agree: Targeting Consensus for Incomplete Preferences through Majority Dynamics
Venue: Conference IJCAI 2022
Year: 2022

We study settings in which agents with incomplete preferences need to make a collective decision. We focus on a process of majority dynamics where issues are addressed one at a time and undecided agents follow the opinion of the majority. We assess the effects of this process on various consensus notions -- such as the Condorcet winner -- and show that in the worst case, myopic adherence to the majority damages existing consensus; yet, simulation experiments indicate that the damage is often mild. We also examine scenarios where the chair of the decision process can control the existence (or the identity) of consensus, by determining the order in which the issues are discussed.
Single-Peaked Opinion Updates
Venue: Conference IJCAI 2022
Year: 2022

We consider opinion diffusion for undirected networks with sequential updates when the opinions of the agents are single-peaked preference rankings. Our starting point is the study of preserving single-peakedness. We identify voting rules that, when given a single-peaked profile, output at least one ranking that is single peaked w.r.t. a single-peaked axis of the input. For such voting rules we show convergence to a stable state of the diffusion process that uses the voting rule as the agents' update rule. Further, we establish an efficient algorithm that maximises the spread of extreme opinions.
Network Creation with Homophilic Agents
Venue: Conference IJCAI 2022
Year: 2022

Network Creation Games are an important framework for understanding the formation of real-world networks. These games usually assume a set of indistinguishable agents strategically buying edges at a uniform price leading to a network among them. However, in real life, agents are heterogeneous and their relationships often display a bias towards similar agents, say of the same ethnic group. This homophilic behavior on the agent level can then lead to the emergent global phenomenon of social segregation. We initiate the study of Network Creation Games with multiple types of homophilic agents and non-uniform edge cost. Specifically, we introduce and compare two models, focusing on the perception of same-type and different-type neighboring agents, respectively. Despite their different initial conditions, both our theoretical and experimental analysis show that the resulting stable networks are almost identical in the two models, indicating a robust structure of social networks under homophily. Moreover, we investigate the segregation strength of the formed networks and thereby offer new insights on understanding segregation.
Optimal Anonymous Independent Reward Scheme Design
Venue: Conference IJCAI 2022
Year: 2022

We consider designing reward schemes that incentivize agents to create high-quality content (e.g., videos, images, text, ideas). The problem is at the center of a real-world application where the goal is to optimize the overall quality of generated content on user-generated content platforms. We focus on anonymous independent reward schemes (AIRS) that only take the quality of an agent's content as input. We prove the general problem is NP-hard. If the cost function is convex, we show the optimal AIRS can be formulated as a convex optimization problem and propose an efficient algorithm to solve it. Next, we explore the optimal linear reward scheme and prove it has a 1/2-approximation ratio, and the ratio is tight. Lastly, we show the proportional scheme can be arbitrarily bad compared to AIRS.
On the Convergence of Fictitious Play: A Decomposition Approach
Venue: Conference IJCAI 2022
Year: 2022

Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in $n$-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable convergence guarantees on zero-sum games and potential games, many real-world problems are often a mixture of both and the convergence property of FP has not been fully studied yet. In this paper, we extend the convergence results of FP to the combinations of such games and beyond. Specifically, we derive new conditions for FP to converge by leveraging game decomposition techniques. We further develop a linear relationship unifying cooperation and competition in the sense that these two classes of games are mutually transferable. Finally, we analyze a non-convergent example of FP, the Shapley game, and develop sufficient conditions for FP to converge.
Voting in Two-Crossing Elections
Venue: Conference IJCAI 2022
Year: 2022

We introduce two-crossing elections as a generalization of single-crossing elections, showing a number of new results. First, we show that two-crossing elections can be recognized in polynomial time, by reduction to the well-studied consecutive ones problem. We also conjecture that recognizing $k$-crossing elections is NP-complete in general, providing evidence by relating to a problem similar to consecutive ones proven to be hard in the literature. Single-crossing elections exhibit a transitive majority relation, from which many important results follow. On the other hand, we show that the classical Debord-McGarvey theorem can still be proven two-crossing, implying that any weighted majority tournament is inducible by a two-crossing election. This shows that many voting rules are NP-hard under two-crossing elections, including Kemeny and Slater. This is in contrast to the single-crossing case and outlines an important complexity boundary between single- and two-crossing. Subsequently, we show that for two-crossing elections the Young scores of all candidates can be computed in polynomial time, by formulating a totally unimodular linear program. Finally, we consider the Chamberlin-Courant rule with arbitrary disutilities and show that a winning committee can be computed in polynomial time, using an approach based on dynamic programming.
Online Approval Committee Elections
Venue: Conference IJCAI 2022
Year: 2022

Assume $k$ candidates need to be selected. The candidates appear over time. Each time one appears, it must be immediately selected or rejected -- a decision that is made by a group of individuals through voting. Assume the voters use approval ballots, i.e., for each candidate they only specify whether they consider it acceptable or not. This setting can be seen as a voting variant of choosing $k$ secretaries. Our contribution is twofold. (1) We assess to what extent the committees that are computed online can proportionally represent the voters. (2) If a prior probability over candidate approvals is available, we show how to compute committees with maximal expected score.
Contests to Incentivize a Target Group
Venue: Conference IJCAI 2022
Year: 2022

We study how to incentivize agents in a target group to produce a higher output in the context of incomplete information, by means of rank-order allocation contests. We describe a symmetric Bayes--Nash equilibrium for contests that have two types of rank-based prizes: prizes that are accessible only to the agents in the target group; prizes that are accessible to everyone. We also specialize this equilibrium characterization to two important sub-cases: (i) contests that do not discriminate while awarding the prizes, i.e., only have prizes that are accessible to everyone; (ii) contests that have prize quotas for the groups, and each group can compete only for prizes in their share. For these models, we also study the properties of the contest that maximizes the expected total output by the agents in the target group.
Insight into Voting Problem Complexity Using Randomized Classes
Venue: Conference IJCAI 2022
Year: 2022

The first step in classifying the complexity of an NP problem is typically showing the problem in P or NP-complete. This has been a successful first step for many problems, including voting problems. However, in this paper we show that this may not always be the best first step. We consider the problem of constructive control by replacing voters (CCRV) introduced by Loreggia et al. (2015) for the scoring rule First-Last, which is defined by $\langle 1, 0, \dots, 0, -1\rangle$. We show that this problem is equivalent to Exact Perfect Bipartite Matching, and so CCRV for First-Last can be determined in random polynomial time. So on the one hand, if CCRV for First-Last is NP-complete then RP = NP, which is extremely unlikely. On the other hand, showing that CCRV for First-Last is in P would also show that Exact Perfect Bipartite Matching is in P, which would solve a well-studied 40-year-old open problem. By considering RP as an option we also gain insight into the complexity of CCRV for 2-Approval, ultimately showing it in P, which settles the complexity of the sole open problem in the comprehensive table from Erdélyi et al. (2021).
Can Buyers Reveal for a Better Deal?
Venue: Conference IJCAI 2022
Year: 2022

We study market interactions in which buyers are allowed to credibly reveal partial information about their types to the seller. Previous recent work has studied the special case of one buyer and one good, showing that such communication can simultaneously improve social welfare and ex ante buyer utility. However, with multiple buyers, we find that the buyer-optimal signalling schemes from the one-buyer case are actually harmful to buyer welfare. Moreover, we prove several impossibility results showing that, with either multiple i.i.d. buyers or multiple i.i.d. goods, maximizing buyer utility can be at odds with social efficiency, which is surprising in contrast with the one-buyer, one-good case. Finally, we investigate the computational tractability of implementing desirable equilibrium outcomes. We find that, even with one buyer and one good, optimizing buyer utility is generally NP-hard but tractable in a practical restricted setting.
Two for One & One for All: Two-Sided Manipulation in Matching Markets
Venue: Conference IJCAI 2022
Year: 2022

Strategic behavior in two-sided matching markets has been traditionally studied in a "one-sided" manipulation setting where the agent who misreports is also the intended beneficiary. Our work investigates "two-sided" manipulation of the deferred acceptance algorithm where the misreporting agent and the manipulator (or beneficiary) are on different sides. Specifically, we generalize the recently proposed accomplice manipulation model (where a man misreports on behalf of a woman) along two complementary dimensions: (a) the two for one model, with a pair of misreporting agents (man and woman) and a single beneficiary (the misreporting woman), and (b) the one for all model, with one misreporting agent (man) and a coalition of beneficiaries (all women). Our main contribution is to develop polynomial-time algorithms for finding an optimal manipulation in both settings. We obtain these results despite the fact that an optimal one for all strategy fails to be inconspicuous, while it is unclear whether an optimal two for one strategy satisfies the inconspicuousness property. We also study the conditions under which stability of the resulting matching is preserved. Experimentally, we show that two-sided manipulations are more frequently available and offer better quality matches than their one-sided counterparts.
Phragmén Rules for Degressive and Regressive Proportionality
Venue: Conference IJCAI 2022
Year: 2022

We study two concepts of proportionality in the model of approval-based committee elections. In degressive proportionality small minorities of voters are favored in comparison with the standard linear proportionality. Regressive proportionality, on the other hand, requires that larger subdivisions of voters are privileged. We introduce a new family of rules that broadly generalize Phragmén's Sequential Rule spanning the spectrum between degressive and regressive proportionality. We analyze and compare the two principles of proportionality assuming the voters and the candidates can be represented as points in an Euclidean issue space.
The Dichotomous Affiliate Stable Matching Problem: Approval-Based Matching with Applicant-Employer Relations
Venue: Conference IJCAI 2022
Year: 2022

While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where agents' preferences indicate dichotomous acceptance or rejection of another agent in the marketplace, both for themselves and their affiliates. We also assume the agent's preferences over entire matchings are determined by a general weighted valuation function of their (and their affiliates') matches. Our results are threefold: (1) we use a human study to show that real-world matching rankings follow our assumed valuation function; (2) we prove that there always exists a stable solution by providing an efficient, easily-implementable algorithm that finds such a solution; and (3) we experimentally validate the efficiency of our algorithm versus a linear-programming-based approach.
Explaining Preferences by Multiple Patterns in Voters’ Behavior
Venue: Conference IJCAI 2022
Year: 2022

In some preference aggregation scenarios, voters' preferences are highly structured: e.g., the set of candidates may have one-dimensional structure (so that voters' preferences are single-peaked) or be described by a binary decision tree (so that voters' preferences are group-separable). However, sometimes a single axis or a decision tree is insufficient to capture the voters' preferences; rather, there is a small number $k$ of axes or decision trees such that each vote in the profile is consistent with one of these axes (resp., trees). In this work, we study the complexity of deciding whether voters' preferences can be explained in this manner. For $k=2$, we use the technique developed by Yang~[2020] in the context of single-peaked preferences to obtain a polynomial-time algorithm for several domains: value-restricted preferences, group-separable preferences, and a natural subdomain of group-separable preferences, namely, caterpillar group-separable preferences. For $k\ge 3$, the problem is known to be hard for single-peaked preferences; we show that this is also the case for value-restricted and group-separable preferences. Our positive results for $k=2$ make use of forbidden minor characterizations of the respective domains; in particular, we establish that the domain of caterpillar group-separable preferences admits a forbidden minor characterization.
Proportional Budget Allocations: Towards a Systematization
Venue: Conference IJCAI 2022
Year: 2022

We contribute to the programme of lifting proportionality axioms from the multi-winner voting setting to participatory budgeting. We define novel proportionality axioms for participatory budgeting and test them on known proportionality-driven rules such as Phragmén and Rule X. We investigate logical implications among old and new axioms and provide a systematic overview of proportionality criteria in participatory budgeting.
Fixing Knockout Tournaments With Seeds
Venue: Conference IJCAI 2022
Year: 2022

Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent aspect of player seeds, which can significantly constrain the chosen bracket. We show that certain structural conditions that guarantee that a player can win a knockout tournament without seeds are no longer sufficient in light of seed constraints. On the other hand, we prove that when the pairwise match outcomes are generated randomly, all players are still likely to be knockout winners under the same probability threshold with seeds as without seeds. In addition, we investigate the complexity of deciding whether a manipulation is possible when seeds are present.