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Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. Traditionally, the primary goal of such models is to maximize a linear function of the constituent matches (e.g., linear social welfare maximization) subject to some constraints. Recent work has studied a new goal of balancing whole-match diversity and economic efficiency, where the objective is instead a monotone submodular function over the matching. Basic versions of this problem are solvable in polynomial time. In this work, we prove that the problem of simultaneously maximizing diversity along several features (e.g., country of citizenship, gender, skills) is NP-hard. To address this problem, we develop the first combinatorial algorithm that constructs provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide a Mixed-Integer Quadratic formulation for the same problem and show that our method guarantees optimal solutions and takes less computation time for a reviewer assignment application. The source code is made available at https://github.com/faezahmed/diverse_matching.
A key problem in Belief-Desire-Intention agents is how an agent progresses its intentions, i.e., which plans should be selected and how the execution of these plans should be interleaved so as to achieve the agent’s goals. Previous approaches to the intention progression problem assume the agent has perfect information about the state of the environment. However, in many real-world applications, an agent may be uncertain about whether an environment condition holds, and hence whether a particular plan is applicable or an action is executable. In this paper, we propose SAU, a Monte-Carlo Tree Search (MCTS)-based scheduler for intention progression problems where the agent’s beliefs are uncertain. We evaluate the performance of our approach experimentally by varying the degree of uncertainty in the agent’s beliefs. The results suggest that SAU is able to successfully achieve the agent’s goals even in settings where there is significant uncertainty in the agent’s beliefs.
We investigate the issue of manipulability for social ranking rules, where the goal is to rank individuals given the ranking of coalitions formed by them and each individual prefers to reach the highest positions in the social ranking. This problem lies at the intersection of computational social choice and the algorithmic theory of power indices. Different social ranking rules have been recently proposed and studied from an axiomatic point of view. In this paper, we focus on rules representing three classical approaches in social choice theory: the marginal contribution approach, the lexicographic approach and the (ceteris paribus) majority one. We first consider some particular members of these families analysing their resistance to a malicious behaviour of individuals. Then, we analyze the computational complexity of manipulation, and complete our theoretical results with simulations in order to analyse the manipulation frequencies and to assess the effects of manipulations.
We consider the classic problem of fairly allocating indivisible goods among agents with additive valuation functions and explore the connection between two prominent fairness notions: maximum Nash welfare (MNW) and envy-freeness up to any good (EFX). We establish that an MNW allocation is always EFX as long as there are at most two possible values for the goods, whereas this implication is no longer true for three or more distinct values. As a notable consequence, this proves the existence of EFX allocations for these restricted valuation functions. While the efficient computation of an MNW allocation for two possible values remains an open problem, we present a novel algorithm for directly constructing EFX allocations in this setting. Finally, we study the question of whether an MNW allocation implies any EFX guarantee for general additive valuation functions under a natural new interpretation of approximate EFX allocations.
Incomplete GDL-based algorithms including Max-sum and its variants are important methods for multi-agent optimization. However, they face a significant scalability challenge as the computational overhead grows exponentially with respect to the arity of each utility function. Generic Domain Pruning (GDP) technique reduces the computational effort by performing a one-shot pruning to filter out suboptimal entries. Unfortunately, GDP could perform poorly when dealing with dense local utilities and ties which widely exist in many domains. In this paper, we present several novel sorting-based acceleration algorithms by alleviating the effect of densely distributed local utilities. Specifically, instead of one-shot pruning in GDP, we propose to integrate both search and pruning to iteratively reduce the search space. Besides, we cope with the utility ties by organizing the search space of tied utilities into AND/OR trees to enable branch-and-bound. Finally, we propose a discretization mechanism to offer a tradeoff between the reconstruction overhead and the pruning efficiency. We demonstrate the superiorities of our algorithms over the state-of-the-art from both theoretical and experimental perspectives.
We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger and relaxed versions that are especially suitable for the allocation of indivisible items. Of particular interest is a concept called group envy-freeness up to one item (GEF1). We then present a clear taxonomy of the fairness concepts. We study which fairness concepts guarantee the existence of a fair allocation under which preference domain. For two natural classes of additive utilities, we design polynomial-time algorithms to compute a GEF1 allocation. We also prove that checking whether a given allocation satisfies GEF1 is coNP-complete when there are either only goods, only chores or both.
We study the problem of allocating indivisible goods among agents that have an identical subadditive valuation over the goods. The extent of fair- ness and efficiency of allocations is measured by the generalized means of the values that the alloca- tions generate among the agents. Parameterized by an exponent term p, generalized-mean welfares en- compass multiple well-studied objectives, such as social welfare, Nash social welfare, and egalitarian welfare. We establish that, under identical subadditive valu- ations and in the demand oracle model, one can efficiently find a single allocation that approximates the optimal generalized-mean welfare—to within a factor of 40—uniformly for all p ∈ (−∞,1]. Hence, by way of a constant-factor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.
We investigate opinion dynamics in multi-agent networks when there exists a bias toward one of two possible opinions; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing the status quo, the system evolves in steps. In each step, one agent selected uniformly at random adopts with some probability a the superior opinion, and with probability 1 - a it follows an underlying update rule to revise its opinion on the basis of those held by its neighbors. We analyze the convergence of the resulting process under two well-known update rules, namely majority and voter. The framework we propose exhibits a rich structure, with a nonobvious interplay between topology and underlying update rule. For example, for the voter rule we show that the speed of convergence bears no significant dependence on the underlying topology, whereas the picture changes completely under the majority rule, where network density negatively affects convergence. We believe that the model we propose is at the same time simple, rich, and modular, affording mathematical characterization of the interplay between bias, underlying opinion dynamics, and social structure in a unified setting.
We present a formal framework that allows individual and group of agents to reason about their trust toward other agents. In particular, we propose a branching time temporal logic BT which includes operators that express concepts such as everyone trust, distributed trust and propagated trust. We analyze the satisfiability and model checking problems of this logic using a reduction technique.
Given a set of individuals qualifying or disqualifying each other, group identification is the task of identifying a socially qualified subgroup of individuals. Social qualification depends on the specific rule used to aggregate individual qualifications. The bribery problem in this context asks how many agents need to change their qualifications in order to change the outcome. Complementing previous results showing polynomial-time solvability or NP-hardness of bribery for various social rules in the constructive (aiming at making specific individuals socially qualified) or destructive (aiming at making specific individuals socially disqualified) setting, we provide a comprehensive picture of the parameterized computational complexity landscape. Conceptually, we also consider a more fine-grained concept of bribery cost, where we ask how many single qualifications need to be changed, and a more general bribery goal that combines the constructive and destructive setting.
Approval-based multiwinner voting rules have recently received much attention in the Computational Social Choice literature. Such rules aggregate approval ballots and determine a winning committee of alternatives. To assess effectiveness, we propose to employ new noise models that are specifically tailored for approval votes and committees. These models take as input a ground truth committee and return random approval votes to be thought of as noisy estimates of the ground truth. A minimum robustness requirement for an approval-based multiwinner voting rule is to return the ground truth when applied to profiles with sufficiently many noisy votes. Our results indicate that approval-based multiwinner voting can indeed be robust to reasonable noise. We further refine this finding by presenting a hierarchy of rules in terms of how robust to noise they are.
Decentralized online planning can be an attractive paradigm for cooperative multi-agent systems, due to improved scalability and robustness. A key difficulty of such approach lies in making accurate predictions about the decisions of other agents. In this paper, we present a trainable online decentralized planning algorithm based on decentralized Monte Carlo Tree Search, combined with models of teammates learned from previous episodic runs. By only allowing one agent to adapt its models at a time, under the assumption of ideal policy approximation, successive iterations of our method are guaranteed to improve joint policies, and eventually lead to convergence to a Nash equilibrium. We test the efficiency of the algorithm by performing experiments in several scenarios of the spatial task allocation environment introduced in [Claes et al., 2015]. We show that deep learning and convolutional neural networks can be employed to produce accurate policy approximators which exploit the spatial features of the problem, and that the proposed algorithm improves over the baseline planning performance for particularly challenging domain configurations.
The Chamberlin-Courant and Monroe rules are fundamental and well-studied rules in the literature of multi-winner elections. The problem of determining if there exists a committee of size k that has a Chamberlin-Courant (respectively, Monroe) dissatisfaction score of at most r is known to be NP-complete. We consider the following natural problems in this setting: a) given a committee S of size k as input, is it an optimal k-sized committee?, and b) given a candidate c and a committee size k, does there exist an optimal k-sized committee that contains c? In this work, we resolve the complexity of both problems for the Chamberlin-Courant and Monroe voting rules in the settings of rankings as well as approval ballots. We show that verifying if a given committee is optimal is coNP-complete whilst the latter problem is complete for Theta_2^P. Our contribution fills an essential gap in the literature for these important multi-winner rules.
In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences (Bredereck, Elkind, Igarashi, AAMAS'19): each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents’ preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem.
In parliamentary elections, parties compete for a limited, typically fixed number of seats. We study the complexity of the following bribery-style problem: Given the distribution of votes among the parties, what is the smallest number of voters that need to be convinced to vote for our party, so that it gets a desired number of seats. We also run extensive experiments on real-world election data and measure the effectiveness of our method.
We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian social cost (OPT). The k'th moment of Distortion is the expected approximation factor with respect to the k'th power of OPT. We consider mechanisms that elicit alternatives by randomly sampling voters for their favorite alternative. We design two families of mechanisms that provide constant (with respect to the number of voters and alternatives) k'th moment of Distortion using just k samples if all voters can then participate in a vote among the proposed alternatives, or 2k-1 samples if only the sampled voters can participate. We also show that these numbers of samples are tight. Such mechanisms deviate from a constant approximation to OPT with probability that drops exponentially in the number of samples, independent of the total number of voters and alternatives. We conclude with simulations on real-world Participatory Budgeting data to qualitatively complement our theoretical insights.
Prompt-LTL extends Linear Temporal Logic with a bounded version of the ``eventually'' operator to express temporal requirements such as bounding waiting times. We study assume-guarantee synthesis for prompt-LTL: the goal is to construct a system such that for all environments satisfying a first prompt-LTL formula (the assumption) the system composed with this environment satisfies a second prompt-LTL formula (the guarantee). This problem has been open for a decade. We construct an algorithm for solving it and show that, like classical LTL synthesis, it is 2-EXPTIME-complete.
We derive conditions under which a peer-consistency mechanism can be used to elicit truthful data from non-trusted rational agents when an aggregate statistic of the collected data affects the amount of their incentives to lie. Furthermore, we discuss the relative saving that can be achieved by the mechanism, compared to the rational outcome, if no such mechanism was implemented. Our work is motivated by distributed platforms, where decentralized data oracles collect information about real-world events, based on the aggregate information provided by often self-interested participants. We compare our theoretical observations with numerical simulations on two public real datasets.
We study proportionality in approval-based multiwinner elections with a variable number of winners, where both the size and identity of the winning committee are informed by voters' opinions. While proportionality has been studied in multiwinner elections with a fixed number of winners, it has not been considered in the variable number of winners setting. The measure of proportionality we consider is average satisfaction (AS), which intuitively measures the number of agreements on average between sufficiently large and cohesive groups of voters and the output of the voting rule. First, we show an upper bound on AS that any deterministic rule can provide, and that straightforward adaptations of deterministic rules from the fixed number of winners setting do not achieve better than a 1/2 approximation to AS even for large numbers of candidates. We then prove that a natural randomized rule achieves a 29/32 approximation to AS.
Network Creation Games(NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is 1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.
We investigate the following many-to-one stable matching problem with diversity constraints (SMTI-DIVERSE): Given a set of students and a set of colleges which have preferences over each other, where the students have overlapping types, and the colleges each have a total capacity as well as quotas for individual types (the diversity constraints), is there a matching satisfying all diversity constraints such that no unmatched student-college pair has an incentive to deviate? SMTI-DIVERSE is known to be NP-hard. However, as opposed to the NP-membership claims in the literature [Aziz et al., AAMAS 2019; Huang,SODA 2010], we prove that it is beyond NP: it is complete for the complexity class Σ^P_2. In addition, we provide a comprehensive analysis of the problem’s complexity from the viewpoint of natural restrictions to inputs and obtain new algorithms for the problem.
We study the controlled school choice problem where students may belong to overlapping types and schools have soft target quotas for each type. We formalize fairness concepts for the setting that extend fairness concepts considered for restricted settings without overlapping types. Our central contribution is presenting a new class of algorithms that takes into account the representations of combinations of student types. The algorithms return matchings that are non-wasteful and satisfy fairness for same types. We further prove that the algorithms are strategyproof for the students and yield a fair outcome with respect to the induced quotas for type combinations. We experimentally compare our algorithms with two existing approaches in terms of achieving diversity goals and satisfying fairness.
Motivated by applications such as college admission and insurance rate determination, we study a classification problem where the inputs are controlled by strategic individuals who can modify their features at a cost. A learner can only partially observe the features, and aims to classify individuals with respect to a quality score. The goal is to design a classification mechanism that maximizes the overall quality score in the population, taking any strategic updating into account. When scores are linear and mechanisms can assign their own scores to agents, we show that the optimal classifier is an appropriate projection of the quality score. For the more restrictive task of binary classification via linear thresholds, we construct a (1/4)-approximation to the optimal classifier when the underlying feature distribution is sufficiently smooth and admits an oracle for finding dense regions. We extend our results to settings where the prior distribution is unknown and must be learned from samples.
Modelling ethics is critical to understanding and analysing social phenomena. However, prior literature either incorporates ethics into agent strategies or uses it for evaluation of agent behaviour. This work proposes a framework that models both, ethical decision making as well as evaluation using virtue ethics and utilitarianism. In an iteration, agents can use either the classical Continuous Prisoner's Dilemma or a new type of interaction called moral interaction, where agents donate or steal from other agents. We introduce moral interactions to model ethical decision making. We also propose a novel agent type, called virtue agent, parametrised by the agent's level of ethics. Virtue agents' decisions are based on moral evaluations of past interactions. Our simulations show that unethical agents make short term gains but are less prosperous in the long run. We find that in societies with positivity bias, unethical agents have high incentive to become ethical. The opposite is true of societies with negativity bias. We also evaluate the ethicality of existing strategies and compare them with those of virtue agents.
We study an information-structure design problem (i.e., a Bayesian persuasion problem) in an online scenario. Inspired by the classic gambler's problem, consider a set of candidates who arrive sequentially and are evaluated by one agent (the sender). This agent learns the value from hiring the candidate to herself as well as the value to another agent, the receiver. The sender provides a signal to the receiver who, in turn, makes an irrevocable decision on whether or not to hire the candidate. A-priori, for each agent the distribution of valuation is independent across candidates but may not be identical. We design good online signaling schemes for the sender. To assess the performance, we compare the expected utility to that of an optimal offline scheme by a prophet sender who knows all candidate realizations in advance. We show an optimal prophet inequality for online Bayesian persuasion, with a 1/2-approximation when the instance satisfies a "satisfactory-status-quo" assumption. Without this assumption, there are instances without any finite approximation factor. We extend the results to combinatorial domains and obtain prophet inequalities for matching with multiple hires and multiple receivers.