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We consider a truthful facility location problem with agents that have private positions on the line of real numbers and known optional preferences over two obnoxious facilities that must be placed at locations chosen from a given set of candidate ones. Each agent wants to be as far away as possible from the facilities that affect her, and our goal is to design mechanisms that decide where to place the facilities so as to maximize the total happiness of the agents as well as provide the right incentives to them to truthfully report their positions. We consider separately the setting in which all agents are affected by both facilities (i.e., they have non-optional preferences) and the general optional setting. We show tight bounds on the approximation ratio of deterministic strategyproof mechanisms for both settings, and almost tight bounds for randomized mechanisms.

We consider a truthful facility location problem in which there is a set of agents with private locations on the line of real numbers, and the goal is to place a number of facilities at different locations chosen from the set of those reported by the agents. Given a feasible solution, each agent suffers an individual cost that is either its total distance to all facilities (sum-variant) or its distance to the farthest facility (max-variant). For both variants, we show tight bounds on the approximation ratio of strategyproof mechanisms in terms of the social cost, the total individual cost of the agents.

We consider a voting problem in which a set of agents have metric preferences over a set of alternatives, and are also partitioned into disjoint groups. Given information about the preferences of the agents and their groups, our goal is to decide an alternative to approximately minimize an objective function that takes the groups of agents into account. We consider two natural group-fair objectives known as Max-of-Avg and Avg-of-Max which are different combinations of the max and the average cost in and out of the groups. We show tight bounds on the best possible distortion that can be achieved by various classes of mechanisms depending on the amount of information they have access to. In particular, we consider group-oblivious full-information mechanisms that do not know the groups but have access to the exact distances between agents and alternatives in the metric space, group-oblivious ordinal-information mechanisms that again do not know the groups but are given the ordinal preferences of the agents, and group-aware mechanisms that have full knowledge of the structure of the agent groups and also ordinal information about the metric space.

We consider a problem where agents have private positions on a line, and public approval preferences over two facilities, and their cost is the maximum distance from their approved facilities. The goal is to decide the facility locations to minimize the total and the max cost, while incentivizing the agents to be truthful. We design a strategyproof mechanism that is simultaneously $11$- and $5$-approximate for these two objective functions, thus improving the previously best-known bounds of $2n+1$ and $9$.

We initiate the study of a novel problem in mechanism design without money, which we term Truthful Interval Covering (TIC). An instance of TIC consists of a set of agents each associated with an individual interval on a line, and the objective is to decide where to place a covering interval to minimize the total social or egalitarian cost of the agents, which is determined by the intersection of this interval with their individual ones. This fundamental problem can model situations of provisioning a public good, such as the use of power generators to prevent or mitigate load shedding in developing countries. In the strategic version of the problem, the agents wish to minimize their individual costs, and might misreport the position and/or length of their intervals to achieve that. Our goal is to design truthful mechanisms to prevent such strategic misreports and achieve good approximations to the best possible social or egalitarian cost. We consider the fundamental setting of known intervals with equal lengths and provide tight bounds on the approximation ratios achieved by truthful deterministic mechanisms. For the social cost, we also design a randomized truthful mechanism that outperforms all possible deterministic ones. Finally, we highlight a plethora of natural extensions of our model for future work, as well as some natural limitations of those settings.

Recently, strategic games inspired by Schelling's influential model of residential segregation have been studied in the TCS and AI literature. In these games, agents of k different types occupy the nodes of a network topology aiming to maximize their utility, which is a function of the fraction of same-type agents they are adjacent to in the network. As such, the agents exhibit similarity seeking strategic behavior. In this paper, we introduce a class of strategic jump games in which the agents are diversity-seeking: The utility of an agent is defined as the fraction of its neighbors that are of different type than itself. We show that in general it is computationally hard to determine the existence of an equilibrium in such games. However, when the network is a tree, diversity-seeking jump games always admit an equilibrium assignment. For regular graphs and spider graphs with a single empty node, we prove a stronger result: The game is potential, that is, the improving response dynamics always converge to an equilibrium from any initial placement of the agents. We also show (nearly tight) bounds on the price of anarchy and price of stability in terms of the social welfare (the total utility of the agents).

We consider a social choice setting in which agents and alternatives are represented by points in a metric space, and the cost of an agent for an alternative is the distance between the corresponding points in the space. The goal is to choose a single alternative to (approximately) minimize the social cost (cost of all agents) or the maximum cost of any agent, when only limited information about the preferences of the agents is given. Previous work has shown that the best possible distortion one can hope to achieve is $3$ when access to the ordinal preferences of the agents is given, even when the distances between alternatives in the metric space are known. We improve upon this bound of $3$ by designing deterministic mechanisms that exploit a bit of cardinal information. We show that it is possible to achieve distortion $1+\sqrt{2}$ by using the ordinal preferences of the agents, the distances between alternatives, and a threshold approval set per agent that contains all alternatives for whom her cost is within an appropriately chosen factor of her cost for her most-preferred alternative. We show that this bound is the best possible for any deterministic mechanism in general metric spaces, and also provide improved bounds for the fundamental case of a line metric.

We study a truthful two-facility location problem in which a set of agents have private positions on the line of real numbers and known approval preferences over two different facilities. Given the locations of the two facilities, the cost of an agent is the total distance from the facilities she approves. The goal is to decide where to place the facilities from a given finite set of candidate locations so as to (a) approximately optimize desired social objectives, and (b) incentivize the agents to truthfully report their private positions. We focus on the class of deterministic strategyproof mechanisms and show bounds on their approximation ratio in terms of the social cost (i.e., the total cost of the agents) and the max cost for several classes of instances depending on the preferences of the agents over the facilities.

We consider a setting with agents that have preferences over alternatives and are partitioned into disjoint districts. The goal is to choose one alternative as the winner using a mechanism which first decides a representative alternative for each district based on a local election with the agents therein as participants, and then chooses one of the district representatives as the winner. Previous work showed bounds on the distortion of a specific class of deterministic plurality-based mechanisms depending on the available information about the preferences of the agents in the districts. In this paper, we first consider the whole class of deterministic mechanisms and show asymptotically tight bounds on their distortion. We then initiate the study of the distortion of randomized mechanisms in distributed voting and show bounds based on several informational assumptions, which in many cases turn out to be tight. Finally, we also experimentally compare the distortion of many different mechanisms of interest using synthetic and real-world data., Comment: Accepted to AAMAS 2023

We consider the distributed single-winner metric voting problem on a line, where agents and alternative are represented by points on the line of real numbers, the agents are partitioned into disjoint districts, and the goal is to choose a single winning alternative in a decentralized manner. In particular, the choice is done by a distributed voting mechanism which first selects a representative alternative for each district of agents and then chooses one of these representatives as the winner. In this paper, we design simple distributed mechanisms that achieve distortion at most $2+\sqrt{5}$ for the average-of-max and the max-of-average social cost objectives, matching the corresponding lower bound shown in previous work for these objectives.

We study the distributed facility location problem, where a set of agents with positions on the line of real numbers are partitioned into disjoint districts, and the goal is to choose a point to satisfy certain criteria, such as optimize an objective function or avoid strategic behavior. A mechanism in our distributed setting works in two steps: For each district it chooses a point that is representative of the positions reported by the agents in the district, and then decides one of these representative points as the final output. We consider two classes of mechanisms: Unrestricted mechanisms which assume that the agents directly provide their true positions as input, and strategyproof mechanisms which deal with strategic agents and aim to incentivize them to truthfully report their positions. For both classes, we show tight bounds on the best possible approximation in terms of several minimization social objectives, including the well-known social cost (total distance of agents from chosen point) and max cost (maximum distance among all agents from chosen point), as well as other fairness-inspired objectives that are tailor-made for the distributed setting., Comment: Accepted to AAMAS 2023

In this article we survey the main research topics of our group at the University of Essex. Our research interests lie at the intersection of theoretical computer science, artificial intelligence, and economic theory. In particular, we focus on the design and analysis of mechanisms for systems involving multiple strategic agents, both from a theoretical and an applied perspective. We present an overview of our group's activities, as well as its members, and then discuss in detail past, present, and future work in multi-agent systems.

Allocating resources to individuals in a fair manner has been a topic of interest since ancient times, with most of the early mathematical work on the problem focusing on resources that are infinitely divisible. Over the last decade, there has been a surge of papers studying computational questions regarding the indivisible case, for which exact fairness notions such as envy-freeness and proportionality are hard to satisfy. One main theme in the recent research agenda is to investigate the extent to which their relaxations, like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can be achieved. In this survey, we present a comprehensive review of the recent progress made in the related literature by highlighting different ways to relax fairness notions, common algorithm design techniques, and the most interesting questions for future research., Comment: This survey unifies and extends preliminary versions that appeared in IJCAI 2022 (arXiv:2202.07551) and SIGecom Exchanges (arXiv:2202.08713). It has been accepted for publication to the journal of Artificial Intelligence (AIJ)

In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social welfare, since the values of the agents remain virtually unknown. This loss in performance because of lack of information is measured by the notion of distortion. A recent array of works put forward the agenda of designing mechanisms that learn the values of the agents for a small number of alternatives via queries, and use this limited extra information to make better-informed decisions, thus improving distortion. Following this agenda, in this work we focus on a class of combinatorial problems that includes most well-known matching problems and several of their generalizations, such as One-Sided Matching, Two-Sided Matching, General Graph Matching, and $k$-Constrained Resource Allocation. We design two-query mechanisms that achieve the best-possible worst-case distortion in terms of social welfare, and outperform the best-possible expected distortion achieved by randomized ordinal mechanisms., Comment: A conference version of this work was accepted in the 36th Conference on Neural Information Processing Systems (NeurIPS 2022)

Allocating resources to individuals in a fair manner has been a topic of interest since the ancient times, with most of the early rigorous mathematical work on the problem focusing on infinitely divisible resources. Recently, there has been a surge of papers studying computational questions regarding various different notions of fairness for the indivisible case, like maximin share fairness (MMS) and envy-freeness up to any good (EFX). We survey the most important results in the discrete fair division literature, focusing on the case of additive valuation functions and paying particular attention to the progress made in the last 10 years.

We extend the recently introduced framework of metric distortion to multiwinner voting. In this framework, $n$ agents and $m$ alternatives are located in an underlying metric space. The exact distances between agents and alternatives are unknown. Instead, each agent provides a ranking of the alternatives, ordered from the closest to the farthest. Typically, the goal is to select a single alternative that approximately minimizes the total distance from the agents, and the worst-case approximation ratio is termed distortion. In the case of multiwinner voting, the goal is to select a committee of $k$ alternatives that (approximately) minimizes the total cost to all agents. We consider the scenario where the cost of an agent for a committee is her distance from the $q$-th closest alternative in the committee. We reveal a surprising trichotomy on the distortion of multiwinner voting rules in terms of $k$ and $q$: The distortion is unbounded when $q \leq k/3$, asymptotically linear in the number of agents when $k/3 < q \leq k/2$, and constant when $q > k/2$., Comment: A preliminary version of this paper appears in AAAI 2022

We revisit the discrete heterogeneous two-facility location problem, in which there is a set of agents that occupy nodes of a line graph, and have private approval preferences over two facilities. When the facilities are located at some nodes of the line, each agent derives a cost that is equal to her total distance from the facilities she approves. The goal is to decide where to locate the two facilities, so as to (a) incentivize the agents to truthfully report their preferences, and (b) achieve a good approximation of the minimum total (social) cost or the maximum cost among all agents. For both objectives, we design deterministic strategyproof mechanisms with approximation ratios that significantly outperform the state-of-the-art, and complement these results with (almost) tight lower bounds.

We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives. Our goal is to choose a single alternative aiming to optimize various objectives that are functions of the distances between agents and alternatives in the metric space, under the constraint that this choice must be made in a distributed way: The preferences of the agents within each group are first aggregated into a representative alternative for the group, and then these group representatives are aggregated into the final winner. Deciding the winner in such a way naturally leads to loss of efficiency, even when complete information about the metric space is available. We provide a series of (mostly tight) bounds on the distortion of distributed mechanisms for variations of well-known objectives, such as the (average) total cost and the maximum cost, and also for new objectives that are particularly appropriate for this distributed setting and have not been studied before.

We initiate the study of the heterogeneous facility location problem with limited resources. We mainly focus on the fundamental case where a set of agents are positioned in the line segment [0,1] and have approval preferences over two available facilities. A mechanism takes as input the positions and the preferences of the agents, and chooses to locate a single facility based on this information. We study mechanisms that aim to maximize the social welfare (the total utility the agents derive from facilities they approve), under the constraint of incentivizing the agents to truthfully report their positions and preferences. We consider three different settings depending on the level of agent-related information that is public or private. For each setting, we design deterministic and randomized strategyproof mechanisms that achieve a good approximation of the optimal social welfare, and complement these with nearly-tight impossibility results.

Schelling's famous model of segregation assumes agents of different types who would like to be located in neighborhoods having at least a certain fraction of agents of the same type. We consider natural generalizations that allow for the possibility of agents being tolerant towards other agents, even if they are not of the same type. In particular, we consider an ordering of the types, and make the realistic assumption that the agents are in principle more tolerant towards agents of types that are closer to their own according to the ordering. Based on this, we study the strategic games induced when the agents aim to maximize their utility, for a variety of tolerance levels. We provide a collection of results about the existence of equilibria, and their quality in terms of social welfare.

The notion of distortion in social choice problems has been defined to measure the loss in efficiency -- typically measured by the utilitarian social welfare, the sum of utilities of the participating agents -- due to having access only to limited information about the preferences of the agents. We survey the most significant results of the literature on distortion from the past 15 years, and highlight important open problems and the most promising avenues of ongoing and future work., Comment: Survey

Schelling's model is an influential model that reveals how individual perceptions and incentives can lead to residential segregation. Inspired by a recent stream of work, we study welfare guarantees and complexity in this model with respect to several welfare measures. First, we show that while maximizing the social welfare is NP-hard, computing an assignment of agents to the nodes of any topology graph with approximately half of the maximum welfare can be done in polynomial time. We then consider Pareto optimality, introduce two new optimality notions based on it, and establish mostly tight bounds on the worst-case welfare loss for assignments satisfying these notions as well as the complexity of computing such assignments. In addition, we show that for tree topologies, it is possible to decide whether there exists an assignment that gives every agent a positive utility in polynomial time; moreover, when every node in the topology has degree at least $2$, such an assignment always exists and can be found efficiently., Comment: Appears in the 35th AAAI Conference on Artificial Intelligence (AAAI), 2021

We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the social welfare. Most of the related literature, however, assumes that the values of the agents are not a priori known, and only access to the ordinal preferences of the agents over the items is provided. Consequently, this incomplete information leads to loss of efficiency, which is measured by the notion of distortion. In this paper, we further assume that the agents can answer a small number of queries, allowing us partial access to their values. We study the interplay between elicited cardinal information (measured by the number of queries per agent) and distortion for one-sided matching, as well as a wide range of well-studied related problems. Qualitatively, our results show that with a limited number of queries, it is possible to obtain significant improvements over the classic setting, where only access to ordinal information is given.

We study the efficiency of simple combinatorial auctions for the allocation of a set of items to a set of agents, with private subadditive valuation functions and budget constraints. The class we consider includes all auctions that allocate each item independently to the agent that submits the highest bid for it, and requests a payment that depends on the bids of all agents only for this item. Two well-known examples of this class are the simultaneous first and second price auctions. We focus on the pure equilibria of the induced strategic games, and using the liquid welfare as our efficiency benchmark, we show an upper bound of 2 on the price of anarchy for any auction in this class, as well as a tight corresponding lower bound on the price of stability for all auctions whose payment rules are convex combinations of the bids. This implies a tight bound of 2 on the price of stability of the well-known simultaneous first and second price auctions, which are members of the class. Additionally, we show lower bounds for the whole class, for more complex auctions (like VCG), and for settings where the budgets are assumed to be common knowledge rather than private information., Comment: Accepted to Theoretical Computer Science

We consider a single-facility location problem, where agents are positioned on the real line and are partitioned into multiple disjoint districts. The goal is to choose a location (where a public facility is to be built) so as to minimize the total distance of the agents from it. This process is distributed: the positions of the agents in each district are first aggregated into a representative location for the district, and then one of the district representatives is chosen as the facility location. This indirect access to the positions of the agents inevitably leads to inefficiency, which is captured by the notion of distortion. We study the discrete version of the problem, where the set of alternative locations is finite, as well as the continuous one, where every point of the line is an alternative, and paint an almost complete picture of the distortion landscape of both general and strategyproof distributed mechanisms.

Recent results in the ML community have revealed that learning algorithms used to compute the optimal strategy for the leader to commit to in a Stackelberg game, are susceptible to manipulation by the follower. Such a learning algorithm operates by querying the best responses or the payoffs of the follower, who consequently can deceive the algorithm by responding as if his payoffs were much different than what they actually are. For this strategic behavior to be successful, the main challenge faced by the follower is to pinpoint the payoffs that would make the learning algorithm compute a commitment so that best responding to it maximizes the follower's utility, according to his true payoffs. While this problem has been considered before, the related literature only focused on the simplified scenario in which the payoff space is finite, thus leaving the general version of the problem unanswered. In this paper, we fill in this gap, by showing that it is always possible for the follower to compute (near-)optimal payoffs for various scenarios about the learning interaction between leader and follower.

We introduce the class of modified Schelling games in which there are different types of agents who occupy the nodes of a location graph; agents of the same type are friends, and agents of different types are enemies. Every agent is strategic and jumps to empty nodes of the graph aiming to maximize her utility, defined as the ratio of her friends in her neighborhood over the neighborhood size including herself. This is in contrast to the related literature on Schelling games which typically assumes that an agent is excluded from her neighborhood whilst computing its size. Our model enables the utility function to capture likely cases where agents would rather be around a lot of friends instead of just a few, an aspect that was partially ignored in previous work. We provide a thorough analysis of the (in)efficiency of equilibria that arise in such modified Schelling games, by bounding the price of anarchy and price of stability for both general graphs and interesting special cases. Most of our results are tight and exploit the structure of equilibria as well as sophisticated constructions.

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.

We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple types; each agent either occupies a node of the graph and never moves away or aims to maximize the fraction of her neighbors who are of her own type. We consider a variant of this model that we call swap Schelling games, where the number of agents is equal to the number of nodes of the graph, and agents may {\em swap} positions with other agents to increase their utility. We study the existence, computational complexity and quality of equilibrium assignments in these games, both from a social welfare perspective and from a diversity perspective., Comment: AAAI 2020

Aggregating the preferences of individuals into a collective decision is the core subject of study of social choice theory. In 2006, Procaccia and Rosenschein considered a utilitarian social choice setting, where the agents have explicit numerical values for the alternatives, yet they only report their linear orderings over them. To compare different aggregation mechanisms, Procaccia and Rosenschein introduced the notion of distortion, which quantifies the inefficiency of using only ordinal information when trying to maximize the social welfare, i.e., the sum of the underlying values of the agents for the chosen outcome. Since then, this research area has flourished and bounds on the distortion have been obtained for a wide variety of fundamental scenarios. However, the vast majority of the existing literature is focused on the case where nothing is known beyond the ordinal preferences of the agents over the alternatives. In this paper, we take a more expressive approach, and consider mechanisms that are allowed to further ask a few cardinal queries in order to gain partial access to the underlying values that the agents have for the alternatives. With this extra power, we design new deterministic mechanisms that achieve significantly improved distortion bounds and, in many cases, outperform the best-known randomized ordinal mechanisms. We paint an almost complete picture of the number of queries required by deterministic mechanisms to achieve specific distortion bounds.

Complexity of voting manipulation is a prominent topic in computational social choice. In this work, we consider a two-stage voting manipulation scenario. First, a malicious party (an attacker) attempts to manipulate the election outcome in favor of a preferred candidate by changing the vote counts in some of the voting districts. Afterwards, another party (a defender), which cares about the voters' wishes, demands a recount in a subset of the manipulated districts, restoring their vote counts to their original values. We investigate the resulting Stackelberg game for the case where votes are aggregated using two variants of the Plurality rule, and obtain an almost complete picture of the complexity landscape, both from the attacker's and from the defender's perspective.

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been significant progress towards this goal, all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a setting in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the final outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data.

We consider the house allocation problem, where $m$ houses are to be assigned to $n$ agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor.

We consider strategic games that are inspired by Schelling's model of residential segregation. In our model, the agents are partitioned into k types and need to select locations on an undirected graph. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. We investigate the existence of equilibria in these games, study the complexity of finding an equilibrium outcome or an outcome with high social welfare, and also provide upper and lower bounds on the price of anarchy and stability. Some of our results extend to the setting where the preferences of the agents over their neighbors are defined by a social network rather than a partition into types.

We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness. We consider the existence of fair allocations under different assumptions on the valuations of the agents. In particular, our results cover cases of arbitrary monotonic, responsive, and additive valuations, while for the case of binary valuations we fully characterize the cardinalities of two groups of agents for which a fair allocation can be guaranteed with respect to both envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). Moreover, we introduce a new model where the agents are not partitioned into groups in advance, but instead the partition can be chosen in conjunction with the allocation of the goods. In this model, we show that for agents with arbitrary monotonic valuations, there is always a partition of the agents into two groups of any given sizes along with an EF1 allocation of the goods. We also provide an extension of this result to any number of groups., Comment: Appears in the 28th International Joint Conference on Artificial Intelligence (IJCAI), 2019

We study the fundamental problem of distributed network formation among mobile agents of limited computational power that aim to achieve energy balance by wirelessly transmitting and receiving energy in a peer-to-peer manner. Specifically, we design simple distributed protocols consisting of a small number of states and interaction rules for the formation of arbitrary and k-ary tree networks. Furthermore, we evaluate (theoretically and also using computer simulations) a plethora of energy redistribution protocols that exploit different levels of knowledge in order to achieve desired energy distributions among the agents which require that every agent has exactly or at least twice the energy of the agents of higher depth, according to the structure of the network. Our study shows that without using any knowledge about the network structure, such energy distributions cannot be achieved in a timely manner, meaning that there might be high energy loss during the redistribution process. On the other hand, only a few extra bits of information seem to be enough to guarantee quick convergence to energy distributions that satisfy particular properties, yielding low energy loss.

We study the social efficiency of several well-known mechanisms for the allocation of a set of available (advertising) positions to a set of competing budget-constrained users (advertisers). Specifically, we focus on the Generalized Second Price auction (GSP), the Vickrey-Clarke-Groves mechanism (VCG) and the Expressive Generalized First Price auction (EGFP). Using the liquid welfare as our efficiency benchmark, we prove a tight bound of 2 on the liquid price of anarchy and stability of these mechanisms for pure Nash equilibria., Comment: Accepted to Information Processing Letters

When a company undergoes a merger or transfers its ownership, the existing governing body has an opinion on which buyer should take over as the new owner. Similar situations occur while assigning the host of big sports tournaments, like the World Cup or the Olympics. In all these settings, the values of the external bidders are as important as the opinions of the internal experts. Motivated by such scenarios, we consider a social welfare maximizing approach to design and analyze truthful mechanisms in {\em hybrid social choice} settings, where payments can be imposed to the bidders, but not to the experts. Since this problem is a combination of mechanism design with and without monetary transfers, classical solutions like VCG cannot be applied, making this a novel mechanism design problem. We consider the simple but fundamental scenario with one expert and two bidders, and provide tight approximation guarantees of the optimal social welfare. We distinguish between mechanisms that use ordinal and cardinal information, as well as between mechanisms that base their decisions on one of the two sides (either the bidders or the expert) or both. Our analysis shows that the cardinal setting is quite rich and admits several non-trivial randomized truthful mechanisms, and also allows for closer-to-optimal welfare guarantees.

We investigate the interesting impact of mobility on the problem of efficient wireless power transfer in ad hoc networks. We consider a set of mobile agents (consuming energy to perform certain sensing and communication tasks), and a single static charger (with finite energy) which can recharge the agents when they get in its range. In particular, we focus on the problem of efficiently computing the appropriate range of the charger with the goal of prolonging the network lifetime. We first demonstrate (under the realistic assumption of fixed energy supplies) the limitations of any fixed charging range and, therefore, the need for (and power of) a dynamic selection of the charging range, by adapting to the behavior of the mobile agents which is revealed in an online manner. We investigate the complexity of optimizing the selection of such an adaptive charging range, by showing that two simplified offline optimization problems (closely related to the online one) are NP-hard. To effectively address the involved performance trade-offs, we finally present a variety of adaptive heuristics, assuming different levels of agent information regarding their mobility and energy.

We study the efficiency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such a mechanism decides the fraction of the resource that each user will receive and a payment that will be collected from her. Users are self-interested and aim to maximize their utility (defined as their value for the resource fraction they receive minus their payment). Starting with the seminal work of Johari and Tsitsiklis [Mathematics of Operations Research, 2004], a long list of papers studied the price of anarchy (in terms of the social welfare --- the total users' value) of resource allocation mechanisms for a variety of allocation and payment rules. Here, we further assume that each user has a budget constraint that invalidates strategies that yield a payment that is higher than the user's budget. This subtle assumption, which is arguably more realistic, constitutes the traditional price of anarchy analysis meaningless as the set of equilibria may change drastically and their social welfare can be arbitrarily far from optimal. Instead, we study the price of anarchy using the liquid welfare benchmark that measures efficiency taking budget constraints into account. We show a tight bound of 2 on the liquid price of anarchy of the well-known Kelly mechanism and prove that this result is essentially best possible among all multi-user resource allocation mechanisms. This comes in sharp contrast to the no-budget setting where there are mechanisms that considerably outperform Kelly in terms of social welfare and even achieve full efficiency. In our proofs, we exploit the particular structure of worst-case games and equilibria, which also allows us to design (nearly) optimal two-player mechanisms by solving simple differential equations.

Social networks on the Internet have seen an enormous growth recently and play a crucial role in different aspects of today's life. They have facilitated information dissemination in ways that have been beneficial for their users but they are often used strategically in order to spread information that only serves the objectives of particular users. These properties have inspired a revision of classical opinion formation models from sociology using game-theoretic notions and tools. We follow the same modeling approach, focusing on scenarios where the opinion expressed by each user is a compromise between her internal belief and the opinions of a small number of neighbors among her social acquaintances. We formulate simple games that capture this behavior and quantify the inefficiency of equilibria using the well-known notion of the price of anarchy. Our results indicate that compromise comes at a cost that strongly depends on the neighborhood size., Comment: 36 pages, 10 figures