Motivated by applications of multi-agent learning in noisy environments, this paper studies the robustness of gradient-based learning dynamics with respect to disturbances. While disturbances injected along a coordinate corresponding to any individual player's actions can always affect the overall learning dynamics, a subset of players can be disturbance decoupled---i.e., such players' actions are

We study secretary problems in settings with multiple agents. In the standard secretary problem, a sequence of arbitrary awards arrive online, in a random order, and a single decision maker makes an immediate and irrevocable decision whether to accept each award upon its arrival. The requirement to make immediate decisions arises in many cases due to an implicit assumption regarding competition. Namely

In order to drive effectively, a driver must be aware of how they can expect other vehicles' behaviour to be affected by their decisions, and also how they are expected to behave by other drivers. One common family of methods for addressing this problem of interaction are those based on Game Theory. Such approaches often make assumptions about leaders and followers in an interaction which can result

The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each successive matching is obtained by satisfying a blocking pair. The sequence produced by Roth and Vande Vate's algorithm is of length $O(n^3)$ where $n$ is the number

We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react when agents

In this note, we prove two new impossibility results for random assignment mechanisms: Bogomolnaia and Moulin (2001) showed that no assignment mechanism can satisfy strategyproofness, ordinal efficiency, and symmetry at the same time, and Mennle and Seuken (2017) gave a decomposition of strategyproofness into the axioms swap monotonicity, upper invariance, and lower invariance. For our first impossibility

In (Mennle and Seuken, 2017), we have introduced partial strategyproofness, a new, relaxed notion of strategyproofness, to study the incentive properties of non-strategyproof assignment mechanisms. In this paper, we present results pertaining to local sufficiency for partial strategyproofness: We show that, for any r in [0,1], r-local partial strategyproofness implies r^2-partial strategyproofness

Envy-free up to one good (EF1) and envy-free up to any good (EFX) are two well-known extensions of envy-freeness for the case of indivisible items. It is shown that EF1 can always be guaranteed for agents with subadditive valuations. In sharp contrast, it is unknown whether or not an EFX allocation always exists, even for four agents and additive valuations. In addition, the best approximation guarantee

Consider a two-class unobservable priority queue, with Poisson arrivals, generally distributed service, and strategic customers. Customers are charged a fee when joining the premium class. We analyze the maximum revenue achievable under the non-preemptive (NP) and preemptive-resume (PR) policies, and show that a provider is always better off implementing the PR policy. Further, the maximum revenue

Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work has shown that when the resource is represented by an interval, a consensus halving with at most $n$ cuts always exists, but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting where the

We propose a multi-agent variant of the classical multi-armed bandit problem, in which there are N agents and K arms, and pulling an arm generates a (possibly different) stochastic reward to each agent. Unlike the classical multi-armed bandit problem, the goal is not to learn the "best arm", as each agent may perceive a different arm as best for her. Instead, we seek to learn a fair distribution over

The uncertainties in plant dynamics remain a challenge for nonlinear control problems. This paper develops a ternary policy iteration (TPI) algorithm for solving nonlinear robust control problems with bounded uncertainties. The controller and uncertainty of the system are considered as game players, and the robust control problem is formulated as a two-player zero-sum differential game. In order to

A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity

We consider the distributed facility location problem, in which there is a set of agents positioned on the real line, who are also partitioned into multiple symmetric districts. The goal is to choose a single location (where a public facility is to be built) so as to minimize the total distance of the agents from that location. Importantly, this process is distributed: the positions of the agents in

In the allocation of resources to a set of agents, how do fairness guarantees impact the social welfare? A quantitative measure of this impact is the price of fairness, which measures the worst-case loss of social welfare due to fairness constraints. While initially studied for divisible goods, recent work on the price of fairness also studies the setting of indivisible goods. In this paper, we resolve

We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -- maximum Nash welfare (MNW) -- provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic

The operation of future intelligent transportation systems (ITSs), communications infrastructure (CI), and power grids (PGs) will be highly interdependent. In particular, autonomous connected vehicles require CI resources to operate, and, thus, communication failures can result in non-optimality in the ITS flow in terms of traffic jams and fuel consumption. Similarly, CI components, e.g., base stations

We study the problem of finding equilibrium strategies in multi-agent games with incomplete payoff information, where the payoff matrices are only known to the players up to some bounded uncertainty sets. In such games, an ex-post equilibrium characterizes equilibrium strategies that are robust to the payoff uncertainty. When the game is one-shot, we show that in zero-sum polymatrix games, an ex-post

We consider a setting where individuals interact in a network, each choosing actions which optimize utility as a function of neighbors' actions. A central authority aiming to maximize social welfare at equilibrium can intervene by paying some cost to shift individual incentives, and the optimal intervention can be computed using the spectral decomposition of the graph, yet this is infeasible in practice

We seek to understand the fundamental mathematics governing infrastructure-scale interactions between humans and machines, particularly when the machines' intended purpose is to influence and optimize the behavior of the humans. To that end, this paper investigates the worst-case congestion that can arise in nonatomic network congestion games when a fraction of the traffic is completely altruistic

The model of streaming algorithms is motivated by the increasingly common situation in which the sheer amount of available data limits the ways in which the data can be accessed. Streaming algorithms are typically allowed a single pass over the data and can only store a sublinear fraction of the data at any time. We initiate the study of classic online selection problems in a streaming model where

We consider a revenue-maximizing single seller with $m$ items for sale to a single buyer whose value $v(\cdot)$ for the items is drawn from a known distribution $D$ of support $k$. A series of works by Cai et al. establishes that when each $v(\cdot)$ in the support of $D$ is additive or unit-demand (or $c$-demand), the revenue-optimal auction can be found in $\operatorname{poly}(m,k)$ time. We show

Data mining and knowledge discovery are two important growing research fields in the last two decades due to the abundance of data collected from various sources. The exponentially growing volumes of generated data urge the development of several mining techniques to feed the needs for automatically derived knowledge. Clustering analysis (finding similar groups of data) is a well-established and widely

Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending previous results, we show that various game theoretic properties of convex-concave two-player zero-sum games are preserved in this generalization. We then generalize

The spontaneous behavioral changes of the agents during an epidemic can have significant effects on the delay and the prevalence of its spread. In this work, we study a social distancing game among the agents of a population, who determine their social interactions during the spread of an epidemic. The interconnections between the agents are modeled by a network and local interactions are considered

We introduce the model of line-up elections which captures parallel or sequential single-winner elections with a shared candidate pool. The goal of a line-up election is to find a high-quality assignment of a set of candidates to a set of positions such that each position is filled by exactly one candidate and each candidate fills at most one position. A score for each candidate-position pair is given

We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several "desirable" manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable solution, and this may be achieved by the manipulative action of reordering some agents' preference lists. We present a comprehensive study of the computational

The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of $\min(m,n)$, where $n$ is the number of machines and $m$ is the number of jobs. They also proved that no truthful mechanism

First-price auctions have very recently swept the online advertising industry, replacing second-price auctions as the predominant auction mechanism on many platforms. This shift has brought forth important challenges for a bidder: how should one bid in a first-price auction, where unlike in second-price auctions, it is no longer optimal to bid one's private value truthfully and hard to know the others'

Flows over time enable a mathematical modeling of traffic that changes as time progresses. In order to evaluate these dynamic flows from a game theoretical perspective we consider the price of anarchy (PoA). In this paper we study the impact of spillback effects on the PoA, which turn out to be substantial. It is known that, in general, the PoA is unbounded in the spillback setting. We extend this

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX$_0$, EFX$^3$ and EF1$^3$ - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1$^3$ allocation. With $-\alpha/0/\alpha$

We study the extent to which decentralized cost-sharing protocols can achieve good price of anarchy (PoA) bounds in network cost-sharing games with $n$ agents. We focus on the model of resource-aware protocols, where the designer has prior access to the network structure and can also increase the total cost of an edge(overcharging), and we study classes of games with concave or convex cost functions

The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain classes of stochastic smooth games. We propose a novel unbiased estimator for the stochastic Hamiltonian gradient descent (SHGD) and highlight its benefits. Using tools

This paper develops a framework for repeated matching markets. The model departs from the Gale-Shapley matching model by having a fixed set of long-lived hospitals match with a new generation of short-lived residents in every period. I show that there are two kinds of hospitals in this repeated environment: some hospitals can be motivated dynamically to voluntarily reduce their hiring capacity, potentially

We introduce the Stackelberg kidney exchange problem. In this problem, an agent (e.g. a hospital or a national organization) has control over a number of incompatible patient-donor pairs whose patients are in need of a transplant. The agent has the opportunity to join a collaborative effort which aims to increase the maximum total number of transplants that can be realized. However, the individual

It can be profitable for vehicle service providers to set service prices based on users' travel demand on different origin-destination pairs. The prior studies on the spatial pricing of vehicle service rely on the assumption that providers know users' demand. In this paper, we study a monopolistic provider who initially does not know users' demand and needs to learn it over time by observing the users'

We study the problem of providing blockchain applications with \emph{economically viable randomness} (EVR), namely, randomness that has significant economic consequences. Applications of EVR include blockchain-based lotteries and gambling. An EVR source guarantees (i) secrecy, assuring that the random bits are kept secret until some predefined condition indicates that they are safe to reveal (e.g.

We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety may become available to the seller at each time and a random number of consumers may enter the market at each time. Each consumer is present in the market for one

Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel combinatorial optimization problems are their generalization, encompassing situations with multiple players taking decisions sequentially. By framing them in a multi-agent

In the classic linear assignment problem, items must be assigned to agents in a manner that minimizes the sum of the costs for each item-agent assignment, where the costs of all possible item-agent pairings are observed in advance. This is a well-known and well-characterized problem, and algorithms exist to attain the solution. In contrast, less attention has been given to the dynamic version of this

This paper introduces an objective for optimizing proper scoring rules. The objective is to maximize the increase in payoff of a forecaster who exerts a binary level of effort to refine a posterior belief from a prior belief. In this framework we characterize optimal scoring rules in simple settings, give efficient algorithms for computing optimal scoring rules in complex settings, and identify simple

Adversarial risk analysis (ARA) is a relatively new area of research that informs decision-making when facing intelligent opponents and uncertain outcomes. It enables an analyst to express her Bayesian beliefs about an opponent's utilities, capabilities, probabilities and the type of strategic calculation that the opponent is using. Within that framework, the analyst then solves the problem from the

The bribery problem in election has received considerable attention in the literature, upon which various algorithmic and complexity results have been obtained. It is thus natural to ask whether we can protect an election from potential bribery. We assume that the protector can protect a voter with some cost (e.g., by isolating the voter from potential bribers). A protected voter cannot be bribed.

This paper seeks to establish a framework for directing a society of simple, specialized, self-interested agents to solve what traditionally are posed as monolithic single-agent sequential decision problems. What makes it challenging to use a decentralized approach to collectively optimize a central objective is the difficulty in characterizing the equilibrium strategy profile of non-cooperative games

In this work, we analyze a sequential game played in a graph called the Multilevel Critical Node problem (MCN). A defender and an attacker are the players of this game. The defender starts by preventively interdicting vertices (vaccination) from being attacked. Then, the attacker infects a subset of non-vaccinated vertices and, finally, the defender reacts with a protection strategy. We provide the

Off-policy evaluation (OPE) is the problem of evaluating new policies using historical data obtained from a different policy. Off-policy learning (OPL), on the other hand, is the problem of finding an optimal policy using historical data. In recent OPE and OPL contexts, most of the studies have focused on one-player cases, and not on more than two-player cases. In this study, we propose methods for

Approval-based committee (ABC) rules are voting rules that output a fixed-size subset of candidates, a so-called committee. ABC rules select committees based on dichotomous preferences, i.e., a voter either approves or disapproves a candidate. This simple type of preferences makes ABC rules widely suitable for practical use. In this survey, we summarize the current understanding of ABC rules from the

In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents suffice for an

Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its destination as fast as possible, the dynamic equilibria are called Nash flows over time. So far, this model has only been considered for networks in which each arc

We consider the facility location problem in two dimensions. In particular, we consider a setting where agents have Euclidean preferences, defined by their ideal points, for a facility to be located in $\mathbb{R}^2$. For the utilitarian objective and an odd number of agents, we show that the coordinate-wise median mechanism (CM) has a worst-case approximation ratio (WAR) of $\sqrt{2}\frac{\sqrt{n^2+1}}{n+1}$

Real-Time Bidding (RTB) display advertising is a method for purchasing display advertising inventory in auctions that occur within milliseconds. The performance of RTB campaigns is generally measured with a series of Key Performance Indicators (KPIs) - measurements used to ensure that the campaign is cost-effective and that it is purchasing valuable inventory. While an RTB campaign should ideally meet

We consider sender-receiver games, where the sender and the receiver are two distinct nodes in a communication network. Communication between the sender and the receiver is thus indirect. We ask when it is possible to robustly implement the equilibrium outcomes of the direct communication game as equilibrium outcomes of indirect communication games on the network. Robust implementation requires that:

Advanced Persistent Threats (APTs) are stealthy attacks that threaten the security and privacy of sensitive information. Interactions of APTs with victim system introduce information flows that are recorded in the system logs. Dynamic Information Flow Tracking (DIFT) is a promising detection mechanism for detecting APTs. DIFT taints information flows originating at system entities that are susceptible

In many game settings, the game is not explicitly given but is only accessible by playing it. While there have been impressive demonstrations in such settings, prior techniques have not offered safety guarantees, that is, guarantees on the game-theoretic exploitability of the computed strategies. In this paper we introduce an approach that shows that it is possible to provide exploitability guarantees

We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability---which is a strictly

This paper presents a recursive reasoning formalism of Bayesian optimization (BO) to model the reasoning process in the interactions between boundedly rational, self-interested agents with unknown, complex, and costly-to-evaluate payoff functions in repeated games, which we call Recursive Reasoning-Based BO (R2-B2). Our R2-B2 algorithm is general in that it does not constrain the relationship among

We consider three important challenges in conference peer review: (i) reviewers maliciously attempting to get assigned to certain papers to provide positive reviews, possibly as part of quid-pro-quo arrangements with the authors; (ii) "torpedo reviewing," where reviewers deliberately attempt to get assigned to certain papers that they dislike in order to reject them; (iii) reviewer de-anonymization

Many non-trivial sequential decision-making problems are efficiently solved by relying on Bellman's optimality principle, i.e., exploiting the fact that sub-problems are nested recursively within the original problem. Here we show how it can apply to (infinite horizon) 2-player zero-sum partially observable stochastic games (zs-POSGs) by (i) taking a central planner's viewpoint, which can only reason

This paper combines two key ingredients for online algorithms - competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) - in the context of a simple online fair division model where items arrive one by one and are allocated to agents via some mechanism. We consider four such online mechanisms: the popular Ranking matching

Two simple and attractive mechanisms for the fair division of indivisible goods in an online setting are LIKE and BALANCED LIKE. We study some fundamental computational problems concerning the outcomes of these mechanisms. In particular, we consider what expected outcomes are possible, what outcomes are necessary, and how to compute their exact outcomes. In general, we show that such questions are