Abstract 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 maximize the sum of distances 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 study a truthful facility location problem where one out of k ≥ 2 available facilities must be built at a location chosen from a set of candidate ones in the interval [0,1]. This decision aims to accommodate a set of agents with private positions in [0,1] and approval preferences over the facilities; the agents act strategically and may misreport their private information to maximize their utility, which depends on the chosen facility and their distance from it. We focus on strategyproof mechanisms that incentivize the agents to act truthfully and bound the best possible approximation of the optimal social welfare (the total utility of the agents) they can achieve. We first show that deterministic mechanisms have unbounded approximation ratio, and then present a randomized mechanism with approximation ratio k, which is tight even when agents may only misreport their positions. For the restricted setting where agents may only misreport their approval preferences, we design a deterministic mechanism with approximation ratio of roughly 2.325, and establish lower bounds of 3/2 and 6/5 for deterministic and randomized mechanisms, respectively.

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 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 average social cost (average total distance of agents from the chosen point) and max cost (maximum distance among all agents from the chosen point), as well as other fairness-inspired objectives that are tailor-made for the distributed setting, in particular, the max-of-average and the average-of-max.

Directional changes (DC) have been shown to form an effective approach in algorithmic trading by converting fixed time series into event-based series and focusing on key events. Previous work has focused on forecasting the inflection point in the market and proposing new indicators under the DC framework, with just a handful of papers concerned with training and using DC indicators through machine learning. Earlier research has shown that genetic programming (GP) combining DC and physical time indicators could achieve positive returns with low risk. However, the fitness function used in that work is simply a risk-adjusted return. In this paper, we investigate whether a multi-objective optimisation approach could improve the performance of GP-based strategies in the market. We evaluate the cumulative return, risk, and rate of return of the proposed approach under 110 datasets from 10 different markets. Furthermore, we compare the proposed strategy against GP-based single objective optimisation (SOO) and buy-and-hold strategies. Our results show that the proposed approach significantly improves the cumulative return compared to SOO, from 14.29% to 62.04%, while also outperforming the buy-and-hold strategy.

Abstract. 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 suffers 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.

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.

Financial Forecasting is a popular and thriving research area that relies on indicators derived from technical and sentiment analysis. In this paper, we investigate the advantages that sentiment analysis indicators provide, by comparing their performance to that of technical indicators, when both are used individually as features into a genetic programming algorithm focusing on the maximization of the Sharpe ratio. Moreover, while previous sentiment analysis research has focused mostly on the titles of articles, in this paper we use the text of the articles and their summaries. Our goal is to explore further on all possible sentiment features and identify which features contribute the most. We perform experiments on 26 different datasets and show that sentiment analysis produces better, and statistically significant, average results than technical analysis in terms of Sharpe ratio and risk.

We consider financial networks, where nodes correspond to banks and directed labeled edges correspond to debt contracts between banks. Maximizing systemic liquidity, i.e., the total money flow, is a natural objective of any financial authority. In particular, the financial authority may offer bailout money to some bank(s) or forgive the debts of others in order to maximize liquidity, and we examine efficient ways to achieve this. We study the computational hardness of finding the optimal debt-removal and budget-constrained optimal bailout policy, respectively, and we investigate the approximation ratio provided by the greedy bailout policy compared to the optimal one. We also study financial systems from a game-theoretic standpoint. We observe that the removal of some incoming debt might be in the best interest of a bank. Assuming that a bank's well-being (i.e., utility) is aligned with the incoming payments they receive from the network, we define and analyze a game among banks who want to maximize their utility by strategically giving up some incoming payments. In addition, we extend the previous game by considering bailout payments. After formally defining the above games, we prove results about the existence and quality of pure Nash equilibria, as well as the computational complexity of finding such equilibria.

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.

Schelling's model considers $k$ types of agents each of whom needs to select a vertex on an undirected graph, where every agent prefers to neighbor agents of the same type. We are motivated by a recent line of work that studies solutions that are optimal with respect to notions related to the welfare of the agents. We explore the parameterized complexity of computing such solutions. We focus on the well-studied notions of social welfare (WO) and Pareto optimality (PO), alongside the recently proposed notions of group-welfare optimality (GWO) and utility-vector optimality (UVO), both of which lie between WO and PO. Firstly, we focus on the fundamental case where $k=2$ and there are $r$ red agents and $b$ blue agents. We show that all solution-notions we consider are $\textsf{NP}$-hard to compute even when $b=1$ and that they are $\textsf{W}[1]$-hard when parameterized by $r$ and $b$. In addition, we show that WO and GWO are $\textsf{NP}$-hard even on cubic graphs. We complement these negative results by an $\textsf{FPT}$ algorithm parameterized by $r, b$ and the maximum degree of the graph. For the general case with $k$ types of agents, we prove that for any of the notions we consider the problem is $\textsf{W}[1]$-hard when parameterized by $k$ for a large family of graphs that includes trees. We accompany these negative results with an $\textsf{XP}$ algorithm parameterized by $k$ and the treewidth of the graph.

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.

With very few exceptions, recent research in fair division has mostly focused on deterministic allocations. Deviating from this trend, we study the fairness notion of interim envy-freeness (iEF) for lotteries over allocations, which serves as a sweet spot between the too stringent notion of ex-post envy-freeness and the very weak notion of ex-ante envy-freeness. iEF is a natural generalization of envy-freeness to random allocations in the sense that a deterministic envy-free allocation is iEF (when viewed as a degenerate lottery). It is also certainly meaningful as it allows for a richer solution space, which includes solutions that are provably better than envy-freeness according to several criteria. Our analysis relates iEF to other fairness notions as well, and reveals tradeoffs between iEF and efficiency. Even though several of our results apply to general fair division problems, we are particularly interested in instances with equal numbers of agents and items where allocations are perfect matchings of the items to the agents. Envy-freeness can be trivially decided and (when it can be achieved, it) implies full efficiency in this setting. Although computing iEF allocations in matching allocation instances is considerably more challenging, we show how to compute them in polynomial time, while also maximizing several efficiency objectives. Our algorithms use the ellipsoid method for linear programming and efficient solutions to a novel variant of the bipartite matching problem as a separation oracle. We also study the extension of interim envy-freeness notion when payments to or from the agents are allowed. We present a series of results on two optimization problems, including a generalization of the classical rent division problem to random allocations using interim envy-freeness as the solution concept.

We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). In this cardinal setting, stable fractional matchings can have much larger social welfare than stable integral ones. Our goal is to understand the computational complexity of finding an optimal (i.e., welfare-maximizing) stable fractional matching. We consider both exact and approximate stability notions, and provide simple approximation algorithms with weak welfare guarantees. Our main result is that, somewhat surprisingly, achieving better approximations is computationally hard. To the best of our knowledge, these are the first computational complexity results for stable fractional matchings in the cardinal model. En route to these results, we provide a number of structural observations that could be of independent interest.

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 it is also a common belief that 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.

When learning how to play a strategy board game, one can measure the relative effectiveness of the learned policies by assessing how often a player wins and how easily these wins are scored. Experimental evidence also shows that when one of the competing players is trained by a sophisticated tutor, performance benefits also flow to the opponent. We present comprehensive experimental evidence that the level of tutor effectiveness is best demonstrated by the improvement of the tutored player's opponent, this performance change is termed the pendulum effect.

We prove a previously stated but incorrectly proved theorem: there is a diameter-3 graph in which replacing any edge $\{v, w\}$ of the graph with $\{v, w'\}$, for any vertex $w'$, does not decrease the total sum of distances from $v$ to all other nodes (a property called sum equilibrium).

Sponsored search auctions are the main source of revenue for search engines. In such an auction, a set of utility maximizing advertisers competes for a set of ad slots. The assignment of advertisers to slots depends on the bids they submit; these bids may be different than the true valuations of the advertisers for the slots. Variants of the celebrated VCG auction mechanism guarantee that advertisers act truthfully and, under some assumptions, lead to revenue or social welfare maximization. Still, the sponsored search industry mostly uses generalized second price (GSP) auctions; these auctions are known to be nontruthful and suboptimal in terms of social welfare and revenue. In an attempt to explain this tradition, we study a Bayesian setting wherein the valuations of advertisers are drawn independently from a common regular probability distribution. In this setting, it is well known from the work of Myerson [1981] that the optimal revenue is obtained by the VCG mechanism with a particular reserve price that depends on the probability distribution. We show that, by appropriately setting the reserve price, the revenue over any Bayes-Nash equilibrium of the game induced by the GSP auction is at most a small constant factor away from the optimal revenue, improving previous results of Lucier et al. [2012]. Our analysis is based on the Bayes-Nash equilibrium conditions and the improved results are obtained by bounding the utility of each player at equilibrium using infinitely many deviating bids and also by developing novel prophet-like inequalities.

In sponsored search auctions, advertisers compete for a number of available advertisement slots of different quality. The auctioneer decides the allocation of advertisers to slots using bids provided by them. Since the advertisers may act strategically and submit their bids in order to maximize their individual objectives, such an auction naturally defines a strategic game among the advertisers. In order to quantify the efficiency of outcomes in generalized second price auctions, we study the corresponding games and present new bounds on their price of anarchy, improving the recent results of Paes Leme and Tardos [16] and Lucier and Paes Leme [13]. For the full information setting, we prove a surprisingly low upper bound of 1.282 on the price of anarchy over pure Nash equilibria. Given the existing lower bounds, this bound denotes that the number of advertisers has almost no impact on the price of anarchy. The proof exploits the equilibrium conditions developed in [16] and follows by a detailed reasoning about the structure of equilibria and a novel relation of the price of anarchy to the objective value of a compact mathematical program. For more general equilibrium classes (i.e., mixed Nash, correlated, and coarse correlated equilibria), we present an upper bound of 2.310 on the price of anarchy. We also consider the setting where advertisers have incomplete information about their competitors and prove a price of anarchy upper bound of 3.037 over Bayes-Nash equilibria. In order to obtain the last two bounds, we adapt techniques of Lucier and Paes Leme [13] and significantly extend them with new arguments.

We study congestion games where players aim to access a set of resources. Each player has a set of possible strategies and each resource has a function associating the latency it incurs to the players using it. Players are non--cooperative and each wishes to follow a strategy that minimizes her own latency with no regard to the global optimum. Previous work has studied the impact of this selfish behavior on system performance. In this article, we study the question of how much the performance can be improved if players are forced to pay taxes for using resources. Our objective is to extend the original game so that selfish behavior does not deteriorate performance. We consider atomic congestion games with linear latency functions and present both negative and positive results. Our negative results show that optimal system performance cannot be achieved even in very simple games. On the positive side, we show that there are ways to assign taxes that can improve the performance of linear congestion games by forcing players to follow strategies where the total latency suffered is within a factor of 2 of the minimum possible; this result is shown to be tight. Furthermore, even in cases where in the absence of taxes the system behavior may be very poor, we show that the total disutility of players (latency plus taxes) is not much larger than the optimal total latency. Besides existential results, we show how to compute taxes in time polynomial in the size of the game by solving convex quadratic programs. Similar questions have been extensively studied in the model of non-atomic congestion games. To the best of our knowledge, this is the first study of the efficiency of taxes in atomic congestion games.