* Asterisks denote alphabetical author order.
The Nash social welfare (NSW) is a well-known social welfare measurement that balances individual utilities and the overall efficiency. In the context of fair allocation of indivisible goods, it has been shown by Caragiannis et al. (EC 2016 and TEAC 2019) that an allocation maximizing the NSW is envy-free up to one good (EF1). In this paper, we are interested in the fairness of the NSW in a budget-feasible allocation problem, in which each item has a cost that will be incurred to the agent it is allocated to, and each agent has a budget constraint on the total cost of items she receives. We show that a budget-feasible allocation that maximizes the NSW achieves a 1/4-approximation of EF1 and the approximation ratio is tight. The approximation ratio improves gracefully when the items have small costs compared with the agents' budgets; it converges to 1/2 when the budget-cost ratio approaches infinity.
We study a fair resource sharing problem, where a set of resources are to be shared among a set of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, whom they share the same resource with. Apparently, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even to decide the existence of such a strongly envy-free assignment is an intractable problem. Thus, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved: an agent i envies another agent j only when i envies both the resource and the mates of j. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dorm-mates. We show that when the capacity of the dorms is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment; nevertheless, the result fails to hold immediately when the capacities increase to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the implications of envy-freeness on proportionality in our model and show that envy-freeness in general implies approximations of proportionality.
We study Stackelberg security game (SSG) with multiple defenders, where heterogeneous defenders need to allocate security resources to protect a set of targets against a strategic attacker. In such games, coordination and cooperation between the defenders can increase their ability to protect their assets, but the heterogeneous preferences of the self-interested defenders often make such cooperation very difficult. In this paper, we approach the problem from the perspective of cooperative game theory and study coalition formation among the defenders. Our main contribution is a number of algorithmic results for the computation problems that arise in this model. We provide a poly-time algorithm for computing a solution in the {\em core} of the game and show that all of the elements in the core are Pareto efficient. We show that the problem of computing the entire core is NP-hard and then delve into a special setting where the size of a coalition is limited up to some threshold. We analyse the parameterized complexity of deciding if a coalition structure is in the core under this special setting, and provide a poly-time algorithm for computing successful deviation strategies for a given coalition.
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.
(A preliminary version of this paper appeared in the Proceedings of IJCAI '19. This full version includes all proofs that were omitted from the conference version as well as additional examples and algorithmic results, such as a pseudo-polynomial time algorithm for the weighted version of the recounting problem for Plurality over Districts when the attacker is limited to regular manipulations, and a polynomial time algorithm for the unweighted version of the recounting problem for Plurality over Districts under an additional technical assumption.)
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.
Recent work studied Stackelberg security games with multiple defenders, in which heterogeneous defenders allocate security resources to protect a set of targets against a strategic attacker. Equilibrium analysis was conducted to characterize outcomes of these games when defenders act independently. Our starting point is the observation that the use of resources in equilibria may be inefficient due to lack of coordination. We explore the possibility of reducing this inefficiency by coordinating the defendersâ€”specifically, by pooling the defendersâ€™ resources and allocating them jointly. The defendersâ€™ heterogeneous preferences then give rise to a collective decision-making problem, which calls for a mechanism to generate joint allocation strategies. We seek a mechanism that encourages coordination, produces efficiency gains, and incentivizes the defenders to report their true preferences and to execute the recommended strategies. Our results show that, unfortunately, even these basic properties clash with each other and no mechanism can achieve them simultaneously, which reveals the intrinsic difficulty of achieving meaningful defense coordination in security games. On the positive side, we put forward mechanisms that fulfill some of these properties and we identify special cases of our setting where more of these properties are compatible.
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 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.
In Stackelberg security games when information about the attacker's payoffs is uncertain, algorithms have been proposed to learn the optimal defender commitment by interacting with the attacker and observing their best responses. In this paper, we show that, however, these algorithms can be easily manipulated if the attacker responds untruthfully. As a key finding, attacker manipulation normally leads to the defender learning a maximin strategy, which effectively renders the learning attempt meaningless as to compute a maximin strategy requires no additional information about the other player at all. We then apply a game-theoretic framework at a higher level to counteract such manipulation, in which the defender commits to a policy that specifies her strategy commitment according to the learned information. We provide a polynomial-time algorithm to compute the optimal such policy, and in addition, a heuristic approach that applies even when the attacker's payoff space is infinite or completely unknown. Empirical evaluation shows that our approaches can improve the defender's utility significantly as compared to the situation when attacker manipulation is ignored.
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.
Information uncertainty is one of the major challenges facing applications of game theory. In the context of Stackelberg games, various approaches have been proposed to deal with the leader's incomplete knowledge about the follower's payoffs, typically by gathering information from the leader's interaction with the follower. Unfortunately, these approaches rely crucially on the assumption that the follower will not strategically exploit this information asymmetry, i.e., the follower behaves truthfully during the interaction according to their actual payoffs. As we show in this paper, the follower may have strong incentives to deceitfully imitate the behavior of a different follower type and, in doing this, benefit significantly from inducing the leader into choosing a highly suboptimal strategy. This raises a fundamental question: how to design a leader strategy in the presence of a deceitful follower? To answer this question, we put forward a basic model of Stackelberg games with (imitative) follower deception and show that the leader is indeed able to reduce the loss due to follower deception with carefully designed policies. We then provide a systematic study of the problem of computing the optimal leader policy and draw a relatively complete picture of the complexity landscape; essentially matching positive and negative complexity results are provided for natural variants of the model. Our intractability results are in sharp contrast to the situation with no deception, where the leader's optimal strategy can be computed in polynomial time, and thus illustrate the intrinsic difficulty of handling follower deception. Through simulations we also examine the benefit of considering follower deception in randomly generated games.
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.
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.
Strong Stackelberg equilibrium (SSE) is the standard solution concept of Stackelberg security games. As opposed to the weak Stackelberg equilibrium (WSE), the SSE assumes that the follower breaks ties in favor of the leader and this is widely acknowledged and justified by the assertion that the defender can often induce the attacker to choose a preferred action by making an infinitesimal adjustment to her strategy. Unfortunately, in security games with resource assignment constraints, the assertion might not be valid; it is possible that the defender cannot induce the desired outcome. As a result, many results claimed in the literature may be overly optimistic. To remedy, we first formally define the utility guarantee of a defender strategy and provide examples to show that the utility of SSE can be higher than its utility guarantee. Second, inspired by the analysis of leader's payoff by Von Stengel and Zamir (2004), we provide the solution concept called the inducible Stackelberg equilibrium (ISE), which owns the highest utility guarantee and always exists. Third, we show the conditions when ISE coincides with SSE and the fact that in general case, SSE can be extremely worse with respect to utility guarantee. Moreover, introducing the ISE does not invalidate existing algorithmic results as the problem of computing an ISE polynomially reduces to that of computing an SSE. We also provide an algorithmic implementation for computing ISE, with which our experiments unveil the empirical advantage of the ISE over the SSE.
Stackelberg security games have received much attention in recent years. While most existing work focuses on single-defender settings, there are many real-world scenarios that involve multiple defenders (e.g., multi-national anti-crime actions in international waters, different security agencies patrolling the same area). In this paper, we consider security games with uncoordinated defenders who jointly protect a set of targets, but may have different valuations for these targets; each defender schedules their own resources and selfishly optimizes their own utility. We generalize the standard (single-defender) model of Stackelberg security games to this setting and formulate an equilibrium concept that captures the nature of strategic interaction among the players. We argue that an exact equilibrium may fail to exist, and, in fact, deciding whether it exists is NP-hard. However, under mild assumptions, every multi-defender security game admits an Ďµ-equilibrium for every Ďµ > 0, and the limit points corresponding to Ďµ â†’ 0 can be efficiently approximated.
To reduce the air pollution and improve the energy efficiency, many countries and cities (e.g., Singapore) are on the way of introducing electric vehicles (EVs) to replace the vehicles serving in current traffic system. Effective placement of charging stations is essential for the rapid development of EVs, because it is necessary for providing convenience for EVs and ensuring the efficiency of the traffic network. However, existing works mostly concentrate on the mileage anxiety from EV users but ignore their strategic and competitive charging behaviors. To capture the competitive and strategic charging behaviors of the EV users, we consider that an EV user's charging cost, which is dependent on other EV users' choices, consists of the travel cost to access the charging station and the queuing cost in charging stations. First, we formulate the Charging Station Placement Problem (CSPP) as a bilevel optimization problem. Then, by exploiting the equilibrium of the EV charging game, we convert the bilevel optimization problem to a single-level one, following which we analyze the properties of CSPP and propose an algorithm Optimizing eleCtric vEhicle chArging statioN (OCEAN) to compute the optimal allocation of charging stations. Due to OCEAN's scalability issue, we furthermore present a heuristic algorithm OCEAN with Continuous variables to deal with large-scale real-world problems. Finally, we demonstrate and discuss the results of the extensive experiments we did. It is shown that our approach outperform baseline methods significantly.
Most existing models of Stackelberg security games ignore the underlying topology of the space in which targets and defence resources are located. As a result, allocation of resources is restricted to a discrete collection of exogenously defined targets. However, in many practical security settings, defense resources can be located on a continuous plane. Better defense solutions could therefore be potentially achieved by placing resources in a space outside of actual targets (e.g., between targets). To address this limitation, we propose a model called Security Game on a Plane (SGP) in which targets are distributed on a 2-dimensional plane, and security resources, to be allocated on the same plane, protect targets within a certain effective distance. We investigate the algorithmic aspects of SGP. We find that computing a strong Stackelberg equilibrium of an SGP is NP-hard even for zerosum games, and these are inapproximable in general. On the positive side, we find an exact solution technique for general SGPs based on an existing approach, and develop a PTAS (polynomial-time approximation scheme) for zero-sum SGP to more fundamentally overcome the computational obstacle. Our experiments demonstrate the value of considering SGP and effectiveness of our algorithms.
Preventing crimes or terrorist attacks in urban areas is challenging. Law enforcement officers need to respond quickly to catch the attacker on his escape route, which is subject to time-dependent traffic conditions on transportation networks. The attacker can strategically choose his escape path and driving speed to avoid being captured. Existing work on security resource allocation has not considered such scenarios with time-dependent strategies for both players. Therefore, in this paper, we study the problem of efficiently scheduling security resources for interdicting the escaping attacker. We propose: 1) a new defender-attacker security game model for escape interdiction on transportation networks; and 2) an efficient double oracle algorithm to compute the optimal defender strategy, which combines mixed-integer linear programming formulations for best response problems and effective approximation algorithms for improving the scalability of the algorithms. Experimental evaluation shows that our approach significantly outperforms baselines in solution quality and scales up to realistic-sized transportation networks with hundreds of intersections.
Taxi service is an indispensable part of public transport in modern cities. To support its unique features, a taxi system adopts a decentralized operation mode in which thousands of taxis freely decide their working schedules and routes. Taxis compete with each other for individual profits regardless of system-level efficiency, making the taxi system inefficient and hard to optimize. Most research into the management and economics of taxi markets has focused on modeling from a macro level the effects of and relationships between various market factors. Less has been done regarding a more important component--drivers' strategic behavior under the decentralized operation mode. The authors propose looking at the problem from a game-theoretic perspective. Combining game-theoretic solution concepts with existing models of taxi markets, they model taxi drivers' strategy-making process as a game and transform the problem of optimizing taxi system efficiency into finding a market policy that leads to the desired equilibrium.
Game theoretic models of security, and associated computational methods, have emerged as critical components of security posture across a broad array of domains, including airport security and coast guard. These approaches consider terrorists as motivated but independent entities. There is, however, increasing evidence that attackers, be it terrorists or cyber attackers, communicate extensively and form coalitions that can dramatically increase their ability to achieve malicious goals. To date, such cooperative decision making among attackers has been ignored in the security games literature. To address the issue of cooperation among attackers, we introduce a novel coalitional security game (CSG) model. A CSG consists of a set of attackers connected by a (communication or trust) network who can form coalitions as connected subgraphs of this network so as to attack a collection of targets. A defender in a CSG can delete a set of edges, incurring a cost for deleting each edge, with the goal of optimally limiting the attackersâ€™ ability to form effective coalitions (in terms of successfully attacking high value targets). We first show that a CSG is, in general, hard to approximate. Nevertheless, we develop a novel branch and price algorithm, leveraging a combination of column generation, relaxation, greedy approximation, and stabilization methods to enable scalable high-quality approximations of CSG solutions on realistic problem instances.
The rapid development of Electric Vehicles (EVs) seen in recent years has been drawing increasing attentions from the public, markets, decision-makers, and academia. Notwithstanding the progress, issues still remain. Because of the widely complained disadvantages of limited battery capacity and long charging time, charging convenience has become a top concern that greatly hinders the adoption of EVs. Specialized EV charging station, which provides more than 10 times faster charging speed than domestic charging, is therefore a critical element for successful EV promotion. While most existing researches focus on optimizing spatial placement of charging stations, they are inflexible and inefficient against rapidly changing urban structure and traffic pattern. Therefore, this paper approaches the management of EV charging stations from the pricing perspective as a more flexible and adaptive complement to established charging station placement. In this paper, we build a realistic pricing model in consideration of residential travel pattern and EV driversâ€™ self-interested charging behavior, traffic congestion, and operating expense of charging stations. We formulate the pricing problem as a mixed integer non-convex optimization problem, and propose a scalable algorithm to solve it. Experiments on both mock and real data are also conducted, which show scalability of our algorithm as well as our solutionâ€™s significant improvement over existing approaches.
Security agencies in the real world often need to protect targets with time-dependent values, e.g., tourist sites where the number of travelers changes over time. Since the values of different targets often change asynchronously, the defender can relocate security resources among targets dynamically to make the best use of limited resources. We propose a game-theoretic scheme to develop dynamic, randomized security strategies in consideration of adversaryâ€™s surveillance capability. This differs from previous studies on security games by considering varying target values and continuous strategy spaces of the security agency and the adversary. The main challenge lies in the computational intensiveness due to the continuous, hence infinite strategy spaces. We propose an optimal algorithm and an arbitrarily near-optimal algorithm to compute security strategies under different conditions. Experimental results show that both algorithms significantly outperform existing approaches.
Many countries like Singapore are planning to introduce Electric Vehicles (EVs) to replace traditional vehicles to reduce air pollution and improve energy efficiency. The rapid development of EVs calls for efficient deployment of charging stations both for the convenience of EVs and maintaining the efficiency of the road network. Unfortunately, existing work makes unrealistic assumption on EV driversâ€™ charging behaviors and focus on the limited mobility of EVs. This paper studies the Charging Station PLacement (CSPL) problem, and takes into consideration 1) EV driversâ€™ strategic behaviors to minimize their charging cost, and 2) the mutual impact of EV driversâ€™ strategies on the traffic conditions of the road network and service quality of charging stations. We first formulate the CSPL problem as a bilevel optimization problem, which is subsequently converted to a single-level optimization problem by exploiting structures of the EV charging game. Properties of CSPL problem are analyzed and an algorithm called OCEAN is proposed to compute the optimal allocation of charging stations. We further propose a heuristic algorithm OCEAN-C to speed up OCEAN. Experimental results show that the proposed algorithms significantly outperform baseline methods.
Taxi service is an indispensable part of public transport in modern cities. However, due to its decentralized operation mode, taxi services in many cities are inefficient. Besides, the decentralized nature also poses significant challenges to analyzing and regulating taxi services. State of the art computational methods for optimizing taxi market efficiency suffer from two important limitations: 1) they cannot be scaled up efficiently; and 2) they cannot address complex real-world market situations where additional scheduling constraints need to be handled. In this paper, we propose two novel algorithmsâ€”FLORA and FLORA-Aâ€”to address the inadequacies. Using convex polytope representation techniques, FLORA provides a fully compact representation for taxi driversâ€™ strategy space and scales up more efficiently than existing algorithms. FLORA-A avoids enumerating the entire exponentially large pure strategy space by gradually expanding the strategy space. It is the first known method capable of handling arbitrary scheduling constraints for optimizing taxi system efficiency. Experimental results show orders of magnitude improvement in speed FLORA provides, and the necessity of using FLORA-A as suggested by changes in the taxi driversâ€™ operation strategy under different market conditions.
Stackelberg security games have been widely deployed in recent years to schedule security resources. An assumption in most existing security game models is that one security resource assigned to a target only protects that target. However, in many important real-world security scenarios, when a resource is assigned to a target, it exhibits protection externalities: that is, it also protects other â€śneighbouringâ€ť targets. We investigate such Security Games with Protection Externalities (SPEs). First, we demonstrate that computing a strong Stackelberg equilibrium for an SPE is NP-hard, in contrast with traditional Stackelberg security games which can be solved in polynomial time. On the positive side, we propose a novel column generation based approachâ€”CLASPEâ€”to solve SPEs. CLASPE features the following novelties: 1) a novel mixed-integer linear programming formulation for the slave problem; 2) an extended greedy approach with a constant-factor approximation ratio to speed up the slave problem; and 3) a linear-scale linear programming that efficiently calculates the upper bounds of target-defined subproblems for pruning. Our experimental evaluation demonstrates that CLASPE enable us to scale to realistic-sized SPE problem instances.
In Beijing, most taxi drivers intentionally avoid working during peak hours despite of the huge customer demand within these peak periods. This dilemma is mainly due to the fact that taxi drivers' congestion costs are not reflected in the current taxi fare structure. To resolve this problem, we propose a new pricing scheme to provide taxi drivers with extra incentives to work during peak hours. This differs from previous studies of taxi market by considering market variance over multiple periods, taxi drivers' profit-driven decisions, and their scheduling constraints regarding the interdependence among different periods. The major challenge of this research is the computational intensiveness to identify optimal strategy due to the exponentially large size of a taxi driver's strategy space and the scheduling constraints. We develop an atom schedule method to overcome these issues. It reduces the magnitude of the problem while satisfying the constraints to filter out infeasible pure strategies. Simulation results based on real data show the effectiveness of the proposed methods, which opens up a new door to improving the efficiency of taxi market in megacities (e.g., Beijing).