arXiv subjects

Dario Paccagnan

Publications and source records attributed to Dario Paccagnan.

At least 37 records · Page 2Linked to original sources

arXiv2022

In Congestion Games, Taxes Achieve Optimal Approximation

In this work, we consider the problem of minimising the social cost in atomic congestion games. For this problem, we provide tight computational lower bounds along with taxation mechanisms yielding polynomial time algorithms with optimal approximation. Perhaps surprisingly, our results show that indirect interventions, in the form of efficiently computed taxation mechanisms, yield the same performance achievable by the best polynomial time algorithm, even when the latter has full control over the agents' actions. It follows that no other tractable approach geared at incentivizing desirable system behavior can improve upon this result, regardless of whether it is based on taxations, coordination mechanisms, information provision, or any other principle. In short: Judiciously chosen taxes achieve optimal approximation. Three technical contributions underpin this conclusion. First, we show that computing the minimum social cost is NP-hard to approximate within a given factor depending solely on the admissible resource costs. Second, we design a tractable taxation mechanism whose efficiency (price of anarchy) matches this hardness factor, and thus is worst-case optimal. As these results extend to coarse correlated equilibria, any no-regret algorithm inherits the same performances, allowing us to devise polynomial time algorithms with optimal approximation.

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arXiv2021

Online Traffic Routing: Deterministic Limits and Data-driven Enhancements

Over the past decade, GPS enabled traffic applications, such as Google Maps and Waze, have become ubiquitous and have had a significant influence on billions of daily commuters' travel patterns. A consequence of the online route suggestions of such applications, e.g., via greedy routing, has often been an increase in traffic congestion since the induced travel patterns may be far from the system optimum. Spurred by the widespread impact of traffic applications on travel patterns, this work studies online traffic routing in the context of capacity-constrained parallel road networks and analyzes this problem from two perspectives. First, we perform a worst-case analysis to identify the limits of deterministic online routing and show that the ratio between the total travel cost of the online solution of any deterministic algorithm and that of the optimal offline solution is unbounded, even in simple settings. This result motivates us to move beyond worst-case analysis. Here, we consider algorithms that exploit knowledge of past problem instances and show how to design data-driven algorithms whose performance can be quantified and formally generalized to unseen future instances. We present numerical experiments based on an application case for the San Francisco Bay Area to evaluate the performance of our approach. Our results show that the data-driven algorithms we develop outperform commonly used greedy online-routing algorithms.

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arXiv2021

When Smoothness is Not Enough: Toward Exact Quantification and Optimization of the Price of Anarchy

The price of anarchy (PoA) is a popular metric for analyzing the inefficiency of self-interested decision making. Although its study is widespread, characterizing the PoA can be challenging. A commonly employed approach is based on the smoothness framework, which provides tight PoA values under the assumption that the system objective consists in the sum of the agents' individual welfares. Unfortunately, several important classes of problems do not satisfy this requirement (e.g., taxation in congestion games), and our first result demonstrates that the smoothness framework does *not* tightly characterize the PoA for such settings. Motivated by this observation, this work develops a framework that achieves two chief objectives: i) to tightly characterize the PoA for such scenarios, and ii) to do so through a tractable approach. As a direct consequence, the proposed framework recovers and generalizes many existing PoA results, and enables efficient computation of incentives that optimize the PoA. We conclude by highlighting the applicability of our contributions to incentive design in congestion games and utility design in distributed welfare games.

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arXiv2021

Optimal Taxes in Atomic Congestion Games

How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing. Within this context, a methodology for designing tolling mechanisms that minimize the system inefficiency (price of anarchy) exploiting solely local information is so far missing in spite of the scientific interest. In this manuscript we resolve this problem through a tractable linear programming formulation that applies to and beyond polynomial congestion games. When specializing our approach to the polynomial case, we obtain tight values for the optimal price of anarchy and corresponding tolls, uncovering an unexpected link with load balancing games. We also derive optimal tolling mechanisms that are constant with the congestion level, generalizing the results of Caragiannis et al. [ACM Transactions on Algorithms, 2010] to polynomial congestion games and beyond. Finally, we apply our techniques to compute the efficiency of the marginal cost mechanism. Surprisingly, optimal tolling mechanism using only local information perform closely to existing mechanism that utilize global information [Bilò and Vinci, ACM Transactions on Economics and Computation, 2019], while the marginal cost mechanism, known to be optimal in the continuous-flow model, has lower efficiency than that encountered levying no toll. All results are tight for pure Nash equilibria, and extend to coarse correlated equilibria.

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arXiv2021

Urgency-aware Optimal Routing in Repeated Games through Artificial Currencies

When people choose routes minimizing their individual delay, the aggregate congestion can be much higher compared to that experienced by a centrally-imposed routing. Yet centralized routing is incompatible with the presence of self-interested agents. How can we reconcile the two? In this paper we address this question within a repeated game framework and propose a fair incentive mechanism based on artificial currencies that routes selfish agents in a system-optimal fashion, while accounting for their temporal preferences. We instantiate the framework in a parallel-network whereby agents commute repeatedly (e.g., daily) from a common start node to the end node. Thereafter, we focus on the specific two-arcs case whereby, based on an artificial currency, the agents are charged when traveling on the first, fast arc, whilst they are rewarded when traveling on the second, slower arc. We assume the agents to be rational and model their choices through a game where each agent aims at minimizing a combination of today's discomfort, weighted by their urgency, and the average discomfort encountered for the rest of the period (e.g., a week). We show that, if prices of artificial currencies are judiciously chosen, the routing pattern converges to a system-optimal solution, while accommodating the agents' urgency. We complement our study through numerical simulations. Our results show that it is possible to achieve a system-optimal solution whilst reducing the agents' perceived discomfort by 14-20% when compared to a centralized optimal but urgency-unaware policy.

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arXiv2021

Tractable mechanisms for computing near-optimal utility functions

Large scale multiagent systems must rely on distributed decision making, as centralized coordination is either impractical or impossible. Recent works approach this problem under a game theoretic lens, whereby utility functions are assigned to each of the agents with the hope that their local optimization approximates the centralized optimal solution. Yet, formal guarantees on the resulting performance cannot be obtained for broad classes of problems without compromising on their accuracy. In this work, we address this concern relative to the well-studied problem of resource allocation with nondecreasing concave welfare functions. We show that optimally designed local utilities achieve an approximation ratio (price of anarchy) of 1-c/e, where c is the function's curvature and e is Euler's constant. The upshot of our contributions is the design of approximation algorithms that are distributed and efficient, and whose performance matches that of the best existing polynomial-time (and centralized) schemes.

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arXiv2021

Utility Design for Distributed Resource Allocation -- Part II: Applications to Submodular, Covering, and Supermodular Problems

A fundamental component of the game theoretic approach to distributed control is the design of local utility functions.Relative to resource allocation problems that are additive over the resources, Part I showed how to design local utilities so as to maximize the associated performance guarantees [Paccagnan et al., TAC 2019] which we measure by the price of anarchy. The purpose of the present manuscript is to specialize these results to the case of submodular, covering, and supermodular problems. In all these cases we obtain tight expressions for the price of anarchy that often match or improve the guarantees associated to state-of-the-art approximation algorithms. Two applications and corresponding numerics are presented: the vehicle-target assignment problem and a coverage problem arising in wireless data caching.

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arXiv2020

Stochastic Strategies for Robotic Surveillance as Stackelberg Games

This paper studies a stochastic robotic surveillance problem where a mobile robot moves randomly on a graph to capture a potential intruder that strategically attacks a location on the graph. The intruder is assumed to be omniscient: it knows the current location of the mobile agent and can learn the surveillance strategy. The goal for the mobile robot is to design a stochastic strategy so as to maximize the probability of capturing the intruder. We model the strategic interactions between the surveillance robot and the intruder as a Stackelberg game, and optimal and suboptimal Markov chain based surveillance strategies in star, complete and line graphs are studied. We first derive a universal upper bound on the capture probability, i.e., the performance limit for the surveillance agent. We show that this upper bound is tight in the complete graph and further provide suboptimality guarantees for a natural design. For the star and line graphs, we first characterize dominant strategies for the surveillance agent and the intruder. Then, we rigorously prove the optimal strategy for the surveillance agent.

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arXiv2020

Assign and Appraise: Achieving Optimal Performance in Collaborative Teams

Tackling complex team problems requires understanding each team member's skills in order to devise a task assignment maximizing the team performance. This paper proposes a novel quantitative model describing the decentralized process by which individuals in a team learn who has what abilities, while concurrently assigning tasks to each of the team members. In the model, the appraisal network represents team member's evaluations of one another and each team member chooses their own workload. The appraisals and workload assignment change simultaneously: each member builds their own local appraisal of neighboring members based on the performance exhibited on previous tasks, while the workload is redistributed based on the current appraisal estimates. We show that the appraisal states can be reduced to a lower dimension due to the presence of conserved quantities associated to the cycles of the appraisal network. Building on this, we provide rigorous results characterizing the ability, or inability, of the team to learn each other's skill and thus converge to an allocation maximizing the team performance. We complement our analysis with extensive numerical experiments.

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arXiv2020

Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability

The price of anarchy and price of stability are three well-studied performance metrics that seek to characterize the inefficiency of equilibria in distributed systems. The distinction between these two performance metrics centers on the equilibria that they focus on: the price of anarchy characterizes the quality of the worst-performing equilibria, while the price of stability characterizes the quality of the best-performing equilibria. While much of the literature focuses on these metrics from an analysis perspective, in this work we consider these performance metrics from a design perspective. Specifically, we focus on the setting where a system operator is tasked with designing local utility functions to optimize these performance metrics in a class of games termed covering games. Our main result characterizes a fundamental trade-off between the price of anarchy and price of stability in the form of a fully explicit Pareto frontier. Within this setup, optimizing the price of anarchy comes directly at the expense of the price of stability (and vice versa). Our second results demonstrates how a system-operator could incorporate an additional piece of system-level information into the design of the agents' utility functions to breach these limitations and improve the system's performance. This valuable piece of system-level information pertains to the performance of worst performing agent in the system.

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arXiv2020

When Smoothness is Not Enough: Toward Exact Quantification and Optimization of the Price-of-Anarchy

Today's multiagent systems have grown too complex to rely on centralized controllers, prompting increasing interest in the design of distributed algorithms. In this respect, game theory has emerged as a valuable tool to complement more traditional techniques. The fundamental idea behind this approach is the assignment of agents' local cost functions, such that their selfish minimization attains, or is provably close to, the global objective. Any algorithm capable of computing an equilibrium of the corresponding game inherits an approximation ratio that is, in the worst case, equal to its price-of-anarchy. Therefore, a successful application of the game design approach hinges on the possibility to quantify and optimize the equilibrium performance. Toward this end, we introduce the notion of generalized smoothness, and show that the resulting efficiency bounds are significantly tighter compared to those obtained using the traditional smoothness approach. Leveraging this newly-introduced notion, we quantify the equilibrium performance for the class of local resource allocation games. Finally, we show how the agents' local decision rules can be designed in order to optimize the efficiency of the corresponding equilibria, by means of a tractable linear program.

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arXiv2019

The Nash Equilibrium with Inertia in Population Games

In the traditional game-theoretic set up, where agents select actions and experience corresponding utilities, an equilibrium is a configuration where no agent can improve their utility by unilaterally switching to a different action. In this work, we introduce the novel notion of inertial Nash equilibrium to account for the fact that, in many practical situations, action changes do not come for free. Specifically, we consider a population game and introduce the coefficients $c_{ij}$ describing the cost an agent incurs by switching from action $i$ to action $j$. We define an inertial Nash equilibrium as a distribution over the action space where no agent benefits in moving to a different action, while taking into account the cost of this change. First, we show that the set of inertial Nash equilibria contains all the Nash equilibria, but is in general not convex. Second, we argue that classical algorithms for computing Nash equilibria cannot be used in the presence of switching costs. We then propose a natural better-response dynamics and prove its convergence to an inertial Nash equilibrium. We apply our results to predict the drivers' distribution of an on-demand ride-hailing platform.

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arXiv2019

Utility Design for Distributed Resource Allocation -- Part I: Characterizing and Optimizing the Exact Price of Anarchy

Game theory has emerged as a fruitful paradigm for the design of networked multiagent systems. A fundamental component of this approach is the design of agents' utility functions so that their self-interested maximization results in a desirable collective behavior. In this work we focus on a well-studied class of distributed resource allocation problems where each agent is requested to select a subset of resources with the goal of optimizing a given system-level objective. Our core contribution is the development of a novel framework to tightly characterize the worst case performance of any resulting Nash equilibrium (price of anarchy) as a function of the chosen agents' utility functions. Leveraging this result, we identify how to design such utilities so as to optimize the price of anarchy through a tractable linear program. This provides us with a priori performance certificates applicable to any existing learning algorithm capable of driving the system to an equilibrium. Part II of this work specializes these results to submodular and supermodular objectives, discusses the complexity of computing Nash equilibria, and provides multiple illustrations of the theoretical findings.

cs.GT↗

arXiv2019

The scenario approach meets uncertain variational inequalities and game theory

Variational inequalities are modelling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle stochastic optimization problems, take decisions based on historical data, and quantify their risk. The overarching goal of this manuscript is to bridge these two areas of research, and thus broaden the class of problems amenable to be studied under the lens of the scenario approach. First and foremost, we provide out-of-samples feasibility guarantees for the solution of variational and quasi variational inequality problems. Second, we apply these results to two classes of uncertain games. In the first class, the uncertainty enters in the constraint sets, while in the second class the uncertainty enters in the cost functions. Finally, we exemplify the quality and relevance of our bounds through numerical simulations on a demand-response model.

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arXiv2019

Optimal Price of Anarchy in Cost-Sharing Games

The design of distributed algorithms is central to the study of multiagent systems control. In this paper, we consider a class of combinatorial cost-minimization problems and propose a framework for designing distributed algorithms with a priori performance guarantees that are near-optimal. We approach this problem from a game-theoretic perspective, assigning agents cost functions such that the equilibrium efficiency (price of anarchy) is optimized. Once agents' cost functions have been specified, any algorithm capable of computing a Nash equilibrium of the system inherits a performance guarantee matching the price of anarchy. Towards this goal, we formulate the problem of computing the price of anarchy as a tractable linear program. We then present a framework for designing agents' local cost functions in order to optimize for the worst-case equilibrium efficiency. Finally, we investigate the implications of our findings when this framework is applied to systems with convex, nondecreasing costs.

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arXiv2019

Distributed control and game design: From strategic agents to programmable machines

Large scale systems are forecasted to greatly impact our future lives thanks to their wide ranging applications including cooperative robotics, mobility on demand, resource allocation, supply chain management. While technological developments have paved the way for the realization of such futuristic systems, we have a limited grasp on how to coordinate the individual components to achieve the desired global objective. This thesis deals with the analysis and coordination of large scale systems without the need of a centralized authority. In the first part of this thesis, we consider non-cooperative decision making problems where each agent's objective is a function of the aggregate behavior of the population. First, we compare the performance of an equilibrium allocation with that of an optimal allocation and propose conditions under which all equilibrium allocations are efficient. Towards this goal, we prove a novel result bounding the distance between the strategies at a Nash and Wardrop equilibrium that might be of independent interest. Second, we show how to derive scalable algorithms that guide agents towards an equilibrium allocation. In the second part of this thesis, we consider large-scale cooperative problems, where a number of agents need to be allocated to a set of resources with the goal of jointly maximizing a given submodular or supermodular set function. Since this class of problems is computationally intractable, we aim at deriving tractable algorithms for attaining approximate solutions. We approach the problem from a game-theoretic perspective and ask the following: how should we design agents' utilities so that any equilibrium configuration is almost optimal? To answer this question we introduce a novel framework that allows to characterize and optimize the system performance as a function of the chosen utilities by means of a tractable linear program.

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arXiv2018

The Importance of System-Level Information in Multiagent Systems Design: Cardinality and Covering Problems

A fundamental challenge in multiagent systems is to design local control algorithms to ensure a desirable collective behaviour. The information available to the agents, gathered either through communication or sensing, naturally restricts the achievable performance. Hence, it is fundamental to identify what piece of information is valuable and can be exploited to design control laws with enhanced performance guarantees. This paper studies the case when such information is uncertain or inaccessible for a class of submodular resource allocation problems termed covering problems. In the first part of this work we pinpoint a fundamental risk-reward tradeoff faced by the system operator when conditioning the control design on a valuable but uncertain piece of information, which we refer to as the cardinality, that represents the maximum number of agents that can simultaneously select any given resource. Building on this analysis, we propose a distributed algorithm that allows agents to learn the cardinality while adjusting their behaviour over time. This algorithm is proved to perform on par or better to the optimal design obtained when the exact cardinality is known a priori.

cs.GT↗

arXiv2018

On the Efficiency of Nash Equilibria in Aggregative Charging Games

Several works have recently suggested to model the problem of coordinating the charging needs of a fleet of electric vehicles as a game, and have proposed distributed algorithms to coordinate the vehicles towards a Nash equilibrium of such game. However, Nash equilibria have been shown to posses desirable system-level properties only in simplified cases. In this work, we use the concept of price of anarchy to analyze the inefficiency of Nash equilibria when compared to the social optimum solution. More precisely, we show that i) for linear price functions depending on all the charging instants, the price of anarchy converges to one as the population of vehicles grows; ii) for price functions that depend only on the instantaneous demand, the price of anarchy converges to one if the price function takes the form of a positive pure monomial; iii) for general classes of price functions, the asymptotic price of anarchy can be bounded. For finite populations, we additionaly provide a bound on the price of anarchy as a function of the number vehicles in the system. We support the theoretical findings by means of numerical simulations.

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