arXiv subjects

Jason R Marden

Publications and source records attributed to Jason R Marden.

4 recordsLinked to original sources

arXiv2024

Bridging the Gap Between Central and Local Decision-Making: The Efficacy of Collaborative Equilibria in Altruistic Congestion Games

Congestion games are popular models often used to study the system-level inefficiencies caused by selfish agents, typically measured by the price of anarchy. One may expect that aligning the agents' preferences with the system-level objective--altruistic behavior--would improve efficiency, but recent works have shown that altruism can lead to more significant inefficiency than selfishness in congestion games. In this work, we study to what extent the localness of decision-making causes inefficiency by considering collaborative decision-making paradigms that exist between centralized and distributed in altruistic congestion games. In altruistic congestion games with convex latency functions, the system cost is a super-modular function over the player's joint actions, and the Nash equilibria of the game are local optima in the neighborhood of unilateral deviations. When agents can collaborate, we can exploit the common-interest structure to consider equilibria with stronger local optimality guarantees in the system objective, e.g., if groups of k agents can collaboratively minimize the system cost, the system equilibria are the local optima over k-lateral deviations. Our main contributions are in constructing tractable linear programs that provide bounds on the price of anarchy of collaborative equilibria in altruistic congestion games. Our findings bridge the gap between the known efficiency guarantees of centralized and distributed decision-making paradigms while also providing insights into the benefit of inter-agent collaboration in multi-agent systems.

cs.GT↗

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.

cs.GT↗

arXiv2020

Distributed Submodular Maximization with Parallel Execution

The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy algorithm which guarantees approximation at least 1/2 of the optimal solution. This greedy algorithm can be implemented with a set of agents, each making a decision sequentially based on the choices of all prior agents. In this paper, we consider a generalization of the greedy algorithm in which agents can make decisions in parallel, rather than strictly in sequence. In particular, we are interested in partitioning the agents, where a set of agents in the partition all make a decision simultaneously based on the choices of prior agents, so that the algorithm terminates in limited iterations. We provide bounds on the performance of this parallelized version of the greedy algorithm and show that dividing the agents evenly among the sets in the partition yields an optimal structure. We additionally show that this optimal structure is still near-optimal when the objective function exhibits a certain monotone property. Lastly, we show that the same performance guarantees can be achieved in the parallelized greedy algorithm even when agents can only observe the decisions of a subset of prior agents.

cs.DC↗

arXiv2020

Stackelberg Equilibria for Two-Player Network Routing Games on Parallel Networks

We consider a two-player zero-sum network routing game in which a router wants to maximize the amount of legitimate traffic that flows from a given source node to a destination node and an attacker wants to block as much legitimate traffic as possible by flooding the network with malicious traffic. We address scenarios with asymmetric information, in which the router must reveal its policy before the attacker decides how to distribute the malicious traffic among the network links, which is naturally modeled by the notion of Stackelberg equilibria. The paper focuses on parallel networks, and includes three main contributions: we show that computing the optimal attack policy against a given routing policy is an NP-hard problem; we establish conditions under which the Stackelberg equilibria lead to no regret; and we provide a metric that can be used to quantify how uncertainty about the attacker's capabilities limits the router's performance.

cs.GT↗