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

Paccagnan, Dario; Marden, Jason R.

doi:10.48550/arxiv.1807.01343

Cited by 3 publications

(8 citation statements)

References 30 publications

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“…Furthermore, no set of local objective functions can perform better. These results have also been extended to resource allocation games in [11].…”

Section: Introductionmentioning

confidence: 88%

“…The price of anarchy is a well established metric, with a number of results on its characterization, complexity, and design [11]. We frame price of anarchy as a backdrop to many of our results, where Nash equilibria are the set of end states following a k-best response round in the limit as k → ∞.…”

Section: B Price Of Best Response and Price Of Anarchymentioning

confidence: 98%

“…Proof. According to a modified version of Theorem 2 in [11], the price of anarchy (PoA) can be written as…”

Section: Proof Of Theoremmentioning

confidence: 99%

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Balancing Asymptotic and Transient Efficiency Guarantees in Set Covering Games

Konda¹,

Chandan²,

Grimsman³

et al. 2021

Preprint

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Game theoretic approaches have gained traction as a robust methodology for designing distributed local algorithms that induce a desired overall system configuration in a multi-agent setting. However, much of the emphasis in these approaches is on providing asymptotic guarantees on the performance of network of agents, and there is a gap in the study of efficiency guarantees along transients of these distributed algorithms. Therefore, in this paper, we study the transient efficiency guarantees of a natural game-theoretic algorithm in the class of set covering games, which have been used to model a variety of applications. Our main results characterize the optimal utility design that maximizes the guaranteed efficiency along the transient of the natural dynamics. Furthermore, we characterize the Pareto-optimal frontier with regards to guaranteed efficiency in the transient and the asymptote under a class of game-theoretic designs. Surprisingly, we show that there exists an extreme trade-off between the long-term and short-term guarantees in that an asymptotically optimal gametheoretic design can perform arbitrarily bad in the transient.

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“…Furthermore, no set of local objective functions can perform better. These results have also been extended to resource allocation games in [11].…”

Section: Introductionmentioning

confidence: 88%

Section: B Price Of Best Response and Price Of Anarchymentioning

confidence: 98%

See 1 more Smart Citation

Balancing Asymptotic and Transient Efficiency Guarantees in Set Covering Games

Konda¹,

Chandan²,

Grimsman³

et al. 2021

Preprint

Self Cite

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“…All the proofs are reported in the Appendix (Section 11.4). The results presented in this chapter have been published in [PCM18;PM18b].…”

Section: Submodular Supermodular Covering Problemsmentioning

confidence: 99%

“…We provide thorough simulation results and show the theoretical and numerical advantages of our approach. The results presented in this chapter have been published in [PM18b].…”

Section: Proof Of Corollarymentioning

confidence: 99%

Distributed Control and Game Design: From Strategic Agents to Programmable Machines

Paccagnan¹

2018

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i sincere thanks goes to you for your support and collaboration during the early stages of my PhD. I remember vividly how much help and enthusiasm you put in teaching me how to write my "first article". If all of this is possible, it is in good part also thanks to you.The atmosphere we breath at IfA is absolutely incredible: a great mix of hardworking, positive energy, and friendship. Sometimes, bent over our papers, we seem to forget how lucky we are. Fortunately (or not), as soon as we step out of the ETH domain, we get reminded of what a privilege this is. I would like to express my greatest gratitude to all those people that made this place what it is. In this regard, there are many colleagues I should thank, but I limit myself to the essential. First of all, I would like to thank Basilio and Francesca for sharing with me a good half of their PhDs, and countless hours on the board conjecturing results that would be proved wrong only a few hours later. I wish both of you a brilliant career as you truly deserve. A very special thanks is due to Nicolò for sharing innumerable moments inside and outside of the office, for the many jokes we have been laughing of, and for the unmissable extra slice of cake (Lucia's). A big thanks goes to the Italian Gang -Basilio, Francesca, Nicolò, Giampaolo, Marcello, Saverio -for the countless adventures, and for making me feel as IfA was the extension of my time in high school. Thank you Tony for being such a positive, cheerful and selfless person. Thank you Peyman for the numerous research discussions we had: I feel there is a lot to learn form you. Thanks to the dream team -Juan, Marcello, Paul -for all the mountains adventures we shared: I will hardly forget when we set foot on the Dammazwillinge for the first time. I am confident you will not forget either. A special thanks goes to Paul for being a terrific office mate, and for sharing the first years of your PhD with me, often out in the Alps. At this point, I feel I owe a big thanks to our secretaries, Sabrina and Tanja, for making everything run incredibly smooth and for being extremely helpful with really anything. "If there is a solution, we will find it" Sabrina told me once, and this pretty much says it all.At a personal level, I would like to thank all my friends in Zurich and elsewhere, in particular Chiara for the gazillions hours we spent climbing together, Federica for being a terrific housemate, Martina and Alessandro for hosting me after my return from the US. A line of his own is needed (and probably not enough) to thank Alessio: a very special thought goes to you for all the things we went through together, way too many to recall. I will never forget the 20-hours day on the Allighesi ferrata, our first climbing route in the dolomites, or simply the usual giro di Ca' Tron. Amongst everything, I would like to thank you for teaching me to be ambitious, to fight, to never give up and to endure pain. Last, I want to thank you for always finding time to meet with me (the usual run) when I come back from Zurich, reg...

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Optimal Design of Best Response Dynamics in Resource Allocation Games

Konda¹,

Chandan²,

Grimsman³

et al. 2022

Preprint

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Designing distributed algorithms for multiagent problems is vital for many emerging application domains, and game-theoretic approaches are emerging as a useful paradigm to design such algorithms. However, much of the emphasis of the game-theoretic approach is on the study of equilibrium behavior, whereas transient behavior is often less explored. Therefore, in this paper we study the transient efficiency guarantees of best response processes in the context of resource-allocation games, which are used to model a variety of engineering applications. Specifically, the main focus of the paper is on designing utility functions of agents to induce optimal short-term system-level behavior under a best-response process. Interestingly, the resulting transient performance guarantees are relatively close to the optimal asymptotic performance guarantees. Furthermore, we characterize a trade-off that results when optimizing for both asymptotic and transient efficiency through various utility designs.

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

Cited by 3 publications

References 30 publications

Balancing Asymptotic and Transient Efficiency Guarantees in Set Covering Games

Balancing Asymptotic and Transient Efficiency Guarantees in Set Covering Games

Distributed Control and Game Design: From Strategic Agents to Programmable Machines

Optimal Design of Best Response Dynamics in Resource Allocation Games

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