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DOI: 10.4230/LIPIcs.ITCS.2026.96

Robust Resource Allocation via Competitive Subsidies

Authors: David X. Lin, Giannis Fikioris, Siddhartha Banerjee, and Éva Tardos

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

A canonical setting for non-monetary online resource allocation is one where agents compete over multiple rounds for a single item per round, with i.i.d. valuations and additive utilities across rounds. With n symmetric agents, a natural benchmark for each agent is the utility realized by her favorite 1/n-fraction of rounds; a line of work has demonstrated one can robustly guarantee each agent a constant fraction of this ideal utility, irrespective of how other agents behave. In particular, several mechanisms have been shown to be 1/2-robust, and recent work established that repeated first-price auctions based on artificial credits have a robustness factor of 0.59, which cannot be improved beyond 0.6 using first-price and simple strategies. In contrast, even without strategic considerations, the best achievable factor is 1-1/e≈ 0.63. In this work, we break the 0.6 first-price barrier to get a new 0.625-robust mechanism, which almost closes the gap to the non-strategic robustness bound. Surprisingly, we do so via a simple auction, where in each round, bidders decide if they ask for the item, and we allocate uniformly at random among those who ask. The main new ingredient is the idea of competitive subsidies, wherein we charge the winning agent an amount in artificial credits that decreases when fewer agents are bidding (specifically, when k agents bid, then the winner pays proportional to k/(k+1), varying the payment by a factor of 2 depending on the competition). Moreover, we show how it can be modified to get an equilibrium strategy with a slightly weaker robust guarantee of 5/(3e) ≈ 0.61 (and the optimal 1-1/e factor at equilibrium). Finally, we show that our mechanism gives the best possible bound under a wide class of auction-based mechanisms.

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David X. Lin, Giannis Fikioris, Siddhartha Banerjee, and Éva Tardos. Robust Resource Allocation via Competitive Subsidies. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 96:1-96:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lin_et_al:LIPIcs.ITCS.2026.96,
  author =	{Lin, David X. and Fikioris, Giannis and Banerjee, Siddhartha and Tardos, \'{E}va},
  title =	{{Robust Resource Allocation via Competitive Subsidies}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{96:1--96:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.96},
  URN =		{urn:nbn:de:0030-drops-253835},
  doi =		{10.4230/LIPIcs.ITCS.2026.96},
  annote =	{Keywords: Online Resource Allocation, Non-Monetary Mechanisms}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.12

Graph Searching with Predictions

Authors: Siddhartha Banerjee, Vincent Cohen-Addad, Anupam Gupta, and Zhouzi Li

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal while moving only a small distance? This problem seems hopeless, even on trees of bounded degree, unless we give the agent some help. This setting with "help" often arises in exploring large search spaces (e.g., huge game trees) where we assume access to some score/quality function for each node, which we use to guide us towards the goal. In our case, we assume the help comes in the form of distance predictions: each node v provides a prediction f(v) of its distance to the goal vertex. Naturally if these predictions are correct, we can reach the goal along a shortest path. What if the predictions are unreliable and some of them are erroneous? Can we get an algorithm whose performance relates to the error of the predictions? In this work, we consider the problem on trees and give deterministic algorithms whose total movement cost is only O(OPT + Δ ⋅ ERR), where OPT is the distance from the start to the goal vertex, Δ the maximum degree, and the ERR is the total number of vertices whose predictions are erroneous. We show this guarantee is optimal. We then consider a "planning" version of the problem where the graph and predictions are known at the beginning, so the agent can use this global information to devise a search strategy of low cost. For this planning version, we go beyond trees and give an algorithms which gets good performance on (weighted) graphs with bounded doubling dimension.

Cite as

Siddhartha Banerjee, Vincent Cohen-Addad, Anupam Gupta, and Zhouzi Li. Graph Searching with Predictions. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{banerjee_et_al:LIPIcs.ITCS.2023.12,
  author =	{Banerjee, Siddhartha and Cohen-Addad, Vincent and Gupta, Anupam and Li, Zhouzi},
  title =	{{Graph Searching with Predictions}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.12},
  URN =		{urn:nbn:de:0030-drops-175158},
  doi =		{10.4230/LIPIcs.ITCS.2023.12},
  annote =	{Keywords: Algorithms with predictions, network algorithms, graph search}
}

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Documents authored by Banerjee, Siddhartha

Robust Resource Allocation via Competitive Subsidies

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Graph Searching with Predictions

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