Robust Equilibria in Shared Resource Allocation via Strengthening Border's Theorem

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David X. Lin, Siddhartha Banerjee, Giannis Fikioris, Éva Tardos

Published: 2026, Last Modified: 07 May 2026SODA 2026EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We consider repeated allocation of a shared resource via a non-monetary mechanism, wherein a single item must be allocated to one of multiple agents in each round. We assume that each agent has i.i.d. values for the item across rounds, and additive utilities. Past work on this problem has proposed mechanisms where agents can get one of two kinds of guarantees: (\(i\)) (approximate) Bayes-Nash equilibria via linkage-based mechanisms which need extensive knowledge of the value distributions, and (\(ii\)) simple distribution-agnostic mechanisms with robust utility guarantees for each individual agent, which are worse than the Nash outcome, but hold irrespective of how others behave (including possibly collusive behavior). Recent work has hinted at barriers to achieving both simultaneously. Our work however establishes this is not the case, by proposing the first mechanism in which each agent has a natural strategy that is both a Bayes-Nash equilibrium and also comes with strong robust guarantees for individual agent utilities. Our mechanism comes out of a surprising connection between the online shared resource allocation problem and implementation theory, and uses a surprising strengthening of Border’s theorem. In particular, we show that establishing robust equilibria in this setting reduces to showing that a particular subset of the Border polytope is non-empty. We establish this via a novel joint Schurconvexity argument. This strengthening of Border’s criterion for obtaining a stronger conclusion is of independent technical interest, as it may prove useful in other settings.*David X. Lin was supported by NSF grant ECCS-1847393. Siddhartha Banerjee was supported in part by AFOSR grant FA9550-23-1-0068, ARO MURI grant W911NF-19-1-0217, and NSF grants ECCS-1847393 and CNS-195599. Giannis Fikioris was supported in part by the Google PhD Fellowship, the Onassis Foundation – Scholarship ID: F ZS 068-1/2022-2023, and ONR MURI grant N000142412742. Éva Tardos was supported in part by AFOSR grant FA9550-23-1-0410, AFOSR grant FA9550-231-0068, and ONR MURI grant N000142412742.