Exact price of anarchy of generalized second-price auctions

Determine the exact price of anarchy of generalized second-price auctions under the aggregate no-overbidding assumption, resolving the currently known interval from 2 to approximately 3.146.

Background

The paper establishes an upper bound of approximately 3.146 for the price of anarchy of coarse correlated equilibria in generalized second-price auctions with budget-constrained bidders and an aggregate no-overbidding assumption. It also provides a budget-free pure Nash equilibrium lower bound of 2. Consequently, the exact price of anarchy remains unresolved within the interval [2, 3.146].

References

Effectively, whenever our analysis of a second-price-type format is tight, budgets come ``for free'': the SSPA and the UPA confirm this, whereas for the GSP the question remains open, as its PoA lies in $[2, 3.146]$.

— Tight Liquid Welfare Guarantees for Auctions with Budgets via LP Duality  (2609.39532 - Kroll et al., 30 Sep 2026) in Conclusion, final paragraph of Section 6