AGV mechanism balances the budget with minimum total transfer variance

Two mechanisms are equivalent if they share the same allocation rules and interim transfer rules, carrying incentive properties from one mechanism to the other. I prove the generalized d’Aspremont-Gérard-Varet (AGV) mechanism achieves minimal liquidity risk. It uniquely minimizes total transfer variance among all ex post budget-balanced mechanisms equivalent to an initial mechanism that balances the budget in expectation. Motivated by the contrast between ex ante and ex post fairness, I characterize the optimal mechanism minimizing payoff volatility. Finally, I show that in single-item auctions, a first-price auction with the optimal reserve price jointly maximizes expected revenue and minimizes revenue variance.