design sgsp social-cost approximation guarantees

This paper investigates the fundamental trade-off between incentive compatibility and social welfare approximation under budget feasibility, particularly when agents may be boundedly rational. Method: It systematically characterizes the efficacy of non-obvious manipulability (NOM) under budget constraints—the first such analysis—introducing two novel mechanism paradigms: “golden-ticket” (BNOM) and “wooden-spoon” (WNOM) mechanisms. It establishes tight deterministic 2-approximation ratios for monotone subadditive valuations under NOM, provides complete necessary and sufficient conditions for BNOM/ WNOM, and constructs randomized BNOM mechanisms achieving expected approximation ratios arbitrarily close to the optimal value of 1. Contribution/Results: The work reveals, for the first time, the performance separation between dominant-strategy incentive-compatible (DSIC) and NOM mechanisms under budget feasibility. By unifying mechanism design, game theory, subadditive analysis, and randomized construction, it significantly enhances robustness and efficiency in practical deployment.

This paper investigates mechanism design for private-good allocation under arbitrary feasibility constraints, focusing on the joint satisfaction of strategy-proofness and Pareto efficiency. Methodologically, it introduces the notion of “local dictatorship” to characterize two-agent mechanisms, establishes a succinct necessary and sufficient condition for group strategy-proofness, and unifies the analysis of classic problems—including house allocation, roommate matching, and social choice—via marginal mechanism decomposition and compositional constraint modeling. Key contributions include: (i) the first complete characterization of strategy-proof and Pareto-efficient mechanisms for two agents; (ii) a proof that all compatible mechanisms for the roommate problem must be generalized sequential dictatorships; (iii) a simplified, reconstructed proof framework for the Gibbard–Satterthwaite theorem; and (iv) the identification and formalization of a novel class of robust matching mechanisms.

This paper studies robust outlier handling in mechanism design: a mechanism may exclude up to $z$ agents to minimize social cost—particularly relevant in online facility location with extreme preferences. Theoretically, we show that no bounded approximation ratio is achievable when the exclusion fraction exceeds one-half; moreover, naive outlier removal can harm efficiency. To address this, we innovatively incorporate prediction information to design an enhanced mechanism achieving both optimal consistency and robustness. Technically, our analysis integrates strategic proofness arguments, order-statistic analysis, and randomized mechanism design. We establish, for the first time, that the $(z+1)$-th order statistic mechanism is deterministic and $2$-approximate optimal; we also derive tight lower bounds for randomized mechanisms. Finally, we provide tight upper and lower bounds for both egalitarian and social-cost objectives.

This paper studies the facility location mechanism design problem in metric spaces with learning-augmented predictions, aiming to design strategyproof (SP) mechanisms that minimize the maximum agent cost under truthful reporting, leveraging imperfect predictions. It introduces, for the first time in this setting, the dual desiderata of *consistency*—improved approximation ratio when predictions are accurate—and *robustness*—preservation of the optimal worst-case guarantee regardless of prediction error. The authors propose a deterministic mechanism, MinMaxP. On the real line, MinMaxP achieves a tight (1 + min{1, η})-approximation ratio, where η quantifies prediction error. They extend MinMaxP to two-dimensional ℓₚ spaces and analyze its group-strategyproofness. The theoretical analysis integrates tools from mechanism design and metric geometry, addressing both deterministic and randomized mechanisms. This work establishes the first optimal framework for learning-augmented mechanism design that simultaneously achieves consistency and robustness.

This paper investigates the design of randomized obviously strategyproof (OSP) mechanisms for additive, unit-demand, and single-minded multi-item auctions, aiming to overcome inherent approximation barriers faced by deterministic OSP mechanisms in social welfare maximization. Leveraging game-theoretic modeling, randomized mechanism design, and tight impossibility proofs, we construct the first randomized OSP mechanism achieving a constant-factor approximation ratio for social welfare. We precisely characterize its optimal approximation capability: an upper bound of 7/8 (87.5%), matched by a tight lower bound—establishing a fundamental separation in expressive power between randomized and deterministic OSP mechanisms. Furthermore, we demonstrate an insurmountable performance gap between randomized OSP and dominant-strategy incentive-compatible (DSIC) mechanisms. These results provide the first nontrivial characterization of the quantitative gain afforded by randomization in OSP theory, resolving a central open question in algorithmic mechanism design.

This work addresses the two-facility location problem without monetary transfers in metric spaces and proposes a novel randomized strategyproof mechanism that improves the approximation ratio for social cost from 4 to $11/3 \approx 3.667$ over all Ptolemaic metric spaces—including Euclidean spaces—thereby breaking the long-standing 4-approximation barrier for the first time. The mechanism integrates the Proportional mechanism with a newly designed Global Pair mechanism, leveraging their complementary performance on different instance types to achieve a tighter approximation. Additionally, the theoretical lower bound is strengthened from 1.045 to $(1+\sqrt{2})/2 \approx 1.207$. By synthesizing randomized mechanism design, strategyproofness analysis, Ptolemaic space theory, and combinatorial optimization techniques, this study significantly advances the theoretical understanding of the problem.

This study addresses strategyproof facility location mechanisms in Euclidean space under the egalitarian objective of minimizing the maximum distance from any agent to the facility. By introducing an “output augmentation” framework—permitting facility placement outside the agents’ domain—and integrating geometric optimization with mechanism design theory, the work overcomes conventional reliance on randomization. The main contributions include establishing a lower bound of \(1 + \sqrt{d/(2(d+1))}\) on the approximation ratio for any strategyproof mechanism in \(\mathbb{R}^d\); presenting a randomized mechanism achieving a \(\sqrt{2}\)-approximation for two agents; devising a deterministic \(\sqrt{2}\)-approximate mechanism for the online setting on the plane; and proposing a group-strategyproof randomized mechanism with a \(3/2\)-approximation when agents lie on the unit circle.