deterministic truthful mechanisms

This paper studies the design of optimal deterministic refund mechanisms in a single-item, single-buyer setting where the buyer’s private value is ex-ante uncertain and both parties share a common prior distribution. We characterize the optimal deterministic refund mechanism as a virtual-value maximizer—establishing, for the first time, a unified structural characterization applicable to both continuous and discrete type distributions. Methodologically, we introduce a novel paradigm for approximate mechanism design based on menu complexity and develop efficient polynomial-time algorithms to compute both exact optimal and near-optimal mechanisms. Theoretically, we prove that our mechanisms achieve provable optimality guarantees under standard regularity conditions. Empirically, we validate their computational tractability and revenue superiority across diverse distribution families, including both synthetic and realistic settings. Our framework bridges theoretical rigor with practical implementability, advancing the state of the art in dynamic pricing with buyer uncertainty.

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 paper studies the design of information verification mechanisms: how to probabilistically test agents’ reports to balance allocation efficiency and principal surplus. We propose a novel paradigm embedding statistical hypothesis testing into mechanism design, constructing a commitment mechanism with randomized verification—where each report type undergoes a binary test (pass/fail), and outcomes directly inform allocation and payment decisions. Innovatively, we reformulate the virtual value function and, under quasilinear preferences, derive the first closed-form solution for the optimal verification mechanism. Theoretically, we prove that higher verification accuracy strictly improves both allocation efficiency and the principal’s share of surplus, and that these two objectives are positively correlated. Our results establish a theoretically rigorous yet practically implementable foundation for credible information elicitation.

This paper studies fair and incentive-compatible allocation of indivisible goods among multiple agents. For agents with additive valuations, it proposes a randomized mechanism design framework that achieves ex-post approximate envy-freeness (EF1 and its generalization EF$^{+u}_{-v}$) and Pareto optimality under ex-ante truthfulness constraints. Key contributions are: (1) the first construction of a randomized mechanism for two agents that strictly satisfies both EF1 and truthfulness; (2) a proof that for any $n$ agents, there exist $u,v = O(n)$—depending only on $n$, not on the number of goods $m$—such that EF$^{+u}_{-v}$ is achievable via a truthful mechanism; and (3) the first mechanism achieving truthfulness, EF1, and Pareto optimality simultaneously under bivalued utilities. The results cover concrete cases including EF$^{+0}_{-1}$ (i.e., EF1) and EF$^{+1}_{-1}$, and extend to trivalued utilities.

This study addresses the problem of dynamic team formation and incentive contract design for a principal facing an online sequence of adversarial agents, with the goal of maximizing the principal’s utility. Integrating economic contract theory with online algorithms, the work models agents’ rational effort decisions under performance-based contracts after team assignment and selects the optimal team under irrevocable elimination constraints. The paper innovatively bridges contract theory and online algorithms by introducing a “balance point” technique, establishing—for the first time—the existence of a randomized online algorithm achieving a competitive ratio of 1/2 under additive rewards, which is provably optimal among all randomized algorithms. Furthermore, it demonstrates that no deterministic algorithm can guarantee a bounded competitive ratio in this setting.

This study investigates whether standard matching mechanisms remain effective in markets populated by large language model (LLM) agents. By comparing decentralized free negotiation with centralized mechanism-based markets in a one-to-one matching setting, the authors systematically evaluate the stability and efficiency of LLM agents as decision-makers. Using controlled simulations with canonical mechanisms—Deferred Acceptance (DA), Efficient DA (EADA), and Top Trading Cycles (TTC)—the experiments reveal that mechanism-driven markets substantially outperform free negotiation. LLM agents report their true preferences significantly more often than humans under DA and EADA, supporting the applicability of matching theory to AI-agent markets. However, TTC does not consistently elicit higher truthfulness, highlighting a partial misalignment between the formal properties of mechanisms and the strategic behavior of LLMs.

This study addresses the design of strategyproof mechanisms for dual-facility location on discrete graphs, where heterogeneous agents must be assigned to one of two facilities they approve, with the objective of minimizing the total social distance cost. For line graphs, the authors propose a novel mechanism combining a fixed parity median rule with a strategyproof local covering scheme, achieving the optimal approximation ratio of 4/3 and thereby closing a long-standing theoretical gap. For general connected graphs, they devise a strategyproof 2-approximation mechanism and establish a lower bound of 3/2 on the approximation ratio for the specific case of $K_{1,3}$ (claw) graphs, revealing an inherent computational hardness tied to this graph structure.

This work studies strategyproof facility location mechanisms in Euclidean space aimed at minimizing social cost. It proposes a randomized mechanism, RR-CWM, which locates the facility randomly among non-agent-reported points and achieves—in two dimensions—the first tight expected approximation ratio of $4/\pi \approx 1.27$, improving upon the $\sqrt{2}$ barrier and thereby separating the performance bounds of randomized and deterministic mechanisms. In $\mathbb{R}^d$, the mechanism yields an approximation ratio within $[1.41 - O(1/\sqrt{d}), 1.547]$. Furthermore, the paper refines the consistency–robustness trade-off for learning-augmented mechanisms and establishes a stronger lower bound for generalized randomized dictator mechanisms.