randomized mechanism analysis

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 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.

Traditional probabilistic laws face persistent challenges—including indeterminate boundaries of physical possibility and acute empirical underdetermination. Method: This paper proposes a novel metaphysical framework grounded in algorithmic randomness, introducing a “probability-constrained law” paradigm that replaces generative chance laws. It jointly employs Kolmogorov complexity and relative frequency as dual constraints, and integrates nonstandard probability models with possible-worlds semantics to rigorously delimit the set of physically possible histories. Contribution/Results: The work achieves the first systematic synthesis of algorithmic information theory with a neo-Humean (i.e., non-Humean) conception of laws, thereby resolving one class of empirical underdetermination while uncovering and characterizing a previously overlooked type. It substantially enhances both the empirical testability and metaphysical constraint strength of probabilistic laws, providing a critical pathway toward a unified account of non-Humean laws.

Existing program logics cannot fully characterize the output distribution of probabilistic concurrent programs, and no distribution-level formal verification methodology exists for such programs. Method: We propose the first distributional verification logic supporting programs combining probabilistic and concurrent features, systematically integrating independence, conditional distributions, and invariants into Outcome Logic, and introducing the first probabilistic concurrent separation principle. By unifying probabilistic separation logic, concurrent separation logic, and Outcome Logic, we design distribution-aware assertions, randomized resource models, and context-compositional proof rules to enable modular, compositional distributional verification. Results: Our logic is the first to precisely model independent execution, conditional dependencies, and concurrency invariants at the distribution level. It supports fully automated formal verification of representative probabilistic concurrent programs, thereby filling a fundamental theoretical gap in distributional verification of concurrent probabilistic programs.

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.

This study addresses the problem of random assignment under two-sided capacity constraints—specifically, minimum and maximum demand requirements for objects, such as enrollment caps and floors in course allocation. To tackle this challenge, the paper proposes the Minimum-demand Probabilistic Serial (MPS) mechanism, which, for the first time, simultaneously achieves Pareto efficiency, envy-freeness, and weak strategy-proofness in settings with such bidirectional constraints. The MPS mechanism generalizes the classical Probabilistic Serial mechanism by integrating insights from random assignment theory and first-order stochastic dominance analysis. The resulting allocation rule strikes a favorable balance between desirable theoretical properties and practical implementability, thereby filling a critical gap in the literature on efficient and fair random assignment mechanisms that accommodate minimum-demand constraints.

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.