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arXiv · 2605.16853

A Truthful Multiunit Profit-Optimal Mechanism for Synthesizing Social Laws

Jun Wu·Jian Huang·Chongjun Wang
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Abstract

This paper studies Social Law Synthesis (SLS) in strategic multi-agent environments as a new multi-unit mechanism design problem. We model SLS as a Bayesian single-parameter procurement auction based on Alternating-time Temporal Logic (ATL) and aim to design a truthful, individually rational, and profit-optimal mechanism. We first prove a representation lemma showing that any valuation respecting alternating bisimulation can be compactly expressed as a feature set of ATL formulae. We then reduce payment determination to allocation determination in polynomial time, resolving the irregular payment issue inherent in multi-unit settings. We further show that allocation determination is \(FP^{NP}\)-complete and encode ATL semantics into integer linear programming (ILP) constraints to make the problem tractable with standard solvers. Based on these results, we present the $\mathcal{PO\text{-}ASL}$ mechanism, which is incentive-compatible, individually rational, and maximizes expected profit. Theoretical guarantees and examples confirm that our approach provides an effective and computationally feasible solution for synthesizing optimal social laws under strategic agent behavior.

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Jun Wu, Jian Huang, Chongjun Wang. 2026-05-16. A Truthful Multiunit Profit-Optimal Mechanism for Synthesizing Social Laws. https://arxiv.org/abs/2605.16853

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