A Truthful Multiunit Profit-Optimal Mechanism for Synthesizing Social Laws

2026-05-16

AI Summary

This work addresses the synthesis of social norms in strategic multi-agent environments by modeling it as a Bayesian single-parameter multi-unit procurement auction grounded in Alternating-time Temporal Logic (ATL). The authors introduce a representation lemma that compresses valuations satisfying alternating bisimulation into a characteristic set of ATL formulas, and reduce payment determination to allocation determination. This reduction enables, for the first time, the transformation of an FP^NP-complete allocation problem into an integer linear program (ILP). The resulting PO-ASL mechanism is theoretically guaranteed to be incentive-compatible, individually rational, and profit-maximizing in expectation, while remaining efficiently implementable using standard ILP solvers.

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.

Problem

• Social Law Synthesis
• Mechanism Design
• Multi-agent Systems
• Profit Optimization
• Truthfulness

Innovation

• Social Law Synthesis
• Alternating-time Temporal Logic
• Multi-unit Mechanism Design
• Truthful Mechanism
• Integer Linear Programming