On amending the Maskin's sufficiency theorem by using complex numbers

TL;DR

This paper proposes a novel approach using complex numbers to amend Maskin's sufficiency theorem, enabling agents to enforce agreements against certain social choice rules under complete information.

Contribution

It introduces a complex-number-based self-enforcing agreement that amends Maskin's theorem by relaxing previous conditions with communication channels.

Findings

Agents can successfully fight bad social choice rules with the proposed agreement.

The amendment applies under complete information and specific monotonicity conditions.

The approach extends the theoretical framework of mechanism design using complex analysis.

Abstract

The Maskin's theorem is a fundamental work in the theory of mechanism design. In this paper, we will propose a self-enforcing agreement by which agents can fight a bad social choice rule which satisfies monotonicity and no-veto if an additional condition is satisfied. The agreement is based on complex numbers and is justified if the designer receives messages from the agents through some communication channels (e.g., Internet). Under the assumption of complete information among agents, the designer cannot prevent the agents from signing such agreement. Thereby, the Maskin's sufficiency theorem is amended.