On amending the Maskin's theorem by using complex numbers

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