Two-agent Nash implementation: A new result

TL;DR

This paper explores two-agent Nash implementation using Wu's quantum mechanism, revealing that certain conditions prevent implementation, and shows the result applies both in quantum and classical contexts.

Contribution

It introduces a new impossibility result for two-agent Nash implementation when combining Condition μ2 with an additional Condition λ' using quantum mechanisms.

Findings

Condition μ2 plus λ' prevents Nash implementation.

The result applies in both quantum and classical settings.

Quantum mechanisms can alter traditional implementation outcomes.

Abstract

[J. Moore and R. Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [B. Dutta and A. Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two important papers on two-agent Nash implementation. Recently, [H. Wu, Quantum mechanism helps agents combat "bad" social choice rules. \emph{International Journal of Quantum Information}, 2010 (accepted). abs/1002.4294 ] broke through traditional results on Nash implementation with three or more agents. In this paper, we will investigate two-agent Nash implementation by virtue of Wu's quantum mechanism. The main result is: A two-agent social choice rule that satisfies Condition $\mu2$ will no longer be Nash implementable if an additional Condition $\lambda'$ is satisfied. Moreover, according to a classical two-agent algorithm, this result holds not only in the quantum world, but also in the macro world.