  [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.
