  In mechanism design theory, a designer would like to implement a social
choice function which specifies her favorite outcome for each possible profile
of agents' private types. The revelation principle asserts that if a social
choice function can be implemented by a mechanism in equilibrium, then there
exists a direct mechanism that can truthfully implement it.
  This paper aims to propose a failure of the revelation principle. We point
out that in any game the format of each agent's strategy is either an
informational message or a realistic action, and the action format is very
common in many practical cases. The main result is that: For any given social
choice function, if the mechanism which implements it has action-format
strategies, then "\emph{honest and obedient}" will no longer be the Bayesian
Nash equilibrium of the direct mechanism, actually the social choice function
can only be implemented "\emph{dishonestly and disobediently}" in Bayesian Nash
equilibrium by the direct mechanism. Consequently, the revelation principle
fails when the format of each agent's strategy is an action.
