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

The revelation principle fails when the format of each agent's strategy is an action