IN A STIMULATING RECENT PAPER, Abreu and Matsushima (1992) (hereafter A-M) show how a class of social choice functions can be virtually implemented in iteratively undominated strategies. This work has several important features: the mechanisms used are finite and not too difficult to understand, and so less objectionable in this regard than many in the literature; the class of social choice functions implemented is large; and the solution concept-Nash equilibrium determined uniquely by iterative elimination of strongly dominated strategies-is relatively uncontroversial. The point of this note is to argue that the mechanisms used by A-M unfortunately tend to generate games in which the iterative removal of strongly dominated strategies sometimes is indeed (or ought to be) controversial.2 We proceed by first examining an example of a related but simpler implementation problem in which the argument is easily exposed, then indicating how the argument applies generally in the A-M setup. Consider the following much-discussed two-player coordination game:

We study a principal–agent model in which the agent is boundedly rational in his ability to understand the principal's decision rule. The principal wishes to elicit an agent's true profile so as to determine whether or not to grant him a certain request. The principal designs a questionnaire and commits himself to accepting certain responses. In designing such a questionnaire, the principal takes into account the bounded rationality of the agent and wishes to reduce the success probability of a dishonest agent who is trying to game the system. It is shown that the principal can construct a sufficiently complex questionnaire that will allow him to respond optimally to agents who tell the truth and at the same time to almost eliminate the probability that a dishonest agent will succeed in cheating.

A speaker wishes to persuade a listener to accept a certain request. The conditions under which the request is justified, from the listener's point of view, depend on the values of two aspects. The values of the aspects are known only to the speaker and the listener can check the value of at most one. A mechanism specifies a set of messages that the speaker can send and a rule that determines the listener's response, namely, which aspect he checks and whether he accepts or rejects the speaker's request. We study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified, given that the speaker maximizes the probability that his request is accepted. We show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the L-principle.