A principal decides which party deserves a prize. Only the parties observe the state that determines who is deserving. The principal gives each party a text describing the conditions under which that party deserves the prize and asks each to report the state. The parties are nonstrategic. Each activates a known cheating procedure whose outcome depends on the state and on the text. Implementation is achieved if, whenever the parties disagree, the liar is identified by the “one-way cheating principle”: The truthful party is the unique party who could not have produced his story had the rival's story been true.

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:

Optimal Risk Adjustment in Markets with Adverse Selection: An Application to Managed Care by Jacob Glazer and Thomas G. McGuire. Published in volume 90, issue 4, pages 1055-1071 of American Economic Review, September 2000

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.