Magical Implementation (joint with Jacob Glazer)

A principal needs to decide which of two parties deserves a prize. Each party privately observes the state of nature that determines which of them deserves the prize. The principal presents each party with a text that truthfully describes the conditions for deserving the prize and asks each of them what the state of nature is. The parties do not behave strategically. Each party can lie by activating a cheating procedure which relates to the state and the text given to him. The principal “magically implements” his goal if he can come up with a pair of texts satisfying that in any dispute, he will recognize the cheater by applying the following rule: the truth is with the party satisfying that if his statement is true, then the other party (using the cheating procedure) could have cheated and made the statement he is making, but not the other way around. Several examples are presented to illustrate the concept.