Losing Face

When person A makes an offer to person B and B rejects it, then A may "lose face". This loss of face is assumed to occur only if B knows for sure of A's offer. While under some circumstances loss of face can be rationalized by the consequences for future reputation, it may also enter directly into the utility function. Loss of face concerns can lead to fewer offers and inefficiency in markets that involve matching, discrete transactions, and offers/proposals in both directions, such as the marriage market, certain types of labor markets, admissions to colleges and universities, and joint ventures and collaborations. We offer a simple model of this, and show that under some circumstances welfare can be improved by a mechanism that only reveals offers when both parties say "yes".