Losing Face

When Al makes an offer to Betty that Betty observes and rejects, Al may “lose face”. This loss of face (LoF) may cost Al utility, either directly or through reputation effects. This can lead to fewer offers and inefficiency in the context of bilateral matching problems, e.g., the marriage market, research partnering, and international negotiations. We offer a simple model with asymmetric information, a continuous signal of an individual’s binary type, and a linear marriage production function. We add a primitive LoF term, characterize the stable equilibria, compare the benchmark without LoF to a case where only one side is vulnerable to LoF, and present comparative statics. A small amount of LoF has no effect on low types’ behavior, but, will make high types on both sides more selective. A stronger LoF drives high types out of the market, and makes low types reverse snobs, further reducing welfare. LoF also makes rejecting strictly preferred to being rejected, making the “high types reject” equilibrium stable. We can eliminate the effects of LoF by letting the vulnerable side move second, or setting up a “Conditionally Anonymous Environment” that only reveals when both parties say yes. We motivate our model with a variety of empirical examples, and we suggest policy and managerial implications.