Relationships, Apology, and Common Knowledge
Ambiguity vs. transparency in relationships.
Posted Oct 13, 2019
One of the most beautiful fields of game theory is called “Common Knowledge.” One of its basic insights is that situations in which two individuals know a certain evidence are intrinsically different than ones in which, in addition to knowing that evidence, both also know that the other party knows it.
Consider the following example: Suppose that you and your spouse are losing track of one another during a busy shopping day at the mall. Suppose that both of you know that the appropriate meeting place in such an event is the information desk at the ground floor. Would you meet one another at that spot? Not necessarily. Suppose that in spite of each of you knowing that the information desk is the appropriate meeting place, each of you believes that the other person would expect you two to meet at the place where you parked the car. This would obviously complicate the matter. However, if, in addition to knowing that the info desk is the right place to meet, each of you knows that the other person knows this as well, then your chances of meeting up at that spot are much greater. If we go one step further and assume that both of you also know the piece of information I just wrote above—that each of you knows that you both know that the other person knows that the info desk is the meeting place—then your chances of finding one another are even greater.
Common knowledge is one of the most elegant fields of game theory, and it is intimately related to mathematical logic. Its inventor is my friend and colleague Nobel Laureate Bob Aumann, and he is also responsible for some of the most important contributions in it. I, too, have made a modest contribution to the field. However, quite unfortunately, this field did not manage to make an enormous impact in understanding economic problems, and in solving them, for two main reasons: First, in spite of the elegant reasoning I discussed above, most people find it hard to distinguish between common knowledge and simple knowledge when making economic decisions. Second, in many economic environments, common knowledge is not really relevant, even when we are aware of it. On the other hand, one environment, indeed non-economic, in which common knowledge is extremely relevant is that of interpersonal relationships.
Here is an example:
Imagine yourself as a young single who has just moved to a new working place a few weeks earlier, and started paying attention to the stunning girl in the office, who’s also single (as you’ve been told by a colleague) and who you feel is really your type. You admit to yourself that you’ve long passed the recovery phase from your former relationship, and you are determined never to forgo a date that might have a chance. You now face two options: You could easily get the girl’s (let’s call her Ora) phone number from your colleague, and you can initiate a short call or send a message. Alternatively, you can ask your colleague to approach Ora, without referring to you as the initiator, and request that he tries to find out whether a date might work well for her.
I’d recommend the second option, especially if you’re about to see Ora on a daily basis at the office. I am actually pretty sure that you would have chosen option 2 yourself even without my advice, not because of your impressive analytical skills, but because of your basic emotional intuition. What’s the difference between these two options? Well, if Ora is interested in you, there is no real difference: A date will take place regardless which option you choose, and whether the date will be successful or not will not really depend on which of these two options got you into it. The difference between these options is made clear only in the case where Ora is not interested in you, when in spite of the fact that she is really your type, you, unfortunately, are not her type at all.
Let’s start with the second option: With your colleague’s mediation he’d still probably tell you the grim truth regarding how Ora feels about you. It’s also quite probable that in spite of trying to hide it, Ora would know that it all came from you. Unpleasant indeed, but not detrimental. You’d both still manage to go on with your daily routine in the office as if nothing happened. From your point of view she’d never be sure that you initiated the whole thing, and hence you don’t have a real reason to feel insulted. From her point of view, you never approached her, and hence she is not compelled to think that she hurt you, and even less so to think that you know that she knows that she hurt you. The ambiguity serves you both.
Instead, with the first option things look very, very different, especially when Ora is not doing well with lying. If Ora answers directly to your invitation by saying, “Sorry, but you are not really my type,” none of you can escape common knowledge. You’ll be hurt, she will know that she hurt you, you’ll know that she knows that she hurt you etc. This is not a simple insult to take. You’d be losing face, and this is likely to affect how you’ll interact with Ora the day after as a colleague, as well as many days to come.
While sometimes ambiguity is an advantage in most cases common knowledge is superior to simple knowledge. When a black cat is crossing the path between you and someone else, e.g. a friend, a relative or a colleague, because one of you is hurt, feels deprived or cheated, both parties would know that there is a problem, but often none will dare to talk about it, fearing that the tension will escalate, or because of not being sure that the grievance is justified, or simply because talking about it is painful. While you would recognize that the relationship is not doing well, you’d lack common knowledge of this fact. Still communication is likely to change, becoming more formal and less intimate. Sometimes you’d use clues and deny them immediately, and sometimes you’d do your best to not encounter the other person. This state of things may last long, very long, sometimes for years, to the extent that you’d forget where it all started.
This is precisely where bringing in common knowledge may save the day and perhaps also your lifetime relationship with that person. In this respect apology days or forgiveness days—such as Yom Kippur in the Jewish tradition—are the social mechanism to facilitate this common knowledge. First, it makes the process less painful because it is a communal activity, but more important, it designates a specific time for the process to take place. Without it, people may turn suspicious regarding the motives behind the apology: “Why now?” “Is there something new that you you’ve done wrongly, or are you just being nice because there’s something you need?”
Yom Kippur yields a good enough reason for apology that makes it sincere and genuine. We shall all take advantage of it even if we are not religious (or not Jewish), but only in cases where we believe that common knowledge is superior to simple knowledge. How should we know? Only by means of healthy intuition.