## Dilemma of the email kiss

A few days ago Julia came to me with a bit of a dilemma.  An older colleague had, for the first time, ended an email with an ‘x’.  This was a colleague towards whom she felt a degree of affection and friendship, so the question was: should she put an ‘x’ at the end of her reply?

Now, I am a simple sheep and unable to really comprehend the deep and subtle factors which go into the etiquette of humans.  But I am a mathematician, and thought it would be fun to analyse the situation with a bit of game theory.  The way I see it, there are three possible reasons for someone putting an x at the end of a message:

1. Accidental.  When you send a text message, for example, it is usually for a close friend or loved one, so you get used to typing an x automatically at the end of a message. One day you might accidentally put one in a message for someone who is not a usual recipient of a kiss.  Similarly, if you are writing an email whilst simultaneously daydreaming about the love of your life, you might put an x at the end without stopping to think who it is you are writing to.
2. Friendship. A kiss in a message usually indicates that the sender bears some affection for the recipient.  When it appears for the first time, it could mean that the sender is happy for the relationship to move from one of professionalism to one of friendship.
3. Love. In some cases, the sender of an x is in love with the recipient, with the symbolic ‘x’ standing for an actual kiss.  (In this situation though, it seems more common for humans to send multiple xx’s!)

So, we can analyse the payoff matrix for the two outcomes of ‘kiss’ or ‘no kiss’ in the reply message for each of the three possible reasons.  Of course, the entries of the matrix are subject to dicussion, but here’s what I think.  The scale goes from -5=very bad to 5=very good, where it is assumed that the preferred outcome is mutual friendship.

Reason for ‘x’
Accidental Friendship Love
Return kiss -3 5 -5

In this table I assume that the ‘Love’ option is to be discouraged, but of course for other people in a similar dilemma this might be different!

The pedants among you may protest that this is not really a payoff matrix in the strict game-theoretic sense, because it is somehow a one-player game.  The sender of the ‘x’ cannot change his ‘strategy’ (i.e. reason for sending).

But ignoring that, can this analysis give us a clue about the optimum strategy for Julia to adopt?  Although the ‘return kiss’ option has a higher maximum outcome, the ‘no kiss’ strategy has a higher average outcome.  So, if she were really unaware of which of the three possible reasons for the x were most likely, then not putting an x on the return email is the best bet.

What if we assign some probabilities to each outcome?  In Julia’s case, the ‘Love’ reason is very unlikely, say 3%,  with ‘Friendship’ at 50% and ‘Accidental’ at 47%.  The expected outcome for the ‘no kiss’ option is then

0.47 * 2 + 0.5 * (-2) + 0.03 * 4 = 0.06

while the ‘return kiss’ option gives us an expected value of

0.47 *(-3) + 0.5 * 5 + 0.03 * (-5) = 0.94

which is clearly a winner!

Have you ever been in a similar situation?  Do you disagree with the analysis?  Please comment and say what your advice would have been!

### 2 responses to this post.

1. Posted by Ewe on April 24, 2010 at 7:17 pm

A thorough analysis, to be commended. x