Lesson Time

This article is part of a series entitled Everyday Game Theory. See also:
1. The Escalator’s Dilemma; 2. Electoral College; 3. Passing Curiosity; 4. Lesson Time

This is (a slightly modified version of) a text message exchange which recently occurred between my violin teacher and me.

  1. Teacher: “Can we meet today instead of tomorrow?”
  2. Me: “That’d be great!”
  3. Teacher: “Cool, see you this afternoon.”
  4. Me: “Ok.”

It would not have been acceptable for me to fail to respond to my teacher’s message (1). If I didn’t respond, my teacher would have no way to know whether I ever received her message – and, hence, whether to come today or tomorrow.

Neither would it have been ok, for that matter, for my teacher to let the conversation end at message (2). Until I receive her confirmation (3), I can in no way be sure whether she has seen or acknowledged my message (2). In other words, with her message (3) unsaid, it could remain the case, for all I know, that my teacher, as yet unaware of my response (2), imagines me unaware of (1) and still intent to come tomorrow.

Even after I received my teacher’s message (3), though, it was important for me to send the further message (4). After all, until she receives my message (4), my teacher may well imagine me unaware of her message (3). In that situation — her thought process might go — I would, unaware of her confirmation (3), be liable to suspect her unaware of my response (2), and hence unsure of my receipt of (1), and so liable to come tomorrow.

Why doesn’t this continue? Continue reading