Friday, April 30, 2010

A real-world example illustrating sunk costs, cost-benefit analysis, decision-making, and game-playing

I am teaching an elective course, Applied Game Theory, this term. According to the course syllabus, there will be in-class final exam, no midterm exam, and class will be held as usual during the midterm exam week. [You see that I do observe and comply with the rules set forth by our school. Are you, my friend, Lady M, also a VP, reading this now?] There is only one task on syllabus for the meeting in midterm exam week, which is “individually check the progress of game-playing assignment.”

On April 26, 2007, the day before the scheduled meeting, an idea stoke me that perhaps I could run the progress-checking in a more cost-effective and more efficient way. So, I sent out an email via e-learning platform to all enrolled students. I stated clearly that nobody would be asked to show up before 4:00 pm. From 4:00 pm to 4:30 pm, about eight students (names given specifically) would go thru the process with me on an one-on-one basis. Another group will be treated from 4:30 pm to 5:00 pm, followed by the third and the fourth group. I thought that everybody would be happy with this arrangement although it was announced just 24 hrs ahead of the time.

Now let me share with you my conversation with Mr. C. Lin on April 27.
At 3:57 pm, Mr. Lin came to my office with no expression on his face: "I have been waiting for you almost one hour."
I replied: "Got you! How many times do I have to remind you of the importance of checking emails sent thru e-learning?"
He calmly stared at me and slowly moved toward the elevator.
"Are you leaving? Hey, if you leave now, very likely I will hold you for being absent for two or three hours (in class meeting). Come on, it is not worthy! You will lose everything." I said.
"I have wasted one hour already. If I choose to stay, I will have to wait for another hour before you run the scheduled check on my case. In total, I will waste two hours and there is still a chance that you may keep me waiting longer. That is why I should be smart and take off." He replied.
"Wait a minute! Have you forgotten about sunk costs I taught in principles of economics? Do stay! I will not break my promise. Trust me"

What happened? At 4:01 pm, I saw Mr. Lin quietly sat in the classroom and waited for his turn. I will say that he was making a rational decision. Why?
Since he did not get that email notification, he paid the price by wasting one hour (from 3:10 pm to 4 pm). But that is the so-called sunk cost, which should be irrelevant in the following argument.
If he chooses to leave at 4 pm (after speaking to me), he will not get the benefit and the cost to him will be two or three hours counted as class absence.
If he chooses to stay, he will get the benefit and the cost to him will be one hour as the foregone waiting time.
Hence, the cost-benefit analysis tells us that Mr. Lin, provided that he is rational, should stay. And he did! Good for him.

Of course, if I do not keep my promise and somehow handle his case around 6 pm, he will get the benefit but the cost to him will be two hours as the foregone time. Even for this worst scenario, it is still better than his leaving at 4 pm. Besides, if he takes my strategic action into consideration, we will have a two-person game. As I assured him of my commitment in keeping my words, neither of us should have thought about the game-playing.

Credits: 雖然C. Lin偶爾會有所謂的嗆聲動作,他時而能夠即時回答問題,也曾對經濟學小考問題,提出有水準的批判見解。比起一些老僧入定或是喬裝乖乖牌的同學,要強多了。文藻週的至少兩天下午,(我個人覺得有些奇怪的)經典閱讀活動曲終人散時,我由走廊經過,只見他一人在教室默默地還原課桌椅。他的動作,令我聯想起電影「天之驕子」裡,男老師於開學第一天,在空教室對齊書本與桌緣之一幕。就憑這些觀察,日後只要他開口要推薦函 (references),我一定樂意相助。