V Pattabhi Ram
China was chatting with Wafers. She was a few years younger to him but they were great friends. He always took it upon himself to impart her with some gyan. She was talking about how people tend to play games of one-upmanship at the cost of good relationship. And China was trying hard to explain why this was normal. Especially if the parties were rational!
“Irrational; you mean” said a surprised Wafers.
“Rational” corrected China. And went on to illustrate it. “Suppose two of you are playing a game. Let’s say the game runs like this:
“If your opponent plays mean, you get one point if you also play mean and zero points if you play nice. If your opponent plays nice you get three points if you play mean and two points if you play nice. Remember, you have no idea whether your opponent will play nice or play mean. Understood? So what would you do?”
Wafers thought for a while. “If I want to optimize my profits I will do this. If my opponent plays mean, I will play mean and pick one point. If my opponent plays nice, I will play mean and pick three points”.
“What would you do if you were the one to start the game?” ventured China.
Wafers again thought for a while. If I play nice my opponent might play mean and leave me with no point. If I begin playing mean I will at least get one point. So I will kick off by playing mean.”
“Well said Wafers” remarked China happy that Wafers was turning out to be smart in analysis. . He then asked her, “So what’s the action?” Wafers didn’t let China down. “Irrespective of what my opponent plays, I will play mean”.
“Yup” said China. “The moral is simple. If you are going to do a one-off transaction and you are rational, you will tend to play mean l
Wafers was now genuinely interested. “What would happen if I play the game several times with my opponent? Say, 50 times? Meaning when I play one game I know there is another game to follow.” China smiled. “Hey, you are the young CA with a flair for analysis. Analyze it.”
“If the two of us are mean throughout the 50 rounds, each of us will get only 1 point each time. But if both of us are nice throughout, each of us will earn 2 points per round. Therefore both of we will always be nice” said Wafers a shade uncertainly
China didn’t give her any clue as to which way his thoughts ran. Instead he asked, “Well, you would begin playing nice hoping the opponent will play nice. When will you turn mean?” Wafers was ready with an answer. “I will turn mean the moment my opponent turns mean”. And suddenly it hit her like a lightening. “Oh! My opponent will play mean only after I have played mean”. After a brief pause she added, “This will apply to my opponent also. He will play nice so long as I play nice. Hence we would play nice throughout” said Wafers.
“What’s the moral?” asked China. Wafers replied, “In any deal where several future transactions are likely to take place people will always tend to pay nice”. And then she rhetorically asked, “Right?”
China would not be China if he answered “Right.” He said “Wrong.” As a stumped Wafers asked “Why”, China got into explanation mode. “What would a rational person do? Remember, when it was a one time deal with no prospects of repeat deals, it was optimal to play mean. In round 50, there are going to be no repeat rounds. So it is in your interest to play mean in round 50. Your opponent too is a rational person. He would know that you would plan mean in round 50. So he would turn mean in round 49.
Bravo. Wafers got the message. “The only reason why I played nice in previous rounds was that my opponent will then play nice in the next round. The only reason why my opponent played nice in previous rounds was that I will then play nice in the next round. Now both of us know we wont play nice in round 50. I know in round 49, he is going to play mean so I would play mean in round 48!”
Seeing China smile Wafers realized she had hit pay dirt. “Knowing that I would play mean in round 50, my opponent will play mean in round 49. Knowing that he will play mean in round 49 I will play mean in round 48. Working backwards we should be playing mean bang in round 1”
China closed out, “So even when there are the prospects of repeated deals, a rational person might chose to play mean in round 1.” Wafers understood it but felt that the logic was inverted. “What does it boil down to?” she asked.
“The only way that I can interpret it is to say that where there is no contemplation of an end to the set of deals, like a supplier will continue to supply interminably, then both parties will play nice forever. Another way to look at it is that when a person first decides to play mean he is looking for short term profits, not long term gains”.
“Like killing the goose that laid the golden egg?” asked Wafers
“Like killing the goose that laid the golden egg,” answered China.