Decision Making

The drama of Breaking Equilibrium

We all know O. Henry’s timeless classic, The Gift of the Magi. It is about a young husband (Jim) and Wife (Della). They were too poor to buy a decent Christmas gift for each other. Finally, Della decides to sell her beautiful hair for 20 dollars and buys a gold watch chain for Jim. When Jim comes home for dinner, Della tells the story and shows the gift, only to find a puzzled Jim and finds out that he sold his watch to buy the combs with jewels as a surprise gift for his beloved’s hair!

What would be a rational analysis of the decisions made by the couple in the story? First, draw the payoff matrix. There are four options: 1) Dell and Jim keep what they have, 2) Dell sells hair, Jim keeps his watch, 3) Dell keeps her hair, Jim sells his watch and 4) they both sell their belongings. The payoffs are 

DellaDella
Not Sell HairSell Hair
JimNot Sell WatchD = 0, J = 0D = 5, J = 10
JimSell Watch D = 10, J = 5D = -10, J = -10

When both decide to have no gifts for Christmas, they maintain the status quo with zero payoffs. One of them selling their belonging to buy a gift that the other person dearly wished for brings happiness to the receiving person (+10) and satisfaction to the giver (+5). Eventually, when they lose their belongings, resulting in no material gain for any of them, they both are on negative payoffs. Their sacrifice was in vain!

The author chose an ending called a coordination failure in the language of game theory. It is an outcome that is out-of-equilibrium. For a short-story writer, this brings drama to his readers and conveys the value of sacrifice. In the eyes of millions of readers, the couple’s payoffs were infinite.

The Gift of Magi by O. Henry

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Game of Chickens

Two teenagers are driving towards each other on a straight road, with an apparent show of courage to prove who can stay longer before turning off. Each teen’s expectation is to stay straight for the longest time and force the other person to swerve. The winner shines as the rebel, and the loser becomes the chicken!

Assume A and B are playing, and you can imagine four possible outcomes. 1) A chickens, 2) B chickens, 3) both chickens and 4) they collide head-on (and possibly die!). What are their payoffs? Let’s write down some, based on assumed reasons why they play this game in the first place – teen energy, naivety, happiness, pride, girls (the stereotypes, you see).

Player A
Player A StaysPlayer A Chickens
Player BPlayer B StaysA =-INF; B = -INF A = -100; B = +100
Player B ChickensA = +100; B = -100A = 0; B = 0

If player A stays and player B chickens, A gets +100, mainly in happiness, pride, etc., whereas B gets -100 (in shame!). The exact opposite happens when the fortunes are reversed.

Let’s understand the chances from player A’s point of view. If Player B stays, A can either stay (-INF) or turn away (-100), turning off and giving a better payoff. If B turns away, A can stay (+100) or move off (0). Unlike the case with the prisoner’s dilemma, the choice for A is not unique.

Given all the possibilities, what is an optimum strategy for both players? Both are courageous and stubborn. Assume player A knows B and also knows player B knows player A. It means they both try for maximum returns, but continuing the status quo will be fatal. So, there must be an exit strategy each of them must hold– to swerve away from the other, but at the last possible moment. 

In my opinion, the best option that minimises the shame and, at the same time, prevents death is when both players turn off a second before the crash!

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Predict the Number – Thaler Experiment

In 1997, American behavioural economist Richard Thaler asked the readers of the Financial Times to submit a number between 0 and 100 so that the person whose number was the closest to 2/3 of the average of all numbers would be the winner. What will be your answer to this question as a rational decision-maker?

Your first step is to eliminate the obvious. The highest possible average from 0 to 100 is 100. It happens when everybody submits the number 100. It would mean the answer to the problem is (2/3) of 100 = 67. So, any number above 67 as a submission is not a rational choice.

You can’t stop there. Once you find that the rational choice for the highest number was 67, this number becomes the new highest average, and the (2/3) is 45! This iterative reasoning continues until you reach zero!

What could be an intuitive answer to this problem? Here, you assume people can randomly guess between 0 and 100, and the average is 50. (2/3) of 50 is 33. If you stop after stage 1, you submit 33 as the answer. If you continue for another round, based on the understanding that the average choice of the crowd is 33, the winner choice is 22. The number becomes 15 in the next stage and ends with 0.

So, the rational answer is 0. However, the average obtained in the actual experiment in Financial Times turned out to be 18; therefore, the winner was the one who submitted 12. The leading choices of the readers were 1, 22 and 33! When he repeated the game later, the average was 17.3, and the leaders were 1, 0 and 22.

Thaler Experiment: Financial Times

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Rational Thinking and Prisoner’s dilemma

The prisoner’s dilemma is a much-discussed subject in game theory. Police arrested two individuals for their involvement in some criminal activities and put them in prison. They have adequate evidence to frame charges and hand them two years of imprisonment but not for a maximum of ten years.

Police approach a prisoner and make an offer in return to testify against the other person. If she betrays the other and the other person remains silent, she can go free. If she keeps quiet and the other person gives evidence against her, she gets the maximum punishment of 10 years. If they both remain silent, the existing term of two years continues. If they both testify against each other, they both get five years.

Imagine A is a rational decision-maker, and she assumes that a similar offer may also have gone to prisoner B. She starts from the point of view of the other person before deciding on her own. Person B has two options: remain silent or betray person A. If B remains silent, A can remain silent (2 years) or cross B (0 years). Betray B is currently the better of the two. If B testifies, A can remain silent (10 years) or betray B (5 years). Betray B is the better one here again. In other words, A has no option but to give evidence against B.

Cooperation vs Competition

Decision-making such as this starts with knowing the potential strategies of the other. Once sorted out, the player will opt for the option that protects her, irrespective of the other’s choice. 

A rational decision may not be the decision that gives the maximum payoff. In the present story, cooperation might appear as that option, where each serves two years in jail. But it was not a cooperative game, where both the parties trust each other and form a joint strategy – to remain silent. Therefore, it is not the optimal option in cases where the players compete against each other.

Cold War and Nuclear Build-Up

The Nuclear build-up between the USSR and the USA during the Cold War period is an example of a prisoner’s dilemma in real life. From the viewpoint of the USA or the USSR, the rational (strategic) option was to pile up more nuclear warheads instead of reducing them, although one has every right to argue that the latter could have been the better choice for humankind.

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The First Post

Here we start. ‘Thoughtful Examinations’ is about life, knowledge, and happiness. It’s about numbers, rationality, and perspectives. I welcome you to the experience.

The Life of Chances

Probability, the mathematics of chances, is tightly woven into the fabric of life. Our existence started, evolved, and was nurtured by countless unlikely events – some are linked, some are not. We all studied the subject at school, the endless tossing of coins! Yet, it’s rarely applied in life. We will see the subject of probability and statistics as a recurring theme of my posts.

The Gates of Knowledge are Open

The gates have been crashed; the doors are open. The Tree of Knowledge is no longer hidden from your sight. The internet has made access to knowledge to each one of us. The democratization of knowledge is complete! Remember chances: yes, the chances that you reach your goals are better than ever before.

The Happiness Project

This page is for all who enjoy learning new things or getting new perspectives. This piece is for people confused by the volume of information out in public, finding it hard to separate the truth from the sea of junk. This one is a happiness project.

Life is about chances, knowledge, and happiness.

Once again, welcome to this journey. I offer whatever that I can to make it enjoyable. Remember: life is about chances, rationality, and decision-making.

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