Sheldon, from The Big Bang Theory, says that if someone buys you a present for Christmas, then “the essence of the custom” is that you have to purchase a gift that is of equal value and represents the same level of perceived friendship that the assistance that you gave me defined.
If you are like Sheldon and have trouble deciding what to get for Christmas or who to give it to, the math of Game Theory can help.
Imagine two people (players 1 and 2) who decide whether or not to give each other a present. Each person can choose between two strategies: either they buy the gift, or they don’t. They get an “E” if they receive a present, and there’s a “C” if they give one. The “C” could be financial or based on the effort.
The possible outcomes of this particular game can be represented in a matrix of payoffs, where each entry is divided into two parts: the gain of player one and the profit of player 2.
The math of generosity. Rachel Norman and Anthony O’Hare are the Authors.
It means that if two players give each other presents, they will both receive a reward equal to the pleasure they feel from receiving the gift minus the price of the present. If one player buys a present and the second does not, the first person receives enjoyment with no cost while the other has cost but no joy. If neither of them purchases a gift, there will be no cost and, therefore, no payoff for either player.
The Prisoner’s Dilemma is a popular game that was created in 1950 by Merrill Flood & Melvin Dresher. It has evolved over the years. The final round of Goldenballs, for example, was a Prisoner’s Dilemma. A particularly good example can be found here:
It seems counterintuitive that both players would benefit from buying each other presents because, in this case, E-C has a positive outcome. It is better to defect if one knows the other will cooperate. That way, they get the gift for free. If both players defect, they will both lose out.
Mathematically, it’s better to avoid exchanging gifts in this game, as we are in a situation called Nash equilibrium, where our actions cannot improve our circumstances.
Last Christmas, I gave you my heart.
The above result assumes we only play the game once. We are facing a more complicated Iterated Prisoner’s Dilemma. If we play against someone, we will be spending many Christmases and who will remember our past actions.
Robert Axelrod wrote a book in 1984 called The Evolution of Cooperation that examined the Iterated Prisoner’s Dilemma. He discovered that greedy strategies are less effective in the long term, while generous plans perform better. Anatol Rapaport proposed the winning design for this iterated version of the game, which is called “tit-for-tat.”
This strategy has you cooperating for the first year and then doing what your opponent did in our game, which would be giving a gift this year, then watching what your friend did and doing the same thing next year.
Some people find it difficult to decide what gifts other people will enjoy. It can be a disaster when they give gifts that are not appreciated. Small children are usually very happy with the skills they receive, and this can be done at a low cost. Teenagers can be tricky. Almost everything they desire is expensive, and even though they may enjoy it, the joy they receive is lessened.
Socks will always be a difficult proposition. They are relatively cheap, but the people don’t necessarily like them. Vouchers, on the other, are a better option so long as the retailer is correct. Their “value” will be clearer.
What is the joy of giving?
If you add the pleasure of giving “J,” however, your game will change completely. If you are able to change your payoff from -C (when buying a gift) to J-C (when giving a present), and that is favorable, then it is best always to purchase gifts, as this becomes the Nash equilibrium.
Leonard Nimoy – A good stocking stuffer? s_bukley
How did Sheldon resolve the problem? He purchased several baskets with varying values and decided to give the one that was closest in value. Penny gifted Sheldon with a napkin that contained “the DNA from Leonard Nimoy.” While the gift’s value was not high, Sheldon valued it so highly that he decided to give her all of the gift baskets.
What can we learn from mathematics? The best thing to do is be generous, especially if the joy of sharing is the most important aspect of Christmas. If our family and friends read this, please don’t ask for Leonard Nimoy’s DNA.
The perfect family harmony recipe is to have holiday rituals. You might have to take three flights, and they are almost certain to be delayed. Your uncle will get drunk again and have a political disagreement with his son-in-law. According to Nobel Prize winner Daniel Kahneman, this will not ruin the experience.
Kahneman’s study shows that we remember only the most memorable moments of our past, and we pay little attention to the rest. The “Peak-End Rule” is what’s known.
The memories of family holidays will be dominated by the rituals, both joyful and silly, the food, the gifts, and the goodbyes at the end of each night after your uncle has reconciled with his son-in-law. You’ll be able to plan for the next holiday when you return home.
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