Eating at my Family’s Place using Game Theory
The applications of Game Theory are omnipresent. In the above article, Presh Talwalkar reasons about eating at an Indian party by using Game Theory. In his humorous article, he explains how in most Indian parties, the host force feeds their guests a lot of food, causing the guests to become stuffed (since in Indian culture wasting food is unacceptable). As a guest, Mr. Talwalkar attempts to strategize the appropriate amount of food to eat, in order to “outsmart” the host, so that he does not feel stuffed. In the article, Mr. Talwalkar constructs a Game Tree, which, through the tree’s branches, illustrates the various decisions he can make, along with the host’s response to those decisions. At the end of each branch, is a leaf which represents the payoffs to both him and the host for the various decisions that they make. Mr. Talwalkar concludes that his dominant strategy is to self-serve his food and eat slowly.
As a fellow Indian, I resonate with this article completely. Whenever I visit my family in India, I usually leave their home feeling completely stuffed. I first eat a lot, and then usually get force fed a second serving, and because I don’t want to waste food, I gobble up the rest. I decided to do what Mr. Talwalkar did, and I modelled eating at my family’s place using game theory. Instead of using a game tree, I used a payoff matrix. I have two strategies, “Eat Lots” or “Eat Little.” The host (my family) has two strategies, “Force feed me a second serving” or “Do not offer a second serving.”
I chose the payoffs for the payoff matrix, by giving my family a payoff of either 1 or -1. If my family makes a lot of food, and force feeds me extra food, they get a payoff of 1 because they don’t waste food. If my family does not force feed me the extra food, they have to waste the food or stuff themselves, so they get a payoff of -1.
On the other hand, if my family does not make much food, the payoffs are exactly the opposite, -1 if they feed me a second serving (because they’ll have less food for themselves), and 1 if they do not offer me a second serving (they’ll have enough food for themselves).
I chose my payoffs more intricately. I get a payoff of 2 if I eat lots and get force fed a second serving. This is because I get to eat an amazing meal which is a payoff of 5 but I end up stuffed (payoff of -3) so I get a payoff of 2. On the other hand, If I eat a little and get force fed a second serving or if I eat a lot but do not get force fed, I get to eat a great meal without feeling stuffed, so I get a payoff of 5. However, if I eat a little but do not get force fed a second serving, not only do I not get to enjoy a great meal, I also end up starving (because I’m always hungry) so I get a payoff of -10.
In 4 out of the 5 times I visit my family, they make a ton of food, and so the payoff matrix looks like the one below.
Clearly, me eating a little and my family force feeding me a second serving is a Nash Equilibrium. Force feeding is a dominant strategy for my family and eating little is my best response to that strategy. So why is it that I always end up stuffed when I visit my family?
This is because of the 1 out of 5 times that my family messes up and makes too little food. If this happens, and I eat little, I will not be offered a second serving as can be seen by the payoff matrix below. In that case my payoff is -10 as can be seen in the payoff matrix below. In this case me eating a lot and my family not force feeding me is a Nash Equilibrium.
Hence, I do not know whether my family will make a lot or little food, but I know that the probability that they will make a lot of food. Let’s calculate my payoffs for eating a lot versus eating a little. If I always eat a lot, 80% of the time I get a payoff of 2, but 20% of the time I get a payoff of 5 so my average payoff is 0.8 * 2 + 0.2 * 5 = 2.6. If I always eat a little, 80% of the time I get a payoff of 5, but 20% of the time I get a payoff of -15 so my average payoff is 0.8 * 4 + 0.2 * -15 = 1. Therefore, it is better for me to always eat a lot, which is why I usually end up stuffed.