Game Theory - notes

Following the reference in Naval’s Farnam Street podcast and this tweet, decided to give it a try to learn Game Theory. Game Theory seems to have application in economics, political science, biology, computer science and even in philosophy – seems to something to learn to better understand the world. One of the references to learn Game Theory from the twitter replies was the Yale University course on Game Theory taught by Ben Polak. Started it today and finished 3 lessons. Taking some notes for future reference.

Lesson 1:-

• What strategy should a rational person choose in the Grade Game (if you and someone had to bid anonymously and the grade depended on the combined choice)?
• “You should never play a strictly dominated strategy” – if you know the strategy which will always be dominated, don’t go for it.
• “Rational play by rational players can lead to bad outcome.” Prisoner’s Dilemma example – most will choose to defect. Morality and trust question.
• “To figure out what actions you should choose in a game, a good  first step is to figure out what are your payoffs (what do you care about) and what are other players' payoffs.”
• “If you do not have a dominated strategy, put yourself in your opponents' shoes to try to predict what they will do. For example, in their shoes, you would not choose a dominated strategy.”

Lesson 2:-

• When you put yourself in someone else's shoes, you should consider not only their goals, but also how sophisticated are they (are they rational?), and how much do they know about you (do they know that you are rational?)
• When considering strategies, eliminate dominated strategies. Choosing a number and winning based on accuracy to match 2/3^rd of the average – if we eliminate dominated strategies (>67), then average is around 30, but if other’s also consider that, then it eliminates >45 as well, then the 2/3^rd of average reduces to around 20 and iteratively to 1. But then some irrational choices also happens, hence the eventual winner is closer to a lower number. If you play again, the value reduces further.

Lesson 3:-

• Median voter theorem – in politics, once we eliminate dominated strategies (political positions on a spectrum that are extreme to left or to right), candidates will swing to the center. Over time, the left candidate will move towards conservative and the right candidate moves towards liberal.
• Best Response - a new idea to get us beyond iterative deletion. Think about our beliefs about what the other player is going to do, and then ask what is the best strategy for us to choose given those beliefs?