Overview
We saw from last class that to deal with games of incomplete information, assuming Bayesian players, we can transform it into a game of complete, but imperfect, information. What does Harsanyi mean by “Bayesian” players? I will now introduce you to the wonderful world of Bayesian statistics — a bit of a detour from game theory, but worth knowing in and of itself. We will then need this in order to solve for equilibria in sequential Bayesian games, coming up next.
The main feature of Bayesian thinking is Bayes’ rule/theorem:
\[P(A|B)=\frac{P(B|A)P(A)}{P(B)}\]
Readings
Bayes’ Rule is very standard in statistics, and so there are lots of great resources explaning it and providing examples. My favorite comes from the Youtube channel 3Blue1Brown:
- 3Blue1Brown Youtube: “Bayes theorem, the geometry of changing beliefs”
- 3Blue1Brown Youtube: “The medical test paradox, and redesigning Bayes’ rule”
- 3Blue1Brown Youtube: “The quick proof of Bayes’ theorem
- The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy
Slides
Below, you can find the slides in two formats. Clicking the image will bring you to the html version of the slides in a new tab. Note while in going through the slides, you can type h to see a special list of viewing options, and type o for an outline view of all the slides.
The lower button will allow you to download a PDF version of the slides. I suggest printing the slides beforehand and using them to take additional notes in class (not everything is in the slides)!
