Higher Order Beliefs:
Introduction
We will use a single, powerful framework to
tackle a series of puzzles…
Need a simple way to represent:
- The world is uncertain
- People have different, or private information
Let’s start with a simple, abstract example…
Quick reminder: what is p?
If other is playing A with probability q, I prefer to play A iff
qa + (1-q)b > qc + (1-q)d
…
q > p = (d-c) / (d-b + a-c)
Notice the role of `higher order beliefs’ (HOB)…
HOB don’t always matter. What if playing the
prisoners’ dilemma?
Who cares? Play D
Who cares? Play D
HOB only matter for games with multiple
equilibria
HOB only matter for games with multiple
equilibria
Also, notice what would happen in an evolutionary process…
Another example, to show how important HOB
are in games with multiple equilibria…
Again, let’s see the relationship to HOB…