ECON-6110
This is an informal note to record what I thought about or what I thought was important in the Game theory class.
Hemi-continuity and fixed point theorem
When I was first learned about hemi-continuity in math camp, I was not sure why we need to know this concept. The only intuition I had was that it is sort of a generalization of the continuity definition to correspondence. But after taking the game theory course, I finally realized that we need this condition to apply Kakutani fixed point theorem. FYI, we need kakutani fixed point theorem to prove that Nash eqm exists.
Ex-ante, interim, ex-post
When talking about (expected) payoff of agents, it is important to know whether the agents are maximizing ex-ante, interim, or ex-post. For example, revenue equivalence theorem in auction is about equivalence of autioneer’s expected payoff ex-ante, not ex-post. Fortunately, chatgpt did a good job in summarizing the definition in a table.
Normal form and extensive form
It is important to note that the main difference between normal form game and extensive form game is not the timing. That is, fundamental difference between normal form and extensive form game is not whether the agents make decisions at the same time or not. For example, think of a game where agents makes decisions at different timing but they cannot observe others’ actions. In this setting, the game is still a normal form. The game becomes “extensive” when some agents can observe other agents’ actions before making their own decisions. Thus, the main factor that differentiates normal form and extensive form is whether agents make their actions after observing other’s actions.
Adverse selection
I thought it was interesting to learn that the key takeaway from adverse selection isn’t just the presence of information asymmetry between agents, but that this asymmetry impacts other agents’ payoffs. In fact, this is the main factor leading to the presence of adverse selection. In the famous lemon market example, adverse selection will not occur if there were separate and independent dimensions of utility for the seller and buyer.
Revenue equivalence theorem
Although I learned this concept in undergraduate micro class, it was still very cool to know that ex-ante expected revenue becomes equivalent for all standard auction games.