 Hello everyone, this is Alice Gao. In this video, I'm going to give a detailed explanation of the clicker question on slide 26 in lecture 22. In this question, we looked at the second normal form games about dancing or running, and the question is does this game have a dominant strategy equilibrium? If it does, then which one of the four outcomes is a dominant strategy equilibrium? The correct answer is that this game has no dominant strategy equilibrium. So even though our intuition tells us that either dancing, dancing, or running and running, both can be reasonable outcomes of this game, but dominant strategy equilibrium does not give us any prediction about how the players would behave. Let's look at how I derived the correct answer. First of all, notice that this game is again symmetric, which means we only have to consider one of the players, and there the analysis for both players would be exactly the same. So let's consider Alice. Now, when we're considering Alice, when we're trying to figure out whether Alice has a dominant strategy, we need to look at if Bob chooses a particular action, then which action does Alice prefer? If Bob chooses another action, then which action does Alice prefer? If we can find one action for Alice such that no matter what Bob does, no matter what action Bob chooses, Alice will always prefer the same action, then that action will be a dominant strategy for Alice. Let's take a look. So there are two choices for Bob. Bob either goes dancing or Bob goes running. So for the first case, when Bob goes dancing, then we can write down the utility for Alice. So the utility for if Alice goes dancing, so this is the first case when Bob goes dancing, if Alice goes dancing, then her utility is two. If she goes running, then her utility is zero. So of course, Alice strictly prefers going dancing than going running. So in this case, dancing is better for Alice. What about if Bob goes running? If Bob goes running, we're looking at the right column, and if Alice goes running, two, then her utility is one. If she goes dancing, then her utility is zero. So when it's better than zero, Alice strictly prefers going running than going dancing. So what's happening here is that depending on Bob's action, Alice has different preferences. If Bob chooses to go dancing, Alice prefers dancing. If Bob goes running, then Alice prefers running. So since Alice prefers different things depending on Bob's action, that means there's no single action that's best for Alice, no matter what Bob does. Because of this, Alice doesn't have a dominant strategy, and if Alice doesn't have a dominant strategy, then the entire game does not have a dominant strategy equilibrium. You can do the entire analysis from Bob's perspective as well, and it will be pretty much identical. So that's everything for this video. Thank you very much for watching. I will see you in the next video. Bye for now.