 Hello, everyone. This is Alice Gao. In this video, I'm going to explain the answer to clicker question on slide 22 in lecture 22. So we're considering the whole more dancing game and this question asks you which one of the outcomes is a dominant strategy equilibrium, or is there even a dominant strategy equilibrium of this game? The correct answer is that dancing dancing is the only dominant strategy equilibrium Let's take a look why? So first of all notice that this game is completely symmetric Right Alice and Bob are completely symmetric So we only need to consider one of the players and the other players the analysis for the other player is Completely the same. So let's focus on Alice Let's look at how Alice wants to play the game Given a particular strategy for Bob. So Bob has two possible actions One is to stay at home and the other one is to go dancing So what happens if Bob stays at home? If Bob stays at home, we are looking at the left column right here I've highlighted that the left column and Given the left column What happens if Alice goes dancing versus Alice stays at home? So if Alice goes dancing her utility would be one as given by the matrix here If Alice stays at home, the her utility will be zero. So one is bigger than zero Therefore Alice prefers Alice prefers going dancing then stay at home What happens if Bob goes dancing? Then we're looking at this right column and Similarly we can look at what happens if Alice goes dancing her utility is two and What happens if Alice stays at home her utility is zero two is better than zero So again Alice prefers going dancing to stay at home In both cases Alice prefers going dancing, right? This means Regardless of what Bob does regardless of Bob's strategy Alice's Utility for going dancing is Better than Alice's utility of staying at home and also notice that both inequalities are striking qualities, right? so this means that Dancing is a dominant strategy for Alice because it satisfies the definition Let's recall the definition the definition should say that if dancing is a dominant strategy for Alice then Alice's utility for going dancing should be Weekly better than her utility for any other strategy Given any strategy for Bob and here that's the case because going dancing is Definitely weekly better than stay at home regardless of Bob's strategy And the second condition is that Alice should strictly prefer going dancing than stay at home for at least one strategy of Bob And in fact for this case for both strategies both actions of Bob Alice prefers going dancing than stay at home Right, so this satisfies the definition which means Dancing is a dominant strategy for Alice and because the game is completely symmetric So dancing is a dominant strategy for Bob as well Therefore dancing dancing is a dominant strategy equilibrium of this game And this is the only dominant strategy equilibrium of the game That's it for this video. Thank you very much for watching. I will see you in the next video. Bye for now