 Hi everyone, this is Alice Gao. In this video, I am going to discuss the clicker question on slide 9 in lecture 23. In this question, we consider the prisoner's dilemma game and we want to characterize dominant strategy equilibrium of this game. So the question asks, does this game have a dominant strategy equilibrium? If it does, then which one of the four outcomes is a dominant strategy equilibrium? The answer is that defect defect is a dominant strategy equilibrium. Let's look at why. Here are the explanations for the answers. Again, this game is symmetric. I think it turns out all the games I've shown you are symmetric. This might be a problem because you might have difficulties if you see a non-symmetric game in a quiz or something. Anyway, this game is symmetric, so it's sufficient to consider only one of the two players. Let's consider Alice. If we want to characterize dominant strategy equilibrium, then we need to first determine, does each player have a dominant strategy? And remember what is a dominant strategy? Right? Dominant strategy says, no matter what the other players decide to do, there's always a best action for me. If that's a case, then that best action is a dominant strategy for me. So let's look at different actions that Bob can take and then see if Alice always has a best action in response to Bob's action. So for our game, let's suppose that Bob cooperates. In that case, we are in this left column. In that case, if Alice also cooperates, she gets you utility of minus one. When you're in prison, if Alice defects, she gets a utility of zero. Zero is better than minus one. Therefore, Alice prefers to defect. Okay, what if Bob defects? Well, in this case, we are in the right column. So we're in the right column defect. And then let's look at what happens for Alice. Well, if she cooperates, she gets three years in prison. Too bad because Bob testified against Alice. If Alice also defects, then she gets two years in prison. So again, defecting is better than cooperating. So again, Alice prefers to defect. Well, looks like no matter what Bob does, Alice always prefers to defect. So defect is a dominant strategy for Alice. And by symmetry, since the two players are completely symmetric, so defect is a dominant strategy for Bob as well. Therefore, defect defect is a dominant strategy equilibrium for this game. That's everything for this video. Thank you for watching and I'll see you in the next video. Bye for now.