 This video is going to introduce the idea of mixed strategies and explain why they're important to Nash Equilibrium. So the example that I want to think about here is the United Nations setting up checkpoints to defend against terrorist attacks at a port in Somalia. And you can see that what happens is they they place a checkpoint on the road, they stop all cars like this taxi here, and they go through the contents of the car to make sure that it doesn't contain any explosives or other dangerous materials. Now, let's think about this situation as a game. So there are a variety of different roads that the UN could choose to set up its checkpoint on every hour. For each one of those roads, the the potential attacker could decide to attack that road, and if it's the case that the defender defended that road and the attacker attacks it, then the attacker gets a large negative payoff because they're captured and their attack is not successful. If, on the other hand, the attacker attacks any other road, then the attack is successful, and then the utility of the attacker depends on the value of the target that was attacked and wasn't defended. Now, it's pretty clear that if the UN were to commit to any deterministic strategy, if they were to choose their action in any deterministic way, things are going to go pretty badly for them because the defender, sorry, the attacker would be able to look at what they're doing. They'd be able to watch for a while, see what strategy the UN is following, and then attack something different, and attacks would always be successful. So it must be that this is not really how checkpoints get set up, and indeed, what really happens is that the checkpoints are set up in a randomized way, so that even if the attackers watch for a while and figure out what the randomized strategy is, they're not able to know on a given hour where the checkpoints are going to be, and this means that their value of an attack is limited. So the Nash equilibrium of a game like this is going to involve the defender defending in a randomized way like this, and this kind of a randomized strategy is called a mixed strategy, and that's going to be the topic of the next sequence of videos.