 Let us look at an example of VCG inaction or the victory park roads mechanism inaction and it'll be a routing transportation problem. So here is a directed network of links. Each link has the cost of the length of it if you wish and the goal is to find a shortest path from A to F. Obviously looking at it, it will be quite obvious that the shortest path is this one. And so this is the path that would be selected by a traveler who wishes to get there from A to F most quickly. Now according to VCG, how much would the owner of the link A F pay? Well, intuitively, he's not part of the path, so we shouldn't have to pay or receive anything. Let's see what VCG says. So the shorter path with AC's declaration of what their cost is is five, right? And so the cost to all the agents is that shortest path totaling five. Had AC not been in the picture and not declared anything there for what would the total cost to the agents have been? Well, it would have been the very same path, so the shortest path. And so the cost would have been five also. And so the amount that AC pays if you wish is the difference between the cost to the agents with him in the picture and the cost without him in the picture, which of course is zero. And this is true for all the other ages, other edges that don't participate in the shortest path. All these edges draw in blue, these edges not participating the shortest path will will neither pay nor seep anything according to VCG. So that's the easy part. What about edges that do participate in the shortest path? So let's look for example at one of them at AB. Well, with the shortest path, as we know, is this one and how much would all agents other than AB itself, what is the cost on the agents on the shortest path? Well, it's one plus one is the cost of two. Had A been not been in the picture, what would have happened? Well, the shortest path would have been this one over here. So this would have been the shortest path of a cost of two plus three plus one. And so the cost to the agent AB is the difference between the cost without them in the picture, which would have been minus six, and the cost with them in the picture, which is minus two, that is the cost to all the other agents, and the difference is minus four. So the cost to AB is minus four. In other words, AB will get a payment of four, making if you wish a profit of one because their cost is three, they'll get a payment of four, and they'll have a benefit of one. So this is for AB. What about BE, for example? Well, it's the same sort of analysis. BE, the cost to all other agents without BE in the picture is minus six. It's still, this would have been the shorter route, had BE not in the picture, and cost would have been minus six. Now the cost to the agents with BE in the picture to the agent other than BE is four. Why is that? It's one plus three, and so the cost to, this is the minus four over here, so the net of it is that the cost imposed on by VCG on the link BE is minus two. In other words, they would get a payment of two, making again a profit of one if you wish. What about EF? Same sort of calculation, although the outcome would be a little different because in their case, they will be getting a payment of three. Why is that? Well, without them in the picture, this would no longer be the shortest path. The shortest path would be a cost of seven, whether it's this one or this one in both cases, the cost of the first path would be seven, so the total cost to the population without them in the picture would be seven. With them, the cost is, again, the one plus three, it's a four, and so they get the difference of three. So the payment would be three, and therefore the net profit, if you wish, it would be three minus one, namely two. So you could ask, why is it the difference? You look at all these links, somehow their net payoff is different, and is that fair? Well, fairness is in the eye of the beholder, but the rationale for it is that they have different market power. The amount of social value they bring is different because without them, the outcome would be different to the population, and that's why they have different sort of payments and different cost structures here. That's an example of VCG in operation.