Michael I. Jordan: uncertainty

Transcript context

…Oh, well, game theory is a discipline, a mathematical discipline, know. It started with Von Neumann in the twenties and it's got many many branches to it. And it's a mathematical way of thinking, really. And 1 way I like to think about it is that it's like f equals m a. It's a set of it'll make predictions, okay? So if I write down a game, just like I wrote down f equals m a in some coordinate system, I can now predict what'll happen. And in the case of f equals m a, I integrate a differential equation. In the case of game theory, write down the game and I calculate the Nash equilibrium or the correlated equilibrium or some other equilibrium concept and I say, here's what will happen in nature. Because my little mathematical model captures the appropriate ingredients. And for f equals ma, yeah, the thing follows a parabolic curve. It means that the theory is right. And then Einstein said it's not quite right and he makes a better 1. And in game theory, same thing. You look at, okay, do those equilibria actually characterize how systems and organizations and people behave? Sometimes yes, sometimes no. But those aren't that's not the end all. So there's all kinds of other equilibria, Stackleburg equilibria and sequential equilibria and various kinds of figures of merit, various social welfare constructs, various regret constructs and all sorts of things. It's a whole huge field of its own. And let's think about it eventually kind of being as big as physics because it's all about strategic interactions and so on, but not molecular interactions. Now, you can also ask the inverse question. In physics, the inverse question was the, I wanna build a bridge. So my goal is not just to see if something follows a parabolic path or something. I want that bridge to stand up. So I invert f equals m a. I go from the goal back to the design that would ensure that that thing stood up. Alright? And so most engineering fields are inverse problems. They go from the goal back to the design. Whereas the the forward direction is science. You say, here's the setup, here's the prediction. And is the prediction realized or not? So okay, yes, it is. That means the model must be good. So what's the inverse of game theory? Okay. Well, it's outside of economics, not talked about perhaps that much. Game theory sounds like it's sort of everything. Well, the inverse of game theory is what's called mechanism design. And mechanism design says, oh, I want a certain outcome in the world that that person gets paid, that the wealth is divided equally, that there's some fairness or some market that's created. What game do I design so that that outcome is realized? So I'm the designer of the game. I'm not just taking the game as given and then looking at what it predicts. Mechanism design has got many pieces too. I work in contract theory. That's a part of mechanism design. esigner of the game. I'm not just taking the game as given and then looking at what it predicts. Mechanism design has got many pieces too. I work in contract theory. That's a part of mechanism design. It says, what if I have 2 entities interacting and they're not symmetric, 1 knows more than the other and they have to interact with each other. That's contract theory. Auction theory is another part of mechanism design where I've got a bunch of people coming in and I think of them as symmetric. I don't know who's got more money than who wants to bid more than others but I have this mechanism called an auction that reveals their value. And the outcome is that the person who wanted the painting the most got it. That's that desire, that's 1 desired outcome. Anyway, long story short, game theory is a super rich, not so old discipline, you know, 100 years now, that's that's continuing to evolve and continue to supply all kinds of algorithmic ideas for those of us who are in the business. So I've been mostly a statistician in my career, kind of worried about uncertainty and probabilities and decision making and uncertainty. But when I go to equilibria and games and or economic ideas, then that game theory is part and parcel of the thinking. You've said that we need to be thinking about I mean, we we've spoken about incentives, we've spoken about collectives. The other big 1 is uncertainty quantification. Now, there there's this wonderful field in machine learning called conformal prediction. Yeah. And it was invented by my professor at university, Volodymyr Vork. Oh. And, you know, so we we learned about about the transductive confidence machine.…

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