Season 4 - Episode 451
What is game theory and how can it shape our understanding of economics, business, politics and more? Baylor’s expert in game theory, Jameson Graber, recently earned a prestigious CAREER Award from the National Science Foundation to conduct interdisciplinary research that seeks answers to important societal questions. In this Baylor Connections, Graber, an assistant professor of math, gives listeners a lesson in “Game Theory 101” and shares more about his research.
Derek Smith:Hello, and welcome to Baylor Connections, a conversation series with the people shaping our future. Each week, we go in depth with Baylor leaders, professors, and more discussing important topics in higher education, research and student life. I'm Derek Smith. And our guest today is Jameson Graber. Dr. Graber serves as Assistant Professor of Mathematics at Baylor. His research focuses on non-linear partial differential equations applied to a wide range of multidisciplinary challenges and questions in areas like economics, political science, and more. Dr. Graber recently earned a coveted NSF Career Award to apply to his research on game theory across these areas. He came to Baylor in 2016, and he has a lot of exciting projects going on these days and appreciate you taking the time in the midst of that to join us. Dr. Graber, thanks so much for joining us on the program today.
Jameson Graber:Thanks for having me.
Derek Smith:Well, it's certainly been an eventful year for you in the midst of the pandemic and all the challenges. You got a significant award, the NSF Career Grant, those are competitive. It's a really arduous process it sounds like to get one and it's a real honor that you received it. So congratulations on that. And I'm curious, how has that career award impacted the last year for you and what does it mean to you and your collaborators?
Jameson Graber:Well, on a personal level, I am very proud to receive this kind of award and it did come as a bit of a shock just because it is such a prestigious award, and I didn't expect to get it right away on the first try, but it was certainly a nice reward after having worked on it during the lock down in 2020 and putting it together over the summer after that. And it all came together. And so I was very happy to receive the news in January that I'd gotten the reward. On a professional level, the biggest impact of the grant is that I have funding to support graduate and undergraduate student research. So they're the most important collaborators on my grant, and being a mentor for student research is one of the most rewarding parts of my job. So I'm very excited about it.
Derek Smith:Visiting with Jameson Graber. And as we talk about your work, we're going to highlight how it's multidisciplinary for maybe people whose math background stopped in high school, or they could just remember the problems that they did when they were in high school or college. Do you have collaborators on this grant? Who are your collaborators that you work with?
Jameson Graber:So I do have some collaborators at Baylor and one is an economist, Wilson Law. And the other is a political scientist, Richard Jordan, and they're mainly to consult with me so that I can actually bring in some interdisciplinary seminars and disseminate these ideas, not just to a mathematical audience.
Derek Smith:Well, as we talk about the award and what your study, we want to really dive into ways that people can apply it or see it in the world around us. So if you were going to try to explain that award to someone who didn't really have a math background, how would you describe what that NSF award is going to? What questions you're trying to answer and how you'll go about that?
Jameson Graber:Right. So the idea of the project is to analyze mathematical models of complex social interactions, like the economy. So for someone with no real math background, I first have to explain what I mean by mathematical model. So we first have to focus our attention on things in the world that can be quantified. So things like time and space, but also things like resources, rate of production, prices, or even your preferences. Then, and this is the hard part, we have to find a precise way to express how those quantities are related to each other. So this can be so difficult that we sometimes invent new mathematics to do it. So for instance, think of Isaac Newton inventing the calculus in order to explain the laws of motion. Now, once we have a model, then we have a mathematical problem to solve just like equations that many of us had to solve when we were in school, right? The solution to that problem is supposed to tell you something that might happen in the real world, because you're talking about a quantity that exists in the real world, like price or like your preferences. So a simple example that freshmen learn in physics is an equation that would allow you to actually determine how long an object that you throw into space would take to come back down to the ground. But unlike the problems that we solve in school, like that one, most mathematical models don't have nice solutions that you can write down on a sheet of paper. And in fact, we often don't know for sure whether there is a solution at all. And if there is, we don't know how to choose which solution is the correct one to apply to the real world. So in other words, you can think of a mathematical model as a kind of machine that takes inputs that you observe and then gives you outputs that are supposed to reveal something about reality. But as a mathematician, I have to ask basic questions like, "Does this machine even work? Is it going to give you a reasonable output?" And we know that for lots of reasons, a mathematical model can never be perfect, can never perfectly respond to reality, but we at least need to verify that it has a chance of being consistent with reality. So specifically my project is all about investigating mathematical models for interactions between large numbers of people. So think about the economy or think about social networks, something like that. Now, just as Newton had to invent his calculus, we have also had to develop some new mathematical concepts in recent years to even write equations that model these sorts of interactions. So part of the interest for me is just to explore how these concepts work. That's why I'm a mathematician. But in addition, I get to see how mathematics might give us new ways to explain what we see happening in a complex global society.
Derek Smith:So, Jameson, we also mentioned at the top of the show, your research in partial differential equations, what are those? And how can those apply to what it is that we're talking about?
Jameson Graber:Yeah. A partial differential equation is an equation that involves functions and their derivatives. So in school, most people at some point had to solve for X, where X was just a number. But now imagine that you have a function that can depend on a bunch of other variables and you have to find that entire function. Well, that's what a partial differential equation is. A function is just a quantity that depends on other quantities, like the amount of wealth you have is a function of the time that you've lived. A derivative is a rate of change. So for example, it can tell you how fast your wealth is increasing at this moment in time. And a partial differential equation can relate several functions and their variables together according to some sort of laws. And so those laws are the product of science, either theory or experiment. And you see partial differential equations everywhere. Literally every science can use some sort of differential equations to model what they're talking about. So we can use differential equations to model the stock market. We can use it to model the flow of glaciers in Antarctica or the spread of infectious diseases, or the spread of all sorts of animals that may or may not be desirable. So it really covers the gamut. Differential equations are everywhere. And a fun example actually is in a lot of the movies that you watch these days, the special effects are actually the product of running computer simulations using PDEs. So yeah, a computer simulation of the solution to a PDE can actually give you something like fluid flow. And that's something that is just amazing these days thanks to computer technology. People literally just solving an equation can make movies of water or even ice that look so real that you think it is real. You have no idea the difference between the computer generated image and the real thing.
Derek Smith:So we're seeing these all over the place, even if we don't always know it.
Jameson Graber:That's absolutely right.
Derek Smith:That's great. And I'm guessing now, as you talk about being interested in relationships between people and how they behave and outcomes, you're talking about derivative and functions, there's almost no limit to the ways you could approach those or find those at those relationships.
Jameson Graber:Yeah, that's absolutely right. And it is a bit more difficult than it is in physics because in physics we just study things that are more inert in the sense that they're not making decisions or anything like that. But when we study... Already biology is complex enough because living things are very complex, but economics and social sciences, these are even more complex because human decision making is probably the most complex thing that we have in front of us. And we're surrounded by it all the time, but to actually model it mathematically is extremely difficult because it's hard to cut through all the weeds and find simple principles behind those interactions.
Derek Smith:This is Baylor connections. We are visiting with Dr. Jameson Graber, Assistant Professor of Mathematics at Baylor, and winner of the NSF Career Award this past summer. I want to ask you about game theory now and how it applies to what we've been talking about. And I know this is the obvious thing to say, but it makes most people who have seen the movie A Beautiful Mind, know at least a little bit about some of the background behind game theory. So maybe that's one hook for people, but what is game theory, and how could any of us who have ever tried to predict how a situation would play out or how people would react to something in our environment, in our lives? How could we envision that?
Jameson Graber:Yeah. Game theory is basically the mathematical analysis of how people interact with each other strategically. So don't think about actual games like chess or video games that you would just play by yourself. A good example to think about actually is driving. So how you drive is affected by other cars on the road. So implicitly your decisions at each moment are a function of other drivers' decisions. And so that's a game, in a game theoretic sense. And by the way, the mathematical modeling of traffic is extremely difficult and potentially quite useful. And this is an ongoing area of research that's pretty active. Another example is a market, of course. So what you buy depends on prices, but prices will depend on what everyone buys. So your decisions are affected by everyone else's decision and that's a game. And that's what we model in game theory, and we try to predict what would be the necessary logical outcome of a situation like that. I will say this about game theory, is that it assumes everyone is rational. Now people tend to scoff at this and with good reason because people don't always make decisions rationally. That's well known. Everybody knows that we have flaws, we didn't sleep enough or we feel sick, or and something, or there's just some sort of quirk in our brains that we don't yet understand psychologically. But that's not the point. The point is that game theory actually reveals surprising conclusions even when everyone is perfectly rational. And that's what I want people to understand about game theory. So a great example of this. My favorite example from economics is the Schelling model. And Schelling came up with a great example of how individuals' decisions can result in an overall situation that no individual actually was going for. So imagine you have circles and squares. Okay. And they all live on a grid. So each one of them has a space on a grid. And if a circle is surrounded by more than 70% squares, that circle wants to move to another tile on the grid. And if a square is surrounded by more than 70% circles, then that square wants to move to another tile on the grid. Okay. So no individual actually cares about being in the majority. They just don't want to be in such a small minority as 30%. Okay. So then you start switching tiles, right? You move this circle to that tile. You move this square to that tile until everybody is happy. And the result that you notice is that actually there are big clumps of squares and big of circles. So they've somehow moved themselves into very segregated communities, even though no individual actually was going for that outcome. It is simply a result of the mathematical realities behind it. So sometimes when we look at a situation and we think, "Well, it has to be that the underlying individuals are making decisions irrationally or wrongly in some way." And actually game theory can reveal that that's not quite right. You have to look at what are the logical consequences of these individual behaviors. And it's not always what you expect.
Derek Smith:That makes sense. So there's kind of those unexpected outcomes or unintended consequences, and it can kind of go back and help you uncover where those are, what the causes of those are?
Derek Smith:Visiting with Jameson Graber. And when did you become interested in game theory and look for ways to apply it whether just in your own interest, hobbies, or your own scholarship?
Jameson Graber:Yeah. It's kind of an interesting story. When I was in graduate school, I studied partial differential equations and I studied mostly physical models. In fact, the first prize I ever got to study research was actually by the Virginia Space Grant Consortium. So I was studying models that were supposed to be applied to things like airplanes and helicopters and the stability of those craft. And so it was a completely different direction, but then I got this postdoc in France and at the time Mean-field game theory was in its infancy and still growing very rapidly. And I just found the mathematical problems to be very interesting. And so, because I was surrounded by this community that was studying this topic, I decided to study it too and found I could make some really interesting contributions. And that's basically how I got to where I am today. And incidentally I've always had a layman's interest in economics. So those two things coming together in my professional life, really, it pleased me a lot.
Derek Smith:So has applied math research, has that always been something you've been interested in? Taking your math research and looking for ways to apply it towards broader real world problems? Or is that something that came later on?
Jameson Graber:Yeah, it's kind of hard to say. I would say that when I entered into graduate school, I really just wanted to study math for its own sake. I was into pure mathematics, but the truth is having applications is rewarding in itself. It's rewarding for two reasons. One is that when you look at real world problems, to actually come up with a mathematical way to analyze them often requires you to come up with new concepts. And so you get new mathematics out of that. But then the payoff in the other direction is that you can potentially have a real world impact. You don't just have to think of yourself as, solving these abstract problems in the ivory tower and never having any point of contact with something outside of your discipline.
Derek Smith:Visiting with Jameson Graber. And how did the idea of applying all this, tying it back to the award that you're working on now, how did that idea develop? What was the genesis of the idea that became this award?
Jameson Graber:Yeah, well, I have to say the core of it came from the research that I was already doing, because I had already made quite a network in the community of Mean-field game theory. And once I had that going for me, I knew that I wanted to expand this into a bigger project, but then the ingredient that really helped it all become a career award, I think was knowing Wilson Law and Richard Jordan, two members of Baylor's faculty who could help me plausibly make a very interdisciplinary project that would incorporate an education component because in the career award, the research is the primary thing, but there also has to be a significant education component and outreach. And so once I realized that I was already talking to these friends and colleagues about game theory, well, I would just incorporate that into sort of a network of ideas on Baylor's campus. And I've also been able to interact with the Mayborn Museum to incorporate some sort of outreach component into the project. And so having all of those ingredients is really what made my research that was already going on into a career award.
Derek Smith:And do I remember correctly that this award is a testament in part to just talking to people at your faculty orientation, a mark in favor of striking good conversations and new situations?
Jameson Graber:That's absolutely right. Yeah. Wilson and Richard, and I have known each other since we just started talking during the break, during our faculty orientation, more than five years ago. So I'm really happy for those spontaneous conversations
Derek Smith:Visiting with Jameson Graber and Jameson as we head to the final few minutes, I want to ask you to kind of help us wrap our arms around this a little bit more, as we've talked about game theory, and we've talked about new problems, there's probably no way to adequately describe it unless you're there, seen it, but the processes of looking for a hooks that allow you to start to sort of tug on where the answers might be or where you go when you have the proverbial blank page or Blackboard, Hey, what are some ways that you approach problems of these magnitude looking for places where you can maybe find a hook to hold on to?
Jameson Graber:Well, thankfully I'm never literally just looking at a blank page. There's always some idea out there already that can help me get started. So I do a lot of reading, and I keep abreast of what's going on in my field. And a lot of what I spend my time thinking about is how can I answer open questions left by others? Or how can I improve upon a concept that was introduced by someone else? I am building on the shoulders of giants after all. And so a lot of it is just taking a problem and staring at it, sort of the way any math student does, when you get a math problem from your teacher, when you're a student, you just have to look at it and think about all of those tricks that you learned and all the concepts that you learned, and figure out how to put them together. And that's what research is, but on a much longer time scale. So you can be staring at the same problem for much longer than a student does.
Derek Smith:Well, as we head into the final one, so I want to ask you, it's a five year project. What are your hopes for the project? Obviously you've got to add questions you're trying to answer about human behavior, economics and et cetera, but what are your hopes for the project long-term?
Jameson Graber:Yeah, that's a really good question. My hopes for the project are first of all, to answer some of the questions that I set out to answer. So I have some specific problems that are very technical, so I won't get into details, but I do want to answer those questions, but the fun in answering questions is always how many questions they leave open. So what I hope to get out of the project is a bigger sense of where do we go from here? I thin Mean-field game theory has made a significant impact on mathematics and on economics and social sciences, but I don't think it's the end all be all. I think there are going to be new mathematical tools that we need to discover in the coming years. And I'd like to be a part of that.
Derek Smith:Well, we look forward to seeing that and seeing what comes of it and talking to you again down the line to see what you've learned and where the project is going. So congratulations again on the award and thanks for taking the time to make game theory, to make it give us a 101 on that, if you will, and tell us more about your research.
Jameson Graber:Thanks. Thanks for having me.
Derek Smith:Thank you, Dr. Jameson Graber, assistant professor of mathematics at Baylor, our guest today on Baylor Connections. I'm Derek Smith. A reminder you can hear this and other programs online at baylor.edu/connections, and you can subscribe to the program on iTunes. Thanks for joining us here on Baylor Connections