Game Theory: A Complex and Beautiful Field

Game theory is a field that has fascinated many with its intricate concepts and complex models. It deals with the study of strategic decision making, particularly in situations where the outcome depends on the actions of multiple individuals or parties. In game theory, each individual or party makes decisions that take into account the potential reactions of others, leading to a complex web of interactions and outcomes.

A fundamental concept in game theory is the idea of equilibrium, which refers to a stable state where no player can improve their outcome by unilaterally changing their strategy, assuming all other players keep their strategies unchanged. This concept was established by John Nash, who proved that under certain conditions, there exists an equilibrium in any finite game. Nash's work not only laid the foundation for game theory but also provided a framework for understanding the behavior of individuals and groups in competitive situations.

Despite its complexity, game theory has many practical applications in real-world scenarios. One of the most significant areas where game theory is applied is in algorithmic game theory, which seeks to develop algorithms that can predict and influence the behavior of multiple players interacting with each other. The study of algorithmic game theory provides a framework for understanding how individuals can make strategic decisions that lead to optimal outcomes.

A key concept in algorithmic game theory is the connection between machine learning and game theory. Machine learning involves developing algorithms that can learn from data and make predictions or decisions based on that data. In the context of game theory, these algorithms can be used to predict the behavior of multiple players and develop strategies that lead to optimal outcomes. This has significant implications for many areas of modern life, including social media platforms and online marketplaces.

For instance, popular driving apps like Google Maps use machine learning algorithms to optimize routes based on the traffic patterns of other users. These algorithms essentially compute a selfish best response for each user in response to what all the others are doing at any given moment. While this may seem beneficial, research has shown that this approach can lead to suboptimal outcomes, as all users collectively driving towards the same equilibrium may end up with higher collective driving times.

This raises an interesting question: is it better for individuals to make decisions based on their own self-interest or to prioritize a more collaborative approach? Game theory provides a framework for understanding the trade-offs between these two approaches and highlights the importance of considering the potential outcomes of individual actions when making strategic decisions.

"WEBVTTKind: captionsLanguage: enspeaking of markets a lot of fascinating aspects of this world arise not from individual humans but from the interaction of human beings you've done a lot of work in game theory first can you say what is game theory and how does help us model and study yeah game theory of course let us give credit where it's due they don't comes from the economist first and foremost but as I'd mentioned before like you know computer scientists never hesitate to wander into other people's turf and so there is now this 20 year old field called algorithmic game theory but you know game game theory first and foremost is a mathematical framework for reasoning about collective outcomes in systems of interacting individuals you know so you need at least two people to get started in game theory and many people are probably familiar with prisoner's dilemma as kind of a classic example of game theory and a classic example where everybody looking out for their own individual interests leads to a collective outcome that's kind of worse for everybody then what might be possible if they cooperate it for example but cooperation is not an equilibrium in prisoner's dilemma and so my work and the field of algorithmic game theory more generally in these areas kind of looks at settings in which the number of actors is potentially extraordinarily large and their incentives might be quite complicated and kind of hard to model directly but you still want kind of algorithmic ways of kind of predicting what will happen or influencing what will happen in the design of platforms so what to you is the most beautiful idea that you've encountered in game theory there's a lot of them I'm a big fan of the field I mean you know I mean technical answers to that of course would include Nash's work just establishing that you know there there's a competitive equilibrium under very very general circumstance which in many ways kind of put the field on a firm conceptual footing because if you don't have equilibria it's kind of hard to ever reason about what might happen since you know there's just no stability so just the idea that stability can emerge when there's multiple who or that it means not that it will necessarily emerge just that it's possible right it's like the existence of equilibrium doesn't mean that sort of natural iterative behavior will necessarily lead to it in the real world yeah maybe answering a slightly less personally than you asked the question I think within the field of algorithmic game theory perhaps the single most important kind of technical contribution that's been made is the real the the realization between close connections between machine learning and game theory and in particular between game theory and the branch of machine learning that's known as no regret learning and and this sort of provides a freight a very general framework in which a bunch of players interacting in a game or a system each one kind of doing something that's in their self-interest will actually kind of reach an equilibrium and actually reach an equilibrium in a you know a pretty you know a rather you know short amount of steps so you kind of mentioned acting greedily can somehow end up pretty good for everybody or pretty bad or pretty bad it will end up stable yeah right and you know stability or equilibrium by itself is not that is not necessarily either a good thing or a bad thing so what's the connection between machine learning and the ideas well if we kind of talked about these ideas already in in kind of a non-technical way which is maybe the more interesting way of understanding them first which is you know we have many systems platforms and apps these days that work really hard to use our data and the data of everybody else on the platform to selfishly optimize on behalf of each user okay so you know let me let me give what the cleanest example which is just driving apps navigation apps like you know Google Maps and ways where you know miraculously compared to when I was growing up at least you know the objective would be the same when you wanted to drive from point A to point B spend the least time driving not necessarily minimize the distance but minimize the time right and when I was growing up like the only resources you had to do that were like maps in the car which literally just told you what roads were available and then you might have like half hourly traffic reports just about the major freeways but not about side roads so you were pretty much on your own and now we've got these apps you pull it out and you say I want to go from point A to point B and in response kind of to what everybody else is doing if you like what all the other players in this game are doing right now here's the the you know the the route that minimizes your driving time so it is really kind of computing a selfish best response for each of us in response to what all of the rest of us are doing at any given moment and so you know I think it's quite fair to think of these apps as driving or nudging us all towards the competitive or Nash equilibrium of that game now you might ask like well that sounds great why is that a bad thing well you know it's it's known both in theory and with some limited studies from actual like traffic data that all of us being in this competitive equilibrium might cause our collective driving time to be higher may be significantly higher than it would be under other solutions and then you have to talk about what those other solutions might be and what what the algorithms to implement them are which we do discuss in the kind of game theory chapter of the book but but similarly you know on social media platforms or on Amazon you know all these algorithms that are essentially trying to optimize our behalf they're driving us in a colloquial sense towards some kind of competitive equilibrium and you know one of the most important lessons of game theory is that just because we're at equilibrium doesn't mean that there's not a solution in which some or maybe even all of us might be better off and then the connection to machine learning of course is that in all these platforms I've mentioned the optimization that they're doing on our behalf is driven by machine learning you know like predicting where the traffic will be predicting what products I'm gonna like predicting what would make me happy in my newsfeed youspeaking of markets a lot of fascinating aspects of this world arise not from individual humans but from the interaction of human beings you've done a lot of work in game theory first can you say what is game theory and how does help us model and study yeah game theory of course let us give credit where it's due they don't comes from the economist first and foremost but as I'd mentioned before like you know computer scientists never hesitate to wander into other people's turf and so there is now this 20 year old field called algorithmic game theory but you know game game theory first and foremost is a mathematical framework for reasoning about collective outcomes in systems of interacting individuals you know so you need at least two people to get started in game theory and many people are probably familiar with prisoner's dilemma as kind of a classic example of game theory and a classic example where everybody looking out for their own individual interests leads to a collective outcome that's kind of worse for everybody then what might be possible if they cooperate it for example but cooperation is not an equilibrium in prisoner's dilemma and so my work and the field of algorithmic game theory more generally in these areas kind of looks at settings in which the number of actors is potentially extraordinarily large and their incentives might be quite complicated and kind of hard to model directly but you still want kind of algorithmic ways of kind of predicting what will happen or influencing what will happen in the design of platforms so what to you is the most beautiful idea that you've encountered in game theory there's a lot of them I'm a big fan of the field I mean you know I mean technical answers to that of course would include Nash's work just establishing that you know there there's a competitive equilibrium under very very general circumstance which in many ways kind of put the field on a firm conceptual footing because if you don't have equilibria it's kind of hard to ever reason about what might happen since you know there's just no stability so just the idea that stability can emerge when there's multiple who or that it means not that it will necessarily emerge just that it's possible right it's like the existence of equilibrium doesn't mean that sort of natural iterative behavior will necessarily lead to it in the real world yeah maybe answering a slightly less personally than you asked the question I think within the field of algorithmic game theory perhaps the single most important kind of technical contribution that's been made is the real the the realization between close connections between machine learning and game theory and in particular between game theory and the branch of machine learning that's known as no regret learning and and this sort of provides a freight a very general framework in which a bunch of players interacting in a game or a system each one kind of doing something that's in their self-interest will actually kind of reach an equilibrium and actually reach an equilibrium in a you know a pretty you know a rather you know short amount of steps so you kind of mentioned acting greedily can somehow end up pretty good for everybody or pretty bad or pretty bad it will end up stable yeah right and you know stability or equilibrium by itself is not that is not necessarily either a good thing or a bad thing so what's the connection between machine learning and the ideas well if we kind of talked about these ideas already in in kind of a non-technical way which is maybe the more interesting way of understanding them first which is you know we have many systems platforms and apps these days that work really hard to use our data and the data of everybody else on the platform to selfishly optimize on behalf of each user okay so you know let me let me give what the cleanest example which is just driving apps navigation apps like you know Google Maps and ways where you know miraculously compared to when I was growing up at least you know the objective would be the same when you wanted to drive from point A to point B spend the least time driving not necessarily minimize the distance but minimize the time right and when I was growing up like the only resources you had to do that were like maps in the car which literally just told you what roads were available and then you might have like half hourly traffic reports just about the major freeways but not about side roads so you were pretty much on your own and now we've got these apps you pull it out and you say I want to go from point A to point B and in response kind of to what everybody else is doing if you like what all the other players in this game are doing right now here's the the you know the the route that minimizes your driving time so it is really kind of computing a selfish best response for each of us in response to what all of the rest of us are doing at any given moment and so you know I think it's quite fair to think of these apps as driving or nudging us all towards the competitive or Nash equilibrium of that game now you might ask like well that sounds great why is that a bad thing well you know it's it's known both in theory and with some limited studies from actual like traffic data that all of us being in this competitive equilibrium might cause our collective driving time to be higher may be significantly higher than it would be under other solutions and then you have to talk about what those other solutions might be and what what the algorithms to implement them are which we do discuss in the kind of game theory chapter of the book but but similarly you know on social media platforms or on Amazon you know all these algorithms that are essentially trying to optimize our behalf they're driving us in a colloquial sense towards some kind of competitive equilibrium and you know one of the most important lessons of game theory is that just because we're at equilibrium doesn't mean that there's not a solution in which some or maybe even all of us might be better off and then the connection to machine learning of course is that in all these platforms I've mentioned the optimization that they're doing on our behalf is driven by machine learning you know like predicting where the traffic will be predicting what products I'm gonna like predicting what would make me happy in my newsfeed you\n"