Galit Ashkenazi-Golan
Description: Galit Ashkenazi-Golan is a professor in the Department of Mathematics at the London School of Economics. Her research focuses on the modeling of strategic interactions using game theory. In this episode we talk broadly about game theory, explaining the fundamentals upon which the field has grown. We then talk about the rise of artificial intelligence and how it impacts the dynamics of game theory models. We explore questions such as how AI impacts corporate pricing models, how AI opens the door for loopholes in antitrust laws, and who bears the responsibility for training data. Professor Golan shares her thoughts on the “moral arms race” for AI superintelligence and the power, both for good and bad, that AI has on our future.
Websites:
European Network for Game Theory (Youtube)
Publications:
Related Materials:
Artificial Intelligence, Algorithmic Pricing and Collusion
Open Problems in Cooperative AI
Frontiers: Algorithmic Collusion: Supra-competitive Prices via Independent Algorithms
Protecting Consumers from Collusive Prices due to AI
News:
Show Notes:
[0:00:01] Introduction and Background in Game Theory
[0:07:03] Explaining Nash Equilibrium and Common Game Examples
[0:09:54] Dominating Strategy in the Prisoner's Dilemma
[0:12:24] Equilibrium and the Need for Social Planning
[0:14:44] The Folk theorem and multiple equilibria in repeated games
[0:23:04] Evolutionary dynamics in game theory
[0:23:53] Algorithms and Reinforcement Learning in Decision-Making
[0:27:48] Introduction to Gradient Learning and Q-Learning
[0:30:15] Access to Coordination Devices in Learning Algorithms
[0:33:31] AI in Pricing Models and Other Applications
[0:35:14] Collusion and Pricing Strategies
[0:38:49] Ethics and Legislation in AI Collusion
[0:42:04] Industries Prone to AI Collusion
[0:45:11] Cooperative AI and sophisticated Nash equilibria
[0:53:01] Not a Strategic Person, but Importance of Communication
[0:54:14] Life as an Infinite Game with Finite Game Rules
[0:58:22] Young People and the Potential of Game Theory
Unedited AI Generated Transcript
Introduction and Background in Game Theory
Brent:
[0:01] Welcome, Professor Galit Ashkenazi-Golan. Thank you for joining us.
Galit:
[0:04] Thank you for having me. It's an honor.
Keller:
[0:06] We'd love to start off by hearing a little bit more about your story.
What got you interested in game theory and how did you end up at the London School of Economics?
Galit:
[0:14] So I come from Israel originally. I was learning in Tel Aviv University.
I thought I was going to be a coder, a software engineer.
But during my studies, during the bachelor studies, I started studying a little bit of game theory, mathematical game theory.
It got me excited. And then I was offered to write a dissertation for a master's in Tel Aviv University in the School of Mathematical Sciences about game theory.
And I found it fascinating.
Later Later I wrote my PhD, again Tel Aviv University, but geographically for personal reasons in Colle Polytechnique in Paris.
And things moved from there. Yeah.
Brent:
[1:04] Is that the typical process in Israel to be invited to write a dissertation about a topic?
Or could you get, like, I want to do this and pursue that?
Galit:
[1:14] So what happens is the School of Mathematical Sciences is not a very huge one.
And during your third year, the actual process was that a friend of mine that was my teaching assistant told me, there is a new professor here, he's into mathematical game theory,fascinating topic, take his classes and make sure you come first in class.
And therefore have a chat afterwards, have a chat about the continuation of this thing. And this is what happened. I took Ehud Lehrer, Professor Ehud Lehrer's classes, I made sure I getgood grades, and therefore...
Continuing.
Keller:
[1:53] Yeah. And what was it about game theory initially that kind of turned you away from computer science and programming?
Galit:
[1:58] I was actually doing some computer science and programming and that was what turned me away from computer science and programming at first.
And you have to remember it was a while ago, so now I'm going back to coding a little bit and I found that it has changed dramatically.
It's much easier and friendlier and you don't spend a whole day wondering what's going wrong just to find out that you forgot a semicolon somewhere.
So it's friendlier now. But also, I think I liked the analytic thought.
I liked the mental challenge of having a riddle, a mathematical riddle, and needing to solve it.
I moved away from research after I finished my PhD for several years and I found that this is the thing that I really missed a lot.
Brent:
[4:23] Perfect. So do you think your background in computer science is what has allowed you now as a mathematician to like get into the AI space?
Galit:
[4:35] I think part of it did. And I think it's also the kind of thinking that you acquire when you study computer science because I did studying for the bachelor's.
So you have this algorithmical thinking in mind even when you look at analytical stuff like mathematical game theory.
You still have this kind of way of thinking in your head.
Keller:
[4:55] Yeah. And as a broad scope, what is game theory?
Galit:
[4:59] So game theory is the mathematical modeling of strategic interaction.
So what is considered a strategic interaction, it's when two decision makers, and they are sometimes called agents or players, and they can be people or firms or any other entity that makesdecisions.
They make decisions, each one of them, and the result, the payoff, the reward that each one of them gets from the whole set of decisions made depends on the whole set of decisions made.
So one good example for that is an auction.
Say government wants to build a road or a desalination plant or something like that, and the government doesn't do it itself. It has to find a firm to do that for it.
So it involves an auction, it sets up an auction, and they're asking firms to participate.
And of course, each firm – suppose it's a closed a sealed bid auction.
So each firm puts on a bid, how much do you want for building this road.
And the result that each firm gets from submitting the bid depends on everybody's actions.
This is a strategic interaction. Several decision makers are involved, and the result is a result of the common action taken by all players combined.
Keller:
[6:18] PWE And does it have to be two agents, or could it be multiple?
Galit:
[6:21] HL. So there are two agents that are quite common because there is some comfort in analyzing them, But there are also multiple agents, and in some cases, sometimes even weassume a continuum of agents.
For example, in congestion games, games that try to help us understand how congestion, for example, in roads work.
So each one of us is just a tiny decision maker in the whole system, so it's useful sometimes to think of us as a continuum of agents.
Each one of us is insignificant but for the congestion in a city, but the common decision affects each one of us.
Brent:
[6:59] Okay. And then could you maybe give us some background on some of the more common
Explaining Nash Equilibrium and Common Game Examples
[7:03] concepts in game theory, like the Nash equilibrium?
Galit:
[7:07] So the Nash equilibrium is something that we call a solution concept.
So suppose we model a game. So we model a strategic interaction.
What does it mean? It means that we know who the players are, who the decision makers are.
For each decision maker, we know what are the actions that are available for them, what is a set of available actions, and then we know what is a set of common actions that might resultin it, and we know the rewards.
Fine. So we know the game.
How will the players actually play this game?
Well, it's not that Nash equilibrium is the way that players should be playing this game, and sometimes there is more than one of them, but it is a concept about stability.
Meaning, if we shake hands and we decide, I'm going to play this, you're going to play that, and you're going to play this, and if this decision, this strategy profile, this set of actions that Ijust described, this, this, and that, if this is a natural equilibrium, it means that none of us has a deviation that is profitable.
So it is a best response for each one of us to play what we just decided that we're going to play.
You can think of it as a self-enforcing agreement.
If we shake hands and decide on playing something that is a Nash equilibrium, none of us has incentive to do something else. Yeah.
Keller:
[8:30] And could you give an example of some of the common games that are used to teach students? So the Prisoner's Dilemma and possibly the Stag Hunt?
Galit:
[8:37] Yeah. The Loser's Dilemma is a game that is, well...
Igniting the imagination of many people for several good reasons.
The story that we tell goes like that. There are two prisoners.
Well, formally, I don't think they're really prisoners, right?
Because they're just held for questioning, according to the story.
But okay, let's go with the title.
So there are two prisoners, and the police kind of knows that they committed a crime together, though they have no concrete evidence against them.
And they are held in two separate rooms, and each one of them is told the following thing. You can cooperate with the police and just confess, tell us what happened, or you can keepsilent.
If both are keeping silent, since we just said the police has no evidence about them, then they are both set free.
[9:32] If both of them confess, then they both go to jail, but for not a huge amount of time.
The interesting situation is when one of them confesses and other one is kept silent. In this case, the one that confesses gets a prize, and the one that kept silent, they are being punishedseverely.
Dominating Strategy in the Prisoner's Dilemma
[9:54] So when you look at this game, and if you draw it in a matrix or a table form, you can see that regardless of the action of your opponent, it's always better for you to confess.
This is called, in game theory, dominating strategy.
Strategy is dominating the strategy of the opponent regardless of the actions of the opponent. It is the best response, it is better for you to confess.
Why is it interesting? Because if they play according to dominating strategies, and it's kind of hard to reasonably argue against using a dominating strategy.
It's the best against anything the opponent can do. Who can ask for more?
What they end up with is both players confessing, and they both go to prison, they both go to jail.
When it was theoretically available for them, the possibility of both of them keeping silent and being free.
So this is kind of sometimes confusing or mind boggling or raising.
So this is one reason why Prisoner's Dilemma is interesting.
The unique Nash Equilibrium, the only Nash Equilibrium we have there, is one that involves using dominating strategies, a very strong thing.
One of them is doing what's best for them, even without knowing what the opponent is going to do, yet they end up in not the best situation.
[11:20] This is one reason. The second reason why we like Prisoner's Dilemma is because it's a very good story to help us think about situations where each one of us is doing what's bestfor our own interest, we all end up in a worse situation.
So there is an economy, something that is called the tragedy of the commons, where if you overexploit a common resource, it's in my interest to exploit more, it's in your interest to exploitmore, each one of us.
But if we all behave this way, then we end up in a situation that is worse for all of us. So kind of egoistic behavior or self-serving behavior, we might all be worse off because of that.
Easy to come up with environmental examples of how it's relevant for our lives.
And I think it highlights sometimes the need of a social planner.
Somebody to look at these incentives and say, well, if each one of us is acting to their own best interests, we're all worse off.
We should change the incentives somehow.
Equilibrium and the Need for Social Planning
Brent:
[12:24] So the equilibrium exists when it's all about the inputs, like the person making the best informed decision that they possibly can, and it doesn't, not an equilibrium of like outputs oroutcomes, correct?
Galit:
[12:36] Hedvig Echikunor Equilibrium, when we say equilibrium, we mean a set of actions.
So for you to do and me to do and him to do. Whether an equilibrium always exists, well, if we allow the players to randomize the theoretical results, it always exists.
Meaning if we allow players to flip a coin and say, if it ends up heads, I do this. If it ends up tail, I do that. Then there is always an equilibrium.
I'm not sure I answered the question. I'm kidding. Ha.
Brent:
[13:05] I think so. I think my focus was more on it's not a everyone's in the best situation.
It's all about everyone took the right action.
Galit:
[13:16] Exactly. So there are good Nash equilibria in the sense that everybody's better off and there are bad Nash equilibria. And when we talk about repeated games, it's going to be evenmore highlighted. There are lots of these things.
Brent:
[13:27] Could you define repeated games or the different type of game scenarios?
Galit:
[13:33] Yeah, so the situation of the prisoners dilemma I just described, I describe it as if it's a game that happens once.
But now suppose these people play this game again and again and again, I guess in the prisoner's story it might not make the best sense, but we can think of, for example, two firmsparticipating in auction one against the other again and again and again.
We can think of other strategic interactions that happen not necessarily every day, but repeatedly.
Firms that compete with each other, they set prices. They're doing it repeatedly.
So this is a repeated game, and the analysis of a repeated game is very different than the analysis of the one-shot game, because there is always a future.
And the future allows us to reward, retaliate, punish, to react to what the opponent is doing.
That we know from our lives is happening.
And this provides a very vast richness of Nash equilibrium.
While in a one-shot game, typically we have a finite number of Nash equilibrium, in a repeated game we have a whole continuum of them.
Very rich set of Nash equilibrium payoffs.
The Folk theorem and multiple equilibria in repeated games
[14:44] This means that indeed, when an interaction repeats itself, we have richness of possible interactions that are stable.
This theorem that says that we have lots and lots of equilibria payoffs when the game repeats itself is called the Folk theorem.
Some people don't like it because they say, if so many things can happen, might happen, there is no predictive power for such a theory.
If I give you a game and you say, oh, there is a whole continuum of payoffs that can be the payoffs of Nash equilibrium, meaning they are stable, nobody has an incentive to deviate, thenwhat are you really saying?
What's the predictive value? What's in it as a prediction?
But I think that there are good things to be said about the fault theorem as well, because it means that if you are already in a repeated interaction and you're stuck in a bad Nashequilibrium, then it's not necessarily the only one.
Quite likely, it's not the only one, and there are other stable situations, other Nash equilibria that are better for everybody and that are available for us if we figure out a way to move there.
And once we move there, since it's a Nash equilibrium, it's stable.
We're going to stay there.
So there is something also about hope in the folk theorem.
Keller:
[16:01] Yeah. And with repeated games, does that relate to games being static or dynamic, or is that more so about with the prisoners?
For it to be static, you just wouldn't know the input of the other player.
Galit:
[16:14] So when we say dynamic games, indeed, repeated game is one example for dynamic games.
Another prominent example is something that we call stochastic games.
So stochastic games are games when things are changing and evolving with time.
In some sense, it's the most general class of games. I have a colleague who says that life is a private case of a stochastic game. You can guess his area of research.
[16:42] You can think, for example, of a stochastic game. Suppose that we have two firms setting prices.
Suppose that if one firm sets a price a little bit high, then it gets a reputation of being an expensive firm.
Suppose that it means that the demand they might have for the next period goes down somehow.
So there is interdependency between periods in the demand.
Now this is a stochastic game because there is a state of the world that is the potential demand that depends on what we did in a previous period, for example.
Again, this game can be played infinitely many times. So dynamic games can be stochastic games, dynamic games can be infinitely repeated games.
There are special classes of stochastic games that form special mathematical challenges.
And there are also MDPs, Markov Decision Processes. it, they can be described as a game with a single player.
So there is one decision-maker, and he's not facing a strategic decision-maker, but rather he's facing, well, the world, the universe.
And the universe is changing and it's evolving, and sometimes the changes are in line or conditioned on the actions that this player is taking.
And they're trying to maximize something, they're trying to optimize something.
This is also a kind of a dynamic game.
Brent:
[18:03] And then for the Markov decision process, is that, How should people think about that? Is the decision to go to a certain college kind of that type of thing?
All these things are changing and reputations are changing, rankings are changing, my potential earnings from one or another, but ultimately it's kind of your choice and you're having tonavigate that. Is that a type of, or an analogy maybe?
Galit:
[18:30] Yeah, it's a good analogy, even though I would hesitate to say that I have the algorithm that will help you choose the optimal college or the optimal university, because this has lotsof aspects.
But when you think about which college do I go to, suppose that you care about the reputation of this college.
So there is a current reputation, but there are also trends, right?
Where things are going. Maybe it specializes in something that now seems to be going up. Maybe this college specializes in something that now seems less trendy.
And therefore, it's not just the current state of the college that you're interested in. It's also the future state of the college you're interested in.
Now it might be too presumptuous to think that a single student enlisting to that college or not will change the reputation of that college, but you can think of it this way.
You do something, it affects the state of the world, it's changing, and you have to take into account the fact that the universe is not constant.
It keeps changing, and you might want to embed that into your decision-making today. Things that might happen tomorrow, how things might unfold.
In the future.
Brent:
[19:42] Yeah.
Keller:
[19:43] Yeah. And then stepping out a little bit, when did artificial intelligence come into game theory and how has that relationship or that collaboration between those two fields grownrecently?
Galit:
[19:54] Yes. So if you, okay, so now these days when we say artificial intelligent people usually think about chat GPT and generative AI.
But what we're researching is learning algorithms.
So what are learning algorithms? Reinforcement learning or otherwise?
So suppose that we know the game, we know the actions, we know the players, we know the payoffs, we know everything.
Suppose that the game is played again and again. How should the players play?
We just said there are lots of Nash equilibrium.
Okay, it's not necessarily easy to know what is actually going to happen.
We have these tools that think about what's going to happen with these analytic tools when we have infinite systems of beliefs and this and that, and Nash equilibrium and all that.
But now, more and more of these decisions are delegated to algorithms.
When we let algorithms play, how do they play?
How do they learn how to best respond to each other?
Now, one way to look at the roots of this type of research goes all the way back to the 50s. So AI was not even a notion then, I think, or only in science fiction or something like that.
So there is something that is called a fictitious play, a notion that goes like that. Suppose the two players are playing a game.
In that case, at the beginning it was just a zero-sum game, a game where the incentives of the players are completely contradicting.
[21:24] And we play the game, and each one of us, separately, independently, looks at the history and says, okay, in the history, my opponent played one-third of the time this, one-fourth ofthe time that, and the remaining this.
What is the best response to the historical distribution of actions?
And the next action I choose is the best response to this historical distribution.
This is a learning algorithm, and we do the learning independently in the sense that I do my computations here, you do your computations there, we don't need to talk to each other, wedon't need to coordinate.
[22:02] And in some sense, without getting into the technical details, in some sense, we end up playing a Nash equilibrium in this case.
So this is one of the first times when game theory began to think about learning to play a game before AI.
Then came people that researched evolution game theory, thinking if there is this species and this is their survival strategy, and then there is another species that have a different survivalstrategy, or the same species that uses another survival strategy.
Suppose that this does better than that, and suppose that the number of offsprings you have depends on how well you're doing today.
So the number of people or the number of items or the number of individuals using a strategy tomorrow depends on how well the individuals that use this strategy today did. How well didthey do?
[22:56] Usually they use something that is called multiplicator dynamics.
Evolutionary dynamics in game theory
[23:04] And so, this is an evolutionary thing.
There are different populations. It can be one population playing against itself, it can be two populations or more populations playing against each other, And in some sense, that alsomight end up playing something stable.
Nash equilibrium, there is also correlated equilibrium, other types of equilibrium.
So each population changing according to past rewards, this kind of dynamics, we can think of it as a way that they learn and they might converge to something stable like a Nashequilibrium.
This literature began in the 60s, 70s, revisited ever since, actually.
Algorithms and Reinforcement Learning in Decision-Making
[23:53] Recently, indeed, with the increasing delegation of decisions to algorithms, especially pricing, came the question of when algorithms try to learn this game, when they use differenttypes of reinforcement learning, what can we expect that might happen? What might happen?
Do they necessarily end up playing a Nash equilibrium? Maybe they cycle around something in some kind of meaningless way. Maybe it goes completely chaotic. What happens there?
There is more and more evidence that they might learn quite a lot of the richness that we have in a repeated game Nash equilibrium kind of thing.
There could be a very interesting variety of interactions, even when it's algorithms that are independently, each one of them doing their own computations, each one of them independentlytrying to improve.
So game theory was busy with learning years ago.
However, there are new ways of thinking about it that are inspired by the kind of things that we see now in AI.
They're reinforcement learning, mainly.
Keller:
[25:07] CB. Yeah. You mentioned reinforced learning. What are some of the other learning models that are used to train the algorithms?
Galit:
[25:14] HA-So even within reinforcement learning, you have Q-learning, you have gradient learning, and you have the multiplication, multiplicative dynamics. There are many dynamics.
They may involve neural networks, so we may add the title deep to this thing.
Deep Q-learning, deep gradient learning, you know, they may not.
So there are many types, and here's another Another interesting question, if I use one method, you use another method, does it matter?
Does one have an advantage over the other?
Actually, the real answer is we still don't know. We still don't know.
Brent:
[25:52] So, how do these learning algorithms decide or put weight on what is the best outcome?
And does that differ by learning style?
Galit:
[26:01] Yeah, it's different. Let's describe two so that you can see the difference.
So, there is Q-learning.
What is Q-learning? Suppose we are playing a game repeatedly and each one of us is trying to improve. How do we improve?
So, I keep something that is called a cue table, a table that tells me that was a situation, here is the action that I took, and that's the payoff that I got.
You keep a similar table saying that's a situation, that's the action that I took, and here is the payoff that I got.
Whenever I encounter a situation, I look back or a state, you can think of it, I look back and I say, in this state, what is the best action?
Meaning, from all the actions that I tried, what gave me the best average reward?
And I choose that with some probability of searching a little bit and exploring a little bit, but I choose that. And I see again what I got and then I update this table again and again so that Islowly learn what is the best that can be done, okay?
[27:01] But I'm doing this, but my opponent is doing the same thing.
So whatever it is that I'm learning affects him as well as whatever it is that he's doing, whatever actions he's taking affects my updates of the table.
So again, proving that this thing, when both of us are simultaneously learning, but somehow also teaching each other in a sense, because what we're doing is affecting the learning of theopponent.
So somehow proving that this thing converges to something that is stable, that's not a very easy technical kind of a proof.
So, this is Q-learning. It's about the table that gets updated.
Brent:
[27:38] CB – And real quick, if there were more players, would the system learn quicker? HG – Not necessarily.
Introduction to Gradient Learning and Q-Learning
Galit:
[27:48] So, here is gradient learning, different type of learning. So, I have an estimation of what is the payoff that I get for each action.
This in some sense relates to the Q-learning.
I'm at a current strategy, there is a distribution of actions that I think I'm using now, and after I'm taking the action, I learn something about the payoffs, and then I take a step towards thegradient.
What does it mean to take a step towards the gradient? It means that actions that I believe have higher payoff will get more weight next time.
So it's not that I played with probability almost one like I described with Q-learning, it slightly different.
But I do try to improve. I do try to somehow move my strategies to push it towards something that will do better against what I have observed so far.
So there are different methods of learning, but what they have in common is that in all of these, the players are trying to optimize.
They're trying to slowly improve. They're trying to do better based on their past experience, which is the basic thing about reinforcement learning.
I did different things, I observed my history, I saw what happens, and now I'm trying to improve, I'm trying to do better.
Brent:
[29:09] So with the Q learning, are they re-implementing a strategy they've already done based on like the, they got the best outcome and it was the most similar to current situations?
And then gradient learning, it's, all right, this is a very similar case, but I'm gonna slightly tweak what I did than to hopefully get a better outcome.
Galit:
[29:26] Habila Etemadi So suppose that there are two actions that give you quite a similar outcome.
In Q-learning, you take the one that has the highest reward, even if it's by a tiny bit and you play it with probability almost one.
In gradient, since they both did very well, you add to the weight, the probability of both of them, something that is quite similar.
So you can think of the Q-learning as more greedy in some sense.
If something is even slightly better, I go full force towards it, while gradient is more subtle in a way. CB.
Brent:
[29:58] Okay.
Keller:
[29:59] And with these algorithms, like for Q-learning for example, let's say I'm Algorithm 1, do I only have access to the outcome of a given game that we played, or do I have access tothe algorithm of the other players and how that is changing as well?
Access to Coordination Devices in Learning Algorithms
Galit:
[30:15] HG So there are two ways of thinking about that, indeed.
One is when both of the players or all of the players have some access to some coordination device, or oracle sometimes they call it, something that helps us organize and coordinate.
Typically, you would think that in a market, when we're talking about firms, that is not the case. They don't have access to a specific correlation device.
It is something that is sometimes called a double oracle. You have your own oracle, you do your computation. I have my own oracle, I do my computation.
But it does change a lot of the situation if there exists such a thing.
Even allowing the players to do something that we call in economy chip talk, just to talk to each other without any commitment power to the talk, even that might change the gamesignificantly because it would allow us to coordinate.
To say, today we do this, we see what happens, tomorrow we do that. This changes things.
Brent:
[31:12] Yeah, so but in most of these scenarios, each player is reading the same inputs or the same environment, and then they might weight things differently, but everyone can see theoutcome played at that given environment.
So, that's how they can learn on one another.
Galit:
[31:32] Habile So, you're asking about the observations of each player during the game.
What do they get to observe? What information flow do they get?
So, you can make different assumptions.
There are assumptions that assume the game is known, the history is public, everything is common knowledge.
This is the clearest, pure vanilla kind of information.
But then you can make different assumptions, and this does not go just to learning, it also goes to repeated games.
[31:59] Suppose that we play a game repeatedly, but I don't observe your actions, the actions of my opponent directly. I just observe a signal that depends on it, is conditioned on itsomehow.
Maybe it's conditioned also on my actions.
It can be a public signal that both of us observe, and it can be a private signal that we observe each one.
So suppose that we are two firms and we're selling the same product, two shops selling the same product.
And suppose that there is some price that we kind of got there somehow, and the price is okay for us. It's not too low. We're interested in keeping this price level.
And we have this kind of unwritten agreement that we're keeping this price level.
But then I begin to see my sales going down one day.
Can I attribute it to a demand shock? People are just less interested in the product.
Or maybe when people come to your shop, you secretly tell them, yeah, I know this is the price that is posted in the window, but only today and only for you and don't tell anybody 20%discount, something that's called secret price cuts.
[33:05] So that's the fact that I don't observe the actions directly, but rather some signal that depends on the action.
How difficult does it make the kind of collusive behavior or cooperation depends on how you want to see it between the different players.
A question that is very interesting in game theory, all in all the question of information is very interesting. So it's for learning as well as for dynamic games in general. CB.
AI in Pricing Models and Other Applications
Brent:
[33:32] Definitely.
Keller:
[33:32] And you mentioned the pricing models. Could you explain a little bit, I guess, how common using AI for pricing models is and some other ways that that might be used?
Galit:
[33:41] HG. So AI for pricing is becoming more and more common.
[33:48] One prominent example is a few prices in Germany.
I think they had access to learning algorithms, everybody, since 2017.
And there is a whole lot of economical analysis trying to figure out how the prices are changing when everybody is employing these learning algorithms.
Right now, I think the common hypothesis is that they end up colluding a little bit. The prices sometimes are higher than what we would expect in a more, say, competitive environment.
What other things are AI used for? Again, I'm not talking about generative AI, I'm talking about learning algorithms.
So purchases of ads, auctions, things like that.
Of course, for it to be very useful in this situation, it needs to be something that you do repeatedly again and again, and then you gather information, you have something to train with.
Yeah, sure. Yeah, that's London.
Collusion and Pricing Strategies
Keller:
[35:14] That's all good. Yeah, so within the pricing models, I think one of the papers mentioned how, and you've mentioned that too, the colluding and pushing the prices up.
Up, do we know why that would be?
Because it's not intrinsic that just having high prices would lead to higher revenue for a firm. Do we have any reasoning behind why the AI are colluding in that direction as opposed toreducing the prices to approach more customers?
Brent:
[35:39] Or also, how? Why and how?
Galit:
[35:41] Yeah, so why that depends on the market structure, of course.
If you have lots of firms competing and you have two firms say that they're trying to collude and increase prices, that's not going to work, right, because customers are just going to go toall the other firms.
But if it's a duopoly or an oligopoly, then yes.
Probably keeping your prices slightly higher than the competitive level is better for the firms and not as good for the customers.
[36:07] It's not just prices, you can also collude on quality.
You might compete on quality, right? We provide a better service and so on and we can all kind of end up providing not so great service because there is no competition.
So there is no risk of customers going somewhere else. So it depends on the market structure.
Sometimes it's profitable to behave this way, and sometimes it's profitable to behave that way. The more competitive the market is, the less likely that it's going to be profitable to keepprices high.
The more firms there are, the more the market is easy to enter for new firms.
How do they learn to do that? This is exactly the mechanism that we're trying to understand now.
So of course, what do we mean when we say that they end up colluding?
What is it that they play?
So recall we said there is a difference between the one-shot game and a repeated game. And we said that when we move from one-shot game to a repeated game, we all of a sudden have alarge variety of Nash equilibrium payoffs that are available for us.
How do we get some payoff as a Nash equilibrium payoff?
How do we get the players to collude on prices?
So the very basic economical mechanism would say the following thing, we decide on a price that is high enough to generate good revenues for both of us. We both keep this level ofprices.
[37:31] For the one-shot game, it's profitable for one of us to deviate and move to a lower price because then they get all the demand and their sales increases, their profit increases.
But we are in a repeated game framework, so the mechanism goes like that.
The minute a firm deviates, if they deviate, and they lower their prices, the other firm punishes them and they go into a price war for several periods.
After everybody calms down, they go back to the high level of prices.
So it requires a future, it requires the existence of a future, it requires the fact that this is a repeated game, that the firms keep interacting with each other strategically again and again andagain.
What is interesting is that there is evidence that algorithms learn to behave this way.
They learn this thing that we try to cooperate on a price without anybody telling them to do so.
We try to cooperate on a price and some evidence, some papers say if one of the pairs deviates and reduces prices, then there is price war for several periods and then they go back to thehigh prices again.
So they actually learn the strategies of the folk theorem in some sense, which is fascinating, but not necessarily good news.
Ethics and Legislation in AI Collusion
Brent:
[38:49] Yeah. And then could you maybe expand on the more practical side of that where it's not good for people like this could violate antitrust laws or like how do we think about, Weknow that if Keller and I are running two different companies, like, hey, let's jack up the prices, we violate the law.
But if an algorithm does it, are they violating the law? Like, how do you think people should think about it? Or where's the literature kind of going in that direction?
Galit:
[39:19] Yeah, so that's a very good question. As many times when technology moves faster than legislation, we just experience some phenomenon, then we begin to think, oh, that'spossible. We need to figure out a way to deal with that.
Indeed, if all you told your algorithm is, learn the situation and just give me good profits, you never told him to collude, and they ended up colluding.
Whose fault is that? Who's to be blamed?
[39:46] And it either is not or just beginning to think about the way to legislate things about the way that the governments should deal with such phenomena.
I'm not sure that there is any clear answer yet. We're just beginning to understand that these things are actually happening.
So that we can think about, is it that you restrict the development of these learning algorithms?
Or maybe you monitor prices somehow and compare them, I don't know, to some benchmark?
Maybe do you have access to information about demand so that you can say that should have been the price, but then this, how much do you want governments and regulators to beinvolved in setting prices in a market?
A different question altogether.
So it's not very clear to me, what are not that I can think of.
Keller:
[40:55] CB Is there currently any liability on the programmers that are training the models or not really?
Galit:
[41:01] HG I don't think so. I'm not aware of any. CB Yeah. HG I don't think so.
Brent:
[41:05] CB Do you think there's ways to set the parameters differently to maybe like, incentivize less collusion or to prevent collusion?
Galit:
[41:17] HG- From what we see right now, yes, the result that you end up playing depends on the initial parameters that you're setting, exactly like you're saying.
In fact, in order to end up in some cases that we managed to really analytically research, it looks like in order to end up in a collusive equilibrium, you need to start pretty close to it, andthen you're kind of converging to it, you're drawn to it.
And if you start far from that, you might end up playing something completely different.
But then, can you forbid someone from programming its code such that it ends up being close to something that hypothetically might if the opponent does this?
And that. I don't know. Yeah.
Industries Prone to AI Collusion
Brent:
[42:04] So do you think this might be a way of, if we see industries that have tended to colluded in the past or they tend to like act as a unit, that might be the areas where AI collusion ismore prominent?
Galit:
[42:21] I think the area where AI is employed excessively by many firms, algorithms, this is where I should look into first.
Like, indeed, petrol prices in Germany, because it's been years.
They had access to it for more than six years now.
So we have enough historical data to take a look at that and see, okay, what's happening? When they begin to use these algorithms, what's happening? And when we see industries, I thinkright now AI is used to set prices for flights, for hotels.
So yeah, the minute that industries begin to heavily use AI for pricing, this is a good time to not be completely relaxed about the effects and the implications of this thing.
Keller:
[43:10] That's funny. Last week or a couple weeks before that, my dad and his friend were booking their flights to come out to Singapore.
Exact same flight, exact same seat basically, completely different prices.
Brent:
[43:23] Yeah.
Keller:
[43:25] And then, with the collusion, is that considered a form of cooperation within AI? And then, what is cooperative AI?
Galit:
[43:35] Is collusion considered a form of cooperation? In game theory, it could.
Because what does it mean? It means that the players, which are the firms, are both taking actions that are beneficial for both of them.
The people that are losing are not in the game because they are the consumers and they're not taking any actions here. which they are just a demand curve in some sense.
So a matrix of payoffs, a matrix that describes how the reward depends on the common action taken, it can model many stories.
And in some stories, you want the players to cooperate. So it's not inherently good or bad, it's just…, what the players end up doing. In some stories, it can be a good thing.
In some stories, it has outside implications.
It has negative externalities for the rest of us, and therefore we try to discourage that.
What is cooperative AI?
When we say non-cooperative AI, we usually mean when players learn independently.
Cooperative AI is usually when there is some mean of correlation, of communication.
And even in non-cooperative AI, like the Q-learning, like the gradient learning, when each one of us independently, each one of us has their own computer doing their own computation,we still might converge to cooperation.
Brent:
[45:01] So most likely, as the world starts to adopt AI more, we're going to tend to see predominantly cooperative AI?
Cooperative AI and sophisticated Nash equilibria
Galit:
[45:11] You don't need necessarily cooperative AI in order to cooperate, but we might, again, I don't know, but we might observe more phenomena like...
Algorithms end up playing sophisticated Nash equilibria where things involve, I do something, you do something, and if you deviate, I do something else.
These reactions that are slightly more complex, they might end up the things that AI agents end up playing. Yes. Yes.
Keller:
[45:45] CB And then we're looking at one of your papers and one of the quotes saying how AI is learning autonomously through active experimentation.
Action. Could you explain a little bit what that means? What are the bounds within that?
Galit:
[45:58] HL. So, in the Q-learning, for example, that we described, with high probability you select the action that did best in that state in your history of playing the game.
But with some probability, you explore.
You trial other actions because if you never try some things, you don't know how well they do, right? So, this is the way that AI works as well.
Yes, It has a guess on what's the best thing to do, but in order to learn, you need to try other things as well.
I know that, for example, online insurance firms experiment.
They try to give you different prices, to give different people different prices.
They have a pretty good idea of what should be the price, but they experiment a little just to get information and to learn from that.
Now you can use old school statistical analysis to learn whatever it is you learned from past experience.
What is the optimal pricing? What is the trend? And so on.
But using AI makes it more efficient in many ways.
So exploration and experimentation, it has already taken place in history.
We know firms change prices, they see how public reacts, they see the demand, they see.
But we're getting more sophisticated with that.
Brent:
[47:11] Yeah. And then as AI adoption becomes more prominent, do you see a runaway threat where more and more collusion starts happening and we are not able to like catch up withlegislation?
Galit:
[47:26] I hope not. I hope not. I think awareness is beginning to increase to that.
I see in conferences and workshops in economic literature, economic theory, more and more people are talking about that.
So, at least some people are raising red flags saying, come on, we should look at that, we should take it into account.
Hopefully, we'll get there.
Brent:
[47:50] Yeah, I think what you just touched on too is very, reassuring the fact that mathematicians and computer science like made up disciplines are working together and the economistsare now looking at that and implementing it into their pricing or like different theories.
And so it seems to be like a very cross disciplinary field, correct?
Galit:
[48:11] Yeah, when in some sense game theory is in the center because game theory is can be seen in as an interface between math and economy.
When you use game theory to research things that are more computer science oriented, like dynamic learning and all that, then indeed you can talk to people in computer science, you cantalk to people in economics, you can talk to people in math, and you can try to see the different angles of the same topic like learning, reinforcement learning and its possible effect oneconomy.
Keller:
[48:50] Yeah. We've been talking about AI, but you mentioned generative AI.
Could you explain how that deviates and how to my understanding that aligns a little bit more with the idea of the super intelligence that is in all the sci-fi movies?
Galit:
[49:06] So generative AI is not necessarily a strategic device.
If you want to write a letter or an an email that is this or that level of formality to this, then you can use generative AI if you want to improve the phrasing of a paragraph.
Yes, you can use generative AI, but it's not playing a strategic game against, or at least not as far as I know, against any strategic opponent and therefore game theory might not be the besttool to analyze such a thing.
Does that answer your question? I'm not sure.
Keller:
[49:44] Yeah.
Galit:
[49:44] Okay.
Brent:
[49:44] And then I think society would probably argue collusion is not good.
It's against like human ethics for like maybe like for the price example.
Galit:
[49:56] In prices, yeah. Because in other cases we should definitely collude. Yeah.
We should definitely collude when we try to preserve our planet, for example. We should work together.
And if AI can help us with that in some way, then then great, something should.
Brent:
[50:16] Yeah, exactly. So, in the scenarios that we deem it unethical, how do we get AI and human ethics to be more aligned?
Galit:
[50:26] This is in general a more general question, right?
Because you can use AI to make recommendations about giving people visas, for example, and then you end up having the risk of AI replicating biases that already exist in our society.
You can have AI sorting out CVs for a desirable job and then again, it might replicate the biases because from their point of view, it's this and that parameters that affect the successwithout knowing that it was a bias of the society that caused this and that parameters to cause a success.
So yes, we should be very much aware of of ethical situations when we use AI, of questions of what is the data that we put in, of how do we keep it fair, how do we keep it accessible, howdo we get different types of people involved in designing it and in questioning the output that we get from it.
Yes, these are questions that I see more and more people asking around me.
And again, it's not as if I think I know the answers, But just raising awareness for that is a first step.
We need to be aware of the fact that if we let it make decisions, we need to question these decisions also from a moral and ethical point of view.
Brent:
[51:52] Yeah, I think just anything human-made is inherently flawed or there will be flaws that come up.
And I think people might not always recognize the fact that AI is human-made, human-trained, so it could perpetuate.
Biases or outcomes that are potentially not as good just because of the fact that those are the parameters it was trained on.
Galit:
[52:13] It's a very powerful tool. I think there is no debate about that anymore.
It's a very powerful tool.
You can use nuclear weapon nuclear to cure cancer and you can use nuclear to bomb the universe. I mean, it's a very powerful tool. Your choice is how to use it, right?
People's choice is how to use it. And yes, when it's a very powerful tool, you want to be aware of the risks. You want to have mechanisms that observe it, that monitor it, that monitor thepeople that are using it. Yes, somehow. Somehow.
Keller:
[52:44] Yeah. We started going into the conversation of morality a little bit.
I was wondering if you could talk to us a little bit about how the study of game theory and of AI has influenced your own perspective on life and your own philosophy on life.
Not a Strategic Person, but Importance of Communication
Galit:
[53:01] So I think in my daily life, I'm not thinking very strategically, not a very strategic person. I don't try to foresee five steps in advance and I don't like chess.
I know it's ironic, but that's the way I am.
However, especially when you spend your time researching repeated interactions, I think thing that is highlighted the most is the important role of information, the important role ofcommunication, of accurate communication, of the ability to talk to each other and to coordinate where is it that we're going, what is it that we want to do.
And I think this is something that I mainly took from game theory.
The importance of clear, accurate communication, of coordination, the understanding that if sometimes incentives are wrong but we need to talk about that, we need to change themechanism, we need to change the incentives to get the people understanding to educate, to get them understanding of what is better for everybody.
I think this is the main thing that I took from game theory.
Importance of information, communication, and coordination.
Life as an Infinite Game with Finite Game Rules
Brent:
[54:14] I think that question was inspired from another conversation we listened to where the person was talking about life being an infinite game with many iterations and peoplesometimes putting finite game rules on certain decisions and how you can use the ideas and game theories and finite games, infinite games to reevaluate how you play games and like whatrules you apply to like certain decisions in your own life.
Galit:
[54:45] Yeah, that's, it's true that sometimes people overlook the future aspects of some decisions that they make.
But I don't know if it's very easy to think in terms of a repeated game, it's a complicated creature, repeated game.
Again, life is more like a stochastic game, but trying to model it.
Doomed to fail.
Keller:
[55:13] PW Do you see life, human life, I guess the individual life, as a more cooperative game or a non-cooperative game?
Galit:
[55:21] When we say cooperative games in game theory, we usually mean games that are about groups of agents and what they can accomplish together, right?
Coalitions and what coalitions can... And therefore, I think life is a mixture.
But I think if you look at repeated games, indeed, the main thing is to see that life is more often than not, not a zero-sum game.
There are typically ways for many parties to profit if they end up working together.
Indeed, we focus in this conversation on collusion in prices, which is an example of when players coordinate, it's bad for the society.
But it's not necessarily the general case. The general case is that if players cooperate and coordinate and they try to get to the good outcomes, then these might be good outcomes foreverybody.
So even in a game that is not non-cooperative game by design, meaning we don't consider coalitions, but we consider individual players, each one of them taking individual actions tryingto profit the most, still cooperation and coordination can lead us to better places.
Brent:
[56:31] Yeah. Is that your general take on like the future of AI and learning and like as long as we're aware of the potential biases or like let's make sure we have the right outcomes inmind, we will be able to use these technologies to really like create a lot of good.
Galit:
[56:47] I hope. I hope. Again, it's a tool with a lot of potential.
You can use it to very quickly look at many scans of health, whatever, and then make decisions that are as informed as professionals and therefore maybe we can get for the same numberof trained physicians, of trained doctors, maybe we can get more health.
We can all use that. So, there are areas where it's very easy to see the potential of AI to help us.
I hope they manage to harness it to help us figure out what to do with environmental issues.
Does it pose risks? Yes, it's powerful. Yeah.
Keller:
[57:30] CB.
Brent:
[57:30] Certainly.
Keller:
[57:32] And as we part, do you have any advice to students broadly that are interested in game theory and are there any opportunities for students to get involved both at LSE or justbroadly, if you're a student curious, ways to get started.
Galit:
[57:45] So how to learn about game theory? There are lots of textbooks, one of them written by my colleague sitting over there, Game Theory Basis by Bernard von Sengel. There are lotsof good textbooks to begin to study from.
I'm not aware of podcasts about that, but maybe there are. more.
And advice. I find game theory fascinating, and I think we're just beginning to discover some of its potential to help us understand and wrap our heads around strategic situations.
Young People and the Potential of Game Theory
[58:22] I would love to see a lot of young people coming and putting their input into game theory, their concerns, their aspirations, their take on the world.
Because you can model many things in game theory. You can model cooperation, you can model wars, you can use it in many ways.
[58:47] When I think about the younger generation, especially again when I think about environmental issues and environmental anxiety, I think sometimes when you're young it's not asclear as when you're old, how intricate and fragile our social systems really are, and how everything depends on the common belief that we're going to be here tomorrow, that theinstitutions are going to be here tomorrow, that banks, that we're going to turn on the plug and there is going to be electricity, there's going to be water, how the infrastructure andeverything is interlaced and depends on a very intricate way on institutions, and how if people begin to lose faith in institutions, to not believe that they're going to be here tomorrow.Things can crumble very easily.
So I think my message is we need to figure out a way to make the institutions that help us sustain society, we need to make them stronger.
We need to find ways to make them stronger for everybody so that we all believe that they're going to be here tomorrow to serve us.
If game theory can help in that, possibly, maybe. But also just a general understanding that we're in this thing together.
Brent:
[1:00:02] Thank you so much. Thank you for your time. Beautiful message.