Actually, in poker it is very effective to study and approximate GTO (either by a human or by machine with counterfactial regret minimization).
But yes, no one is looking for GTO in trading. The game is not well-defined. There are thousands of participants each with totally different objectives and win conditions. That makes it not zero sum in the first place. Pension funds, banks, HFT firms can all make money while trading with each other.
It's is also worth to mention that once adversary figure out that you're employing GTO in your decision making it's very easy to exploit.
To give it another context: imagine a seasoned chess player playing with a novice who just studied an opening. Once the more experienced player realize that his opponent is playing "sicilian" he knows his opponent game plan, next five moves and can set traps accordingly.
GTO means unexploitable. If the player were actually GTO, the worst case would be a draw. The novice playing a standard opening loses because he is a novice, not because he is playing GTO (he is not).
In a symmetric two player game, being unexploitable means that a draw is the worst case. There is mild black-white asymmetry in chess but that’s a minor point - can just playing 2+ games and alternate colors.
For anyone else reading this wondering how it is hedge funds can fail spectacularly, this is why...
People get enamored by theory but forget that the theory depends on subtle details and preconditions that often don't apply in the real world, and end up coming to conclusions that are sound on paper but will not hold up in reality.
You are not guaranteed a draw in poker if you play optimally, you can still lose. It is true that being unexploitable and playing optimally yields a expectation of at least 0 (assuming no rake/fee), but expectation over an infinite number of trials is not the same as guaranteeing a draw.
There is also variance, which can cause sufficient losses in the short run and given that in the real world people only have a finite amount of resources with which to participate, a sufficiently high variance can knock you out of the competition before you ever get a chance to realize the benefit of a long term positive (or even zero) expectation.
Since every seller is matched with a buyer, how can everyone make money trading with each other? The only way additional money comes into the system is if a new investor appears, or a stock pays dividends.
Trading is only zero-sum at very small time scales. Over longer times scales, the stock market is not a closed system. Traders who run out of money will either exit the market entirely, or find more money from somewhere else. That money comes from either economic profits, or the economy's money-creation process. In the US economy, that process is fractional reserve banking[0].
Different people value resources differently overall and also differently over time. Trading a resource you don't value as much to someone who does value it for something you value leads you both to be better off.
In a very simple form, if you're a fisherman you may have a surplus of fish, much more than you can eat before they go bad. Fish is not worth much to you, but maybe you need cloth for sails, the someone in the village collects and mends and sews cloth. They have a lot, but need food. Trading fish for cloth benefits you both.
Money is just an abstraction to smooth trades between people for resources they need. Scale to whatever level you want.
But we're talking about stocks, not fish. You can do four things with stocks: exert control over the company, collect dividends, lend it, and sell it. Funds generally aren't buying so they can create wealth by exerting control. Lending and selling are both zero-sum.
Apple the company issues stock. They are the seller, and some investor is the buyer. Apple uses the money to invest in operations, and the stock goes up over time. Who lost?
Forget about stocks - this is the whole point of trade in general. People have different resources and different needs, time horizons, risk tolerance etc., so the default assumption should be that voluntary trade is positive sum - just like Ford selling a car is positive sum even though there is a buyer and a seller.
Apple issues stock at $200/share. Bob buys one share. Apple is now $200 richer, Bob is $200 poorer.
Later, Apple goes up to $300/share. Bob sells his stock to Charlie. Bob is now $100 richer, Charlie is $300 poorer. Total change: zero.
Apple is more valuable and that (probably) means wealth was created, but that increase in wealth comes from Apple doing things, not from the trading.
Non-stock trading creates wealth because different people value things differently. A sandwich is worth less to Subway than it is to me, so total wealth increases when I pay them for a sandwich. But stocks don't really work that way. Unless you're buying a stock to exert control over the company, the only thing you're doing with it is using it to make money money. If you're making money by selling at a higher price later, then that comes from someone else paying that higher price, and it's all zero-sum.
I was responding to "Pension funds, banks, HFT firms can all make money while trading with each other." I readily accept that economic activity is not zero-sum, creates wealth, and that trading stocks can help enable that. But just trading by itself doesn't make money.
Everyone can make or lose money depending on whether the value of the stock goes up or down and whether the participants own the stock or are borrowing it (short/negative ownership).
You mention two factors that can introduce new capital into the system, new investors and dividends, but seem to imply they are negligible or can be ignored... on the contrary those two factors are quite significant contributors and according to some theories dividends are the ultimate and total source of value in the stock market:
The value of the stock going up doesn't mean everyone makes money. Everybody's stuff is worth more on paper, but they can't convert it to money unless they sell it, which means someone else had to buy it and convert their money into stock. The total amount of money remains constant.
I didn't mean to imply that those two factors are negligible. Only that they're not part of "trading," i.e. trading is zero-sum but these make the system as a whole not zero-sum. I was responding to "Pension funds, banks, HFT firms can all make money while trading with each other." Which suggests that you don't need other things for everyone to make money, it can happen purely by trading.
If you just mean a closed group of people are passing around stock among each other, never able to collect a dividend or add new participants, then sure such a system would not be positive sum.
But the participants listed, pension funds, banks, HFTs, etc... are not just trading with each other in a closed system. These participants can all trade with each other and all gain from one another precisely because there are dividends paid out, and new participants.
Pension funds need to liquidate or rebalance their portfolio on a short notice or daily basis, so they benefit from trading with HFTs who can take on virtually arbitrary inventory and quickly hedge it, charging a very small and implied fee (usually from a spread or some other implied mechanism), who in turn offload that inventory onto a bank or another pension fund, etc etc...
These participants can all benefit from one another's involvement in the market instead of competing against each other.
Actually, in poker it is very effective to study and approximate GTO (either by a human or by machine with counterfactial regret minimization).
But yes, no one is looking for GTO in trading. The game is not well-defined. There are thousands of participants each with totally different objectives and win conditions. That makes it not zero sum in the first place. Pension funds, banks, HFT firms can all make money while trading with each other.
It's is also worth to mention that once adversary figure out that you're employing GTO in your decision making it's very easy to exploit.
To give it another context: imagine a seasoned chess player playing with a novice who just studied an opening. Once the more experienced player realize that his opponent is playing "sicilian" he knows his opponent game plan, next five moves and can set traps accordingly.
GTO means unexploitable. If the player were actually GTO, the worst case would be a draw. The novice playing a standard opening loses because he is a novice, not because he is playing GTO (he is not).
Unexploitable does not guarantee a draw. You can play optimally and still lose.
However your main point, that GTO can not be exploited, is correct.
In a symmetric two player game, being unexploitable means that a draw is the worst case. There is mild black-white asymmetry in chess but that’s a minor point - can just playing 2+ games and alternate colors.
For anyone else reading this wondering how it is hedge funds can fail spectacularly, this is why...
People get enamored by theory but forget that the theory depends on subtle details and preconditions that often don't apply in the real world, and end up coming to conclusions that are sound on paper but will not hold up in reality.
You are not guaranteed a draw in poker if you play optimally, you can still lose. It is true that being unexploitable and playing optimally yields a expectation of at least 0 (assuming no rake/fee), but expectation over an infinite number of trials is not the same as guaranteeing a draw.
There is also variance, which can cause sufficient losses in the short run and given that in the real world people only have a finite amount of resources with which to participate, a sufficiently high variance can knock you out of the competition before you ever get a chance to realize the benefit of a long term positive (or even zero) expectation.
Since every seller is matched with a buyer, how can everyone make money trading with each other? The only way additional money comes into the system is if a new investor appears, or a stock pays dividends.
Trading is only zero-sum at very small time scales. Over longer times scales, the stock market is not a closed system. Traders who run out of money will either exit the market entirely, or find more money from somewhere else. That money comes from either economic profits, or the economy's money-creation process. In the US economy, that process is fractional reserve banking[0].
---
[0]: https://en.wikipedia.org/wiki/Fractional-reserve_banking#Mon...
Different people value resources differently overall and also differently over time. Trading a resource you don't value as much to someone who does value it for something you value leads you both to be better off.
In a very simple form, if you're a fisherman you may have a surplus of fish, much more than you can eat before they go bad. Fish is not worth much to you, but maybe you need cloth for sails, the someone in the village collects and mends and sews cloth. They have a lot, but need food. Trading fish for cloth benefits you both.
Money is just an abstraction to smooth trades between people for resources they need. Scale to whatever level you want.
But we're talking about stocks, not fish. You can do four things with stocks: exert control over the company, collect dividends, lend it, and sell it. Funds generally aren't buying so they can create wealth by exerting control. Lending and selling are both zero-sum.
Apple the company issues stock. They are the seller, and some investor is the buyer. Apple uses the money to invest in operations, and the stock goes up over time. Who lost?
Forget about stocks - this is the whole point of trade in general. People have different resources and different needs, time horizons, risk tolerance etc., so the default assumption should be that voluntary trade is positive sum - just like Ford selling a car is positive sum even though there is a buyer and a seller.
Apple issues stock at $200/share. Bob buys one share. Apple is now $200 richer, Bob is $200 poorer.
Later, Apple goes up to $300/share. Bob sells his stock to Charlie. Bob is now $100 richer, Charlie is $300 poorer. Total change: zero.
Apple is more valuable and that (probably) means wealth was created, but that increase in wealth comes from Apple doing things, not from the trading.
Non-stock trading creates wealth because different people value things differently. A sandwich is worth less to Subway than it is to me, so total wealth increases when I pay them for a sandwich. But stocks don't really work that way. Unless you're buying a stock to exert control over the company, the only thing you're doing with it is using it to make money money. If you're making money by selling at a higher price later, then that comes from someone else paying that higher price, and it's all zero-sum.
I was responding to "Pension funds, banks, HFT firms can all make money while trading with each other." I readily accept that economic activity is not zero-sum, creates wealth, and that trading stocks can help enable that. But just trading by itself doesn't make money.
Everyone can make or lose money depending on whether the value of the stock goes up or down and whether the participants own the stock or are borrowing it (short/negative ownership).
You mention two factors that can introduce new capital into the system, new investors and dividends, but seem to imply they are negligible or can be ignored... on the contrary those two factors are quite significant contributors and according to some theories dividends are the ultimate and total source of value in the stock market:
https://en.wikipedia.org/wiki/Dividend_discount_model
The value of the stock going up doesn't mean everyone makes money. Everybody's stuff is worth more on paper, but they can't convert it to money unless they sell it, which means someone else had to buy it and convert their money into stock. The total amount of money remains constant.
I didn't mean to imply that those two factors are negligible. Only that they're not part of "trading," i.e. trading is zero-sum but these make the system as a whole not zero-sum. I was responding to "Pension funds, banks, HFT firms can all make money while trading with each other." Which suggests that you don't need other things for everyone to make money, it can happen purely by trading.
If you just mean a closed group of people are passing around stock among each other, never able to collect a dividend or add new participants, then sure such a system would not be positive sum.
But the participants listed, pension funds, banks, HFTs, etc... are not just trading with each other in a closed system. These participants can all trade with each other and all gain from one another precisely because there are dividends paid out, and new participants.
Pension funds need to liquidate or rebalance their portfolio on a short notice or daily basis, so they benefit from trading with HFTs who can take on virtually arbitrary inventory and quickly hedge it, charging a very small and implied fee (usually from a spread or some other implied mechanism), who in turn offload that inventory onto a bank or another pension fund, etc etc...
These participants can all benefit from one another's involvement in the market instead of competing against each other.
And “GTO” means…? (Authors, please expand acronyms at first use.)
Game Theory Optimal
This page has more details: https://blogs.cornell.edu/info2040/2021/11/03/game-theory-op...