[HN Gopher] On Zero Sum Games (The Informational Meta-Game)
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On Zero Sum Games (The Informational Meta-Game)
Author : ocean_moist
Score : 38 points
Date : 2025-02-21 20:55 UTC (3 days ago)
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(TXT) w3m dump (rohan.ga)
| russfink wrote:
| And "GTO" means...? (Authors, please expand acronyms at first
| use.)
| jasonhong wrote:
| Game Theory Optimal
|
| This page has more details:
| https://blogs.cornell.edu/info2040/2021/11/03/game-theory-op...
| ocean_moist wrote:
| Will keep this in mind for the future.
| highfrequency wrote:
| 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.
| zeroq wrote:
| 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.
| highfrequency wrote:
| 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).
| Maxatar wrote:
| 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.
| highfrequency wrote:
| 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
| play 2+ games and alternate colors.
| Maxatar wrote:
| 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.
| highfrequency wrote:
| Read the comment from zeroq. We are talking about chess,
| and the poster was confusing GTO with having a
| predictable and naive strategy. There is no randomness in
| chess; GTO will draw in the worst case as long as both
| players get to play white the same number of times. I
| don't even know what "draw" means in the context of
| poker.
|
| In heads up poker, GTO is worst case zero EV. Obviously
| this does not mean that the worst case in a single hand
| is a $0 payout - that is a fairly absurd straw man. I can
| play Federer at tennis for one point and it is possible
| he will lose. There is nothing interesting in that
| statement.
| Maxatar wrote:
| Your claim that a symmetric two player game always
| results in a draw is what I was replying to. That is only
| true for a strictly determined game.
|
| As far as chess is concerned, it's unknown what perfect
| play yields, but if a round of chess consists of playing
| white once and playing black once, then a perfect game of
| chess is guaranteed to do no worse than a draw as you
| say.
|
| The term GTO is used exclusively for poker, you won't
| find that term used for any other game, gambling or
| otherwise. I can see how the mixing of games and
| terminology could result in me misinterpreting what you
| meant though.
|
| >In heads up poker, GTO is worst case zero EV. Obviously
| this does not mean that the worst case in a single hand
| is a $0 payout - that is a fairly absurd straw man.
|
| The strawman is thinking that if EV is zero or even
| positive, then you only need to worry about a single hand
| or even a few hands.
|
| On the contrary EV can positive or even infinite and yet
| you can still be guaranteed to lose in the long run due
| to variance:
|
| https://en.wikipedia.org/wiki/Kelly_criterion
| highfrequency wrote:
| Agree with you - sounds like we are on the same page and
| only confusion is on semantics. With nondeterministic
| games like poker, the draw guarantee only makes sense in
| the context of a sufficiently large number of hands.
| There are no guarantees on a single hand regardless of
| skill difference. Chess and other deterministic games
| essentially reach the "infinite hands" condition in a
| single game because there is no randomness, so the
| nonnegative EV is realized immediately.
| wat10000 wrote:
| 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.
| Maxatar wrote:
| 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
| wat10000 wrote:
| 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.
| Maxatar wrote:
| 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.
| highfrequency wrote:
| 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.
| wat10000 wrote:
| 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.
| lotsofpulp wrote:
| "Making money" at the same exact time does not have to be
| the goal. Bob might want more liquidity and lower
| volatility now, so he wants US dollars (USD) from
| Charlie. Charlie might want less liquidity now, but wants
| to bet on $300 worth of AAPL will have more purchasing
| power at some point in the future than $300 of USD.
| kbenson wrote:
| 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.
| wat10000 wrote:
| 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.
| kbenson wrote:
| > Lending and selling are both zero-sum
|
| Why? Lending is just giving people money they value more
| now than you do, so much so they agree to pay back more
| later. The utility at the current time of that money is
| better than the utility later for the lendee, and the
| opposite is true for the lender (they will happily forego
| some money available now for more money available later).
|
| If I take a loan out to buy a car which lets me find a
| better job because I can travel for efficiently, and I
| get a better job that pays more which allows me to much
| more money and paying back that loan is itself even
| easier, is that transaction zero-sum when examined over
| time?
| Paul-Craft wrote:
| _TL;DR:_
|
| > Everything is worth what its purchaser will pay for it.
|
| - _The Moral Sayings of Publius Syrus,_ maxim 847.
| Paul-Craft wrote:
| 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...
| ocean_moist wrote:
| Yeah, almost necessary at a high level (and online), however I
| play against fish most of the time. I am also 18 and lack
| connections/capital/time to enter high level games.
|
| I would say markets are approx. zero-sum on small time-scales.
| And low-beta alpha is better sourced from treating the market
| as zero-sum. Short-term price movements are primarily driven by
| the redistribution of wealth between market participants rather
| than by the creation of new fundamental value, making strategic
| positioning against other traders more effective for generating
| uncorrelated returns.
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