[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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