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Author Topic: Bitcoin as Lottery, Prospect Theory, and Unprofitable Mining  (Read 1300 times)
socrates1024
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October 01, 2013, 02:04:59 PM
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tl;dr Here's an unusual theory: Bitcoin is decentralized only when mining is unprofitable on average. This is fine - people will participate anyway, for the same reason they play state lotteries and satoshi dice.

Introduction
The Bitcoin whitepaper sketches a consensus proof assuming 51% of the mining power is honest. But this assumption isn't meant to be swallowed whole - it's the role of Bitcoin's incentive scheme to *keep* the majority honest, by encouraging lots of users to participate independently. To date there's been no formal justification of the particular incentive scheme, nor any economic model to clarify what rationality assumptions are necessary, nor a usable definition for what "decentralized" means. Here's a description of a simple economic game that characterizes all this.

Decentralized Mining Game
First assume there is a population of potential participants (later I'll make assumptions about their budgets, preferences, etc). The game has two phases, a negotiation/bidding phase and a mining phase.
- In the negotiation phase, every participant decides how much money to spend on Bitcoin mining. Since each participant's payoff depends on the total amount of hashpower (everyone else's participation), this requires many rounds of negotiation or a magic auctioneer who knows everyone's curve. Imagine that it works like this: each participant is told the total hashpower of everyone else's bids, and is given the choice of changing their own bid. This is repeated until no one changes their current bid so an equilibrium is reached.
- In the mining phase, everyone mines at the rate of their final bid. The game ends after the first (or some finite number) of blocks is found, and everyone learns their payoff.

This is a bit pedantic and oversimplified, especially because the mining and bidding are separate phases, and the game ends rather than running forever, but it's abstract and amenable to analysis this way. Now suppose the population consists of two types of participants, Clients (which represent solo miners and pool participants), and Servers (which represent large professional mining operations. I can now define "decentralized" as a desirable outcome for the bidding phase: an incentive scheme is "decentralized" if some minimum fraction of the total hashpower comes from the Clients, and not just from the Servers.

Expected Value rationality model
To make things interesting, suppose that the Servers enjoy a discount on hashpower due to bulk economies of scale, and that every participant only tries to maximize their expected profit. This leads to an undesirable result for Bitcoin. If the Servers are in equilibrium, then the marginal profit from adding more mining power is zero. When this is the case, then it is *unprofitable* for Clients to mine at all.

Cumulative Prospect Theory rationality model
Even though "maximize expected value" is the common wisdom for deciding whether to bet on a risk, it's known this doesn't predict very well how people *actually* make risky decisions. (See Allais Paradox) There'd be no casinos (except for fraud), no state lotteries, and no satoshidice. There's a popular alternate model of rationality called Cumulative Prospect Theory that's almost as simple and describes empirical evidence much better. It essentially says that people overweight small probabilities and underweight near certainties. This predicts, in particular, that people play lotteries with sufficiently large jackpots, even when the chance of winning is small. Not everyone's curves are the same - a related phenomenon is that poor people tend to play lotteries with much lower variance and smaller jackpots (Are All Lotteries Regressive? Evidence from the Powerball).

So this suggests an alternate rational model, where the Servers are wealthy (above median), and are essentially the same as expected-profit maximizing (except around really large multi-million dollar jackpots), while Clients are poorer (below median?) and overweight small probabilities, even for smaller jackpots (like thousands of dollars or less).

In this model, there's a solution where the jackpot size is chosen appropriately, such that it's unprofitable on average for everyone, including the Servers, yet Clients continue to play anyway.

Discussion
The reward right now for winning a single block is several thousand dollars. This is probably not enough to excite a billionaire or large firm to invest in mining Bitcoin directly. (Selling mining equipment or hosted mining is another story though.) In fact, the prevalence of pooled mining suggests there's an appetite for even *lower* variance and smaller jackpots, which could mean even lower block bonuses may be sustainable. Modern lotteries are designed to appeal to as wide a market as possible, and typically involve a large number of games with different jackpots and probabilities. In this view, Bitcoin's payout scheme, with only one game, is very primitive and suboptimal. Pure gambling sites like SatoshiDice compete directly against Bitcoin mining for the same market. There is obviously a lot more subtlety to include in the economic model, such as the improvement in miner efficiency over time, fixed costs, and the fact that mining is continuous rather than a one shot game. This also doesn't account for other reasons to mine, like entertainment value or altruistically contributing to the network. I'm not sure whether any of these would change the main outcome.

I really like the lottery model of Bitcoin participation. Bitcoin doesn't just compete with state monopoly on currency, it also competes with the state monopoly on lotteries! State lotteries are a form of voluntary tax - they are typically justified by directing lottery profits towards a public good, such as education. Historically, lotteries were used to fund defense, like armies and even the Great Wall of China. Unprofitable Bitcoin mining can be seen as a mechanism for raising funds towards the public good of securing digital transactions.

I anticipate that one reaction to this theory is that I'm calling Bitcoin miners foolish for participating in unprofitable bets. To the contrary, I am beginning to think that this CPT is not just a better descriptive rationality model than EU, but maybe it's also a reasonable prescriptive one too. Perhaps the overweighting of small probabilities is an evolved behavioral trait that leads self-interested individuals to contribute to public goods without coercion. Bitcoin might simply be harnessing this more effectively than state lotteries.

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October 01, 2013, 04:41:59 PM
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this is such a good post

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gmaxwell
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October 01, 2013, 04:53:01 PM
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We seem to have a different outcome in Bitcoin... with people racing to the lowest variance possible even with rather high fees to get there.

I've understood this to be at least partially as a result of misunderstandings about mining, since people seem to strongly prefer variances lower than just about any business venture would have anywhere. Do you have a different argument?
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October 02, 2013, 08:14:23 AM
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We seem to have a different outcome in Bitcoin... with people racing to the lowest variance possible even with rather high fees to get there.

I've understood this to be at least partially as a result of misunderstandings about mining, since people seem to strongly prefer variances lower than just about any business venture would have anywhere. Do you have a different argument?

I think this may be due to the fact that currently miners are placing bets on future difficulty instead of on finding blocks. Its a different kind of bet, but the same arguments of the OP apply.

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October 02, 2013, 01:55:00 PM
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Bitcoin mining as lottery would be a sucker's game.
The risk of getting your block orphaned when solo mining is just too high (much higher than satoshi dice house advantage)

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October 02, 2013, 01:58:04 PM
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Bitcoin mining as lottery would be a sucker's game.
The risk of getting your block orphaned when solo mining is just too high (much higher than satoshi dice house advantage)

Why does that even matter? Even if 90% of all blocks would be orphaned (for everyone), how does that change anything? Just calculate the odds and revenue of finding a valid block and compare it to the running costs.

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socrates1024
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October 02, 2013, 02:31:09 PM
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We seem to have a different outcome in Bitcoin... with people racing to the lowest variance possible even with rather high fees to get there.

I've understood this to be at least partially as a result of misunderstandings about mining, since people seem to strongly prefer variances lower than just about any business venture would have anywhere. Do you have a different argument?

I can't really justify my speculations on *why* people actually mine now. Bitcoin is relatively new, so, like you say, mining isn't so well understood yet, and the narrative (gamble or investment or labor?) hasn't quite settled. Also the rapid growth of Bitcoin's user base and mining-equipment tech cycles make this 'equilibrium' analysis inapplicable. At the same time it's hard to extrapolate from current behavior how people *will* mine years from now, which is why models based on mainstream economic laboratory experiments (with "pure lotteries") are appealing. So this gives a glimpse of what mining might might look like in the future, when the market is saturated and novelty wears off.

What I speculate (totally unsubstantiated) is that many people *have* lost money mining by buying equipment behind the curve but don't want to admit it, in part because it's assumed that Bitcoin mining must be profitable for it to succeed. Also by "lost money" I only mean not performing as well as buying Bitcoins directly - buying Bitcoin has mostly been a good investment so far, whether directly or indirectly through mining.

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October 02, 2013, 03:12:44 PM
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What I speculate (totally unsubstantiated) is that many people *have* lost money mining by buying equipment behind the curve but don't want to admit it, in part because it's assumed that Bitcoin mining must be profitable for it to succeed....

I've noticed something to this effect in the classified ads on BFL's site ( https://forums.butterflylabs.com/classifieds.php ).
There is a real unwillingness to people to sell their pre-orders for below the price they have paid, even though it is clear that they will not achieve ROI (assuming that they all eventually receive their machines). They don't want to admit to a loss. It could be a question of just wanting to find a Greater Sucker, and those listings don't take into account final deals that may be below purchase price, but people don't want to admit that they lost out.

and great post btw!
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October 02, 2013, 03:14:28 PM
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Bitcoin mining as lottery would be a sucker's game.
The risk of getting your block orphaned when solo mining is just too high (much higher than satoshi dice house advantage)

Why does that even matter? Even if 90% of all blocks would be orphaned (for everyone), how does that change anything? Just calculate the odds and revenue of finding a valid block and compare it to the running costs.

Not for everyone, just for you because you don't run 100 nodes all of which are well connected. For the regular guy pool mining
for x hours and then trying to get '1 block' via satoshi dice has better chance of success than solo mining for x hours.
And if pool mining isn't profitable, it's better to just buy the bitcoins for all s dice gambling needs.

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October 02, 2013, 03:44:34 PM
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Interesting theory.

But I don't buy it. I don't believe acting according to CPT is beneficial, or that we should rely on it for Bitcoin's security, or that it is needed to do so in order to keep mining decentralized.

We seem to have a different outcome in Bitcoin... with people racing to the lowest variance possible even with rather high fees to get there.

I've understood this to be at least partially as a result of misunderstandings about mining, since people seem to strongly prefer variances lower than just about any business venture would have anywhere. Do you have a different argument?
I think this may be due to the fact that currently miners are placing bets on future difficulty instead of on finding blocks. Its a different kind of bet, but the same arguments of the OP apply.
Yes, people who buy mining hardware take a speculative position on the future integral of inverse difficulty, but they don't do it because they like risks, but because they believe the expected gain is sufficient to justify the risk. They don't want variance in the block finding process on top of it.

Also by "lost money" I only mean not performing as well as buying Bitcoins directly - buying Bitcoin has mostly been a good investment so far, whether directly or indirectly through mining.
Not a fair comparison. Buying mining hardware is less risky than buying bitcoins (because while the BTC price can make crazy swings, the difficulty will adjust to make mining marginally profitable), and you need to compare "buying $X worth of mining hardware" with "buying $Y worth of bitcoins with similar risk". Some modeling can give us an idea for what the ratio Y/X would be, but it will be less than 1.

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socrates1024
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October 02, 2013, 04:04:43 PM
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But I don't buy it. I don't believe acting according to CPT is beneficial, or that we should rely on it for Bitcoin's security, or that it is needed to keep mining decentralized.

I'd be very interested if you have any suggestions for other economic models that capture "decentralization" in some way and allow the incentive scheme to be evaluated. Do you have anything else in mind?

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October 02, 2013, 04:09:33 PM
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But I don't buy it. I don't believe acting according to CPT is beneficial, or that we should rely on it for Bitcoin's security, or that it is needed to keep mining decentralized.
I'd be very interested if you have any suggestions for other economic models that capture "decentralization" in some way and allow the incentive scheme to be evaluated. Do you have anything else in mind?
I don't have a complete game-theoretic model, but I do have some analysis which may suggest how mining can remain decentralized with profit-seeking players. A discussion in Amsterdam sparked some more thinking about this, and I intend to write about it soon.

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October 02, 2013, 09:15:36 PM
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I have written about my view of the economics of decentralized mining in my new blog.
http://fieryspinningsword.com/2013/10/02/asic-will-not-centralize-bitcoin-mining/

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October 07, 2013, 08:41:53 AM
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I can't really justify my speculations on *why* people actually mine now.

I think people mine now, since alternate choices of hardware vendors and their unknown capability to deliver on their promises adds enough variety of bets to the relatively boring scheme of block rewards.

Let us hope potential technological improvements will continue to add extra excitement, so people risk again even though mining remains unprofitable in total.

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October 07, 2013, 09:18:42 AM
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I made a killing shorting the difficulty  Cheesy

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