Footnotes and Edits for “Behavioral Crypto-Economics”


Footnote 1. It is interesting to note that the Byzantine Generals’ Problem is a classical problem in cryptography which, to my knowledge, was never seen as related to game theory in any way. (At least until the emergence of game-theoretic approaches to cryptography around 2008). Indeed, the big breakthrough in Nakamoto’s solution is that it injects incentive design to a problem where financial incentives never played a role. In retrospect, of courseit’s hard to stop generals from cheating when cheating has no negative repercussions.
In general, adding financial incentives makes many cryptographic problems easier to solve (e.g. decentralized voting). In technical terms, adding an incentive systems allows us to reduce the malicious attacker model to be close to an honest-but-curious attacker model, which is much easier to solve. This is one striking example tothe power of cryptoeconomic system design: marrying cryptography and game theory produces a whole that is larger than the sum of its parts.

Footnote 2. The game-theoretic guarantees of Bitcoin were recently made more accurate, formalized and proved. In fact, the statement “to damage bitcoin you must recruit 51% of the mining power” is a folk theorem, and turns out to be not completely accurate. Eyal & Gun Sirer show that a highly-strategic player can do quite a bit of damage over time even when controlling a smaller fraction of the mining pool, by slowly incentivizing miners to move over to cheating mining pools.
Overall, Bitcoin’s assumptions are much weaker, and much better understood, than those of Steemit, Augur, IOTA, or many others of the newer systems. We also suspect that future academic research will further prove the game-theoretic and behavioral robustness of Bitcoin.

For more reading on Bitcoin’s cryptoeconomic security, see Emin Gün Sirer & [Eyal & Gun Sirer Section 7] for a literature survey. For other cryptoeconomic research, see for example Vitalik’s talks, Trent McConaghy’s recent post series, Jacob Horne on cryptoeconomic primitives, or this reading list.

Footnote 3. In the rest of that blog series, Trent McConaghy discusses concerns similar to the ones we raise here. As Chris Burniskesummarizes his argument:

“How often does an academic economist (or anyone, really) get a chance to deploy an economy?” Such an opportunity happens each time a crypto network is launched, as it spawns a new economy with a native unit of account and supply schedule to incentivize unique behavior — a responsibility we can’t take lightly. […]
In crypto right now we are mechanism design cavemen. And while we originally control the design of blockchains, once in the wild these systems (will) control the design of society.

Footnote 4. Note that these axes are a simplification of a complicated reality, and that the placement of the projects in the figure are simplifications of the projects themselves. For example, for non-honest Bitcoin miners, the size of the action space is actually very larger, and there is much more room for human involvement. The axes just describe the characteristics of the system for honest stakeholders.

Also note that the placement on the chart does not constitute a judgement on the quality of the depicted projects. The more top-right a project is, the more rigor and good design is needed to compensate for the extra complications. Some projects might sit in the bottom right and not satisfy this rigor, some projects might sit in the top-right and do.


  • March 18, 2018: Applied Edward A Thomson‏’s Correction to the description of Bitcoin’s incentives. Also, updated Figure 1 to lower IOTA on the “action space” axis and to add Dai Stablecoin. The top-left part of the chart looks a bit empty: tell me if you think of a cryptoeconomic system that has a large action space and high automatibility.
  • March 21, 2018: Moved footnotes and edits to this page, to improve readability.

Elad Verbin

Written by

Berlin-based Computer Scientist. Algorithms developer. Investing in early-stage algo-tech: ML, blockchain, zero knowledge, infrastructural algos. Partner @ BIV.

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