By extracting only the relevant portions, the author will investigate how game theory is often unnoticed in the realm of network attacks. A principal derivation of this study, specifically for Bitcoin, is Feather Forking or Block Discouraging. For the sake of argument, the former will represent the negative and the latter, the positive censorship capacities of mining centralization. Of greatest concern, is that this technique does not require a majority of the network’s hashrate to lance an attack.

Bitcoin is Multidisciplinary

Modern game theory represents, in many ways, the intersection of economics, computer science, and psychology. Thus, it isn’t difficult to quickly imagine its relevance for something like cryptocurrencies. But, to make both threats and opportunities clear, the author will use Bitcoin’s network as the principal model with which to unfold attack vectors via game theory. The pioneer currency is the most well-known and has the most robust mining community comparatively.

Things I wasn't interested in before #Bitcoin:

Information theory
Game theory
Computer science

— Gabriel ⚡️⚡️⚡️ (@GabrielDVine) June 25, 2017

In Bitcoin, there are two agents; miners and users. Miners secure the network and users inject, via speculation and adoption, value.  

For the sake of brevity, the handful of other factors that make up this robust ecosystem will be put aside. Plus, Feather Forking is a maneuver undertaken by miners and their direct access to the blockchain. Block Discouraging is similar and involves, from an exclusively technical perspective, only miners and users as well.

The Nash Equilibrium and Bitcoin

Miners could leverage their position in the network in four ways: include invalid transactions to increase coin reward, continue mining on invalid blocks for the same reasons, add blocks regardless of Proof of Work (PoW), and mine on top of non-premium blocks.

Naturally, if any of these were to really occur en masse, it would spell the end of Bitcoin.

Fortunately, the network relies on mathematical transparency, specifically the Nash Equilibrium, to mitigate moral fallibility. Bitcoin evangelist Andreas Antonopoulos explained this as a “simple equation [that] creates a system of incentives where it’s far better to play with the rules than against the rules.”

The first and fourth point above, for instance, do not occur because blockchain mechanics prevent other miners from also pursuing invalid blocks or non-competitive blocks. Without a majority of miners moving to the invalid block, agents mining these invalid blocks waste resources as nothing is gained (i.e., no incentive).

In this way, the ecosystem is rewarded for supporting itself in pursuit of the majority, of which we can define as lucrative (valid) blocks on the blockchain. Herein lies one of the strengths of this technology; its capacity to self-moderate and shift trust away from third parties.

Punitive Forking versus Feather Forking

Punitive Forking was the subject of a talk given by Max Fang at the Stanford Cyber Initiative on January 30, 2018. Fang’s presentation on Game Theory and Network Attacks: How to Destroy Bitcoin outlined a handful of different mining malpractices that are already occurring or could occur in the Bitcoin network. Our focus will of his presentation will be the section Game-Theory Based Censorship.

In this portion, Fang compares Punitive Forking with Feather Forking. The former requires a 51 percent majority of the network hashrate in order to execute, while the latter can be achieved without and could thus be argued as more dangerous. Otherly, Feather Forking offers a censorship solution that can block specific transactions from being validated.

Fang ironically uses Gary Johnson, an overt libertarian figure, as a victim of censorship by the Chinese government. Assuming China cannot amass the required majority and blacklist Johnson’s transactions via Punitive Forking, they can, explains Fang, go about it in the following:

“As an attacker you say, ‘ok, I’m going to attempt to fork if I see a block from Gary Johnson, but, you know if that doesn’t work out, I’m just going to give up again and then go back to the main chain.’”

This “giving up” point arrives after Johnson’s block has received k number of confirmations. Fang then unfolds a number of different dynamics to frame the example:

  • Let q equal the proportion of mining power you have, 0 < q < 1
  • Let k = 1: You will give up after 1 confirmation (one additional block)
    • Chance of successfully orphaning (invalidating) the Johnson block = q [squared]
  • If q = .2, then q[squared] = 4 percent chance of orphaning block. Not very good.

In Fang’s example, he assumes that q equals 20 percent of the network hashrate and from this deducts a four percent chance of censoring Johnson’s transactions. Remember that based on game theory this strategy is perfectly visible to other members of mining pool.

This visibility means that other agents are aware that, if it includes Johnson’s transactions, there is a slight chance that their block could be orphaned. In order to better weigh the dilemma, miners must consider the following formula:

  • Expected Value (including Johnson’s transaction) = (1 – q[squared]) * BlockReward + Johnson’s transaction fee.
  • Expected Value (don’t include) = BlockReward

From this reasoning, Johnson will have to pay a much higher fee for his transaction to remain incentive compatible. The higher fee calculated as q[squared] times the blockreward.

The blockreward at present is 12.5 bitcoin, then multiplied by the above four percent (assuming that q also equals 20 percent of the network hashrate, we arrive at 0.5 bitcoin or $3,763.655 based on prices at the time of writing. Concluding, Gary Johnson would have to pay roughly $3,700 in transaction fees simply to be eligible for his transactions to be mined and made valid.

Fang finishes this portion of his presentation with:

“We have just shown how with 20 percent of the network hashrate we can make it prohibitively expensive for someone to participate in the Bitcoin network.”

For a frame of reference, operates roughly 25.1 percent of the network hashrate, followed by AntPool (17.2 percent) and SlushPool (12.3 percent).

The positive side to this mining technique, Block Discouragement, is something proposed and discussed by Bitcoin Core developer Gary Maxwell.

In a thread discussing Feather Forking, and soft ways of blacklisting users, Maxwell explained how its “been proposed not as an attack but as a safer way to implement some kinds miner behavior shaping. E.g. ‘discouraging’  blocks that we know reorg the chain, or which do not include transactions (when we know our mempool had many).”

The threats to the network are thus becoming varied, complex, and highly political. If anything, Feather Forking should redefine immutability in a society post-bitcoin. Perhaps a blockchain cannot be altered once a transaction is confirmed, but it may very well be because this transaction has been blocked by miners leveraging strategies that follow from game theory. In practice, such malicious behavior from miners has not been observed yet and the theoretical implications may not fully materialize in the real world.

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