Originally designed to validate transactions in the Bitcoin virtual currency network, blockchain technology looks set to revolutionise 21st-century finance. Expected effects include the disappearance of obsolete intermediaries, improved security and drastic reduction in transaction costs. Catherine Casamatta teamed up with fellow TSE researchers Bruno Biais and Christophe Bisière, as well as McGill University’s Matthieu Bouvard, to analyse the stability of blockchain protocol using game theory.
Blockchain technology represents a very effective solution to a generic problem: how to maintain a decentralised, shared register of transactions and assets when its participants do not necessarily trust each other?
How does a proof-of-work blockchain protocol work?
In a blockchain, the flow of transactions to be validated is directed to participants called “miners”. Each miner stores these transactions in a block, adds a special transaction corresponding to his reward for that block, then tries to validate that block. To do this, the miner must solve a difficult numerical problem, using the brute force of trial and error. The successful miner disseminates this block and its solution (the “proof-of-work”) within the network. The other miners check the solution is correct, and the transactions in the block are valid, and mark their acceptance by abandoning their current block and by mining a new block of transactions, attached to the winning “parent” block. The process of searching for and sharing solutions continues, creating a sequence of validated blocks, representing the current state of the register. A single chain, like that in Figure 1, reflects a perfect consensus among participants about validated transactions.
Miners, however, may choose to discard certain blocks, starting a fork that deviates from the original chain, as illustrated in Figure 2. This creates competing versions of the ledger, reducing the credibility and reliability of the blockchain, especially if the fork is persistent. Even if, eventually, all miners agree to attach their blocks to the same chain, the occurrence of the fork is not innocuous. The blocks in the chain eventually abandoned are orphaned. They have been mined in vain, and the corresponding computing power and energy have been wasted. Moreover, the transactions recorded in the orphaned blocks may be called in question.
To analyse blockchain’s stability, Catherine and her colleagues build a model in which miners instantaneously observe transactions and solved blocks, and are only rewarded for solving blocks. Their analysis uncovers two important economic forces at play in the blockchain.
First, miners’ actions are strategic complements. Indeed, their rewards depend on the credibility of the chain on which they are solving blocks. This credibility is higher if more miners are active on it. Hence, miners benefit from coordinating on a single chain, which they can achieve by playing the “longest chain rule”, that is by considering the longest chain to be the correct one (Nakamoto, 2008). However, the same coordination motives sustain equilibria with forks. If a miner anticipates all other miners will create a fork, his best response is to follow them.
Second, they identify a countervailing force: if a miner has accumulated rewards on a given chain, the miner has a “vested interest” in this chain remaining active. Vested interests may counteract coordination motives, inducing miners to keep working on a minority chain, and sustaining persistent forks. Unlike temporary forks that only rely on coordination motives and would arise with atomistic miners, equilibria with persistent forks depend on miners taking into account how their actions affect the value of their rewards.
Overall, this analysis suggests that the blockchain design, by generating complementarities and vested interest, is subject to instability.
Consensus and dissensus
The researchers also investigate how frictions typically associated with dissensus and forks relate to these economic forces. For instance, communication delays may generate transient forks as some miners do not immediately realise that a new block has been solved. Some miners may also derive extrinsic benefits from creating a fork: it can allow them to void previous transactions and recover the corresponding cryptocurrencies (“double-spending”), or to push technical solutions that give them a competitive edge (“upgrades”). The researchers incorporate these frictions in their model and show that while they may act as triggers (instead of sunspots), the same fundamental interplay of coordination motives and vested interests as in the frictionless case underlies equilibria with forks.
Finally, they look at the computing capacity that each miner installs. Because the difficulty of the mining process is typically adjusted upwards when the total computing capacity in the network increases, a miner’s investment in computing power exerts a negative externality on all other miners. This gives rise to an arms race in which each miner ends up over-investing. This analysis points to another source of inefficiency in blockchain’s decentralised design.
The researchers’ analysis suggests that miners’ incentives are key to the production of a robust consensus in a blockchain. While miners benefit from coordinating on a single chain, thereby maintaining consensus, coordination motives may also lead them to abandon portions of the blockchain. This jeopardises the blockchain’s key function, i.e., producing a stable and immutable history of transactions. In addition, vested interests, by counteracting coordination motives, may lead to the persistence of multiple active chains.