A Proposal to Tackle Algorithmic Collusion in Cryptocurrencies and Beyond

By Giovanna Massarotto

Collusion is one of the greatest threats to cryptocurrencies like Bitcoin, which has surpassed $100,000 in value, and its network currently processes around 450,000 transactions per day. Many argue that Bitcoin could challenge the U.S. dollar’s global dominance by enabling a decentralized, peer-to-peer payment system. Bitcoin transactions are verified by a decentralized network of computers, and the network reaches agreement on the transaction history through consensus algorithms rather than relying on a central authority like a bank. Although the Bitcoin network is open to anyone, mining—which secures the network and issues new bitcoins—requires massive computational resources. Miners compete to solve complex cryptographic puzzles, and those with greater computational power have a higher likelihood of success. To improve their odds, miners often join forces in so-called mining pools, where they combine their resources and share rewards. But what if major mining pools collude and gain majority control of Bitcoin’s computational power? They could disrupt the network by reversing transactions and undermining trust in the system. While Bitcoin wouldn’t simply stop working, confidence in its integrity could collapse, potentially triggering a major crash in the broader crypto market, which is valued at over $3 trillion.

Collusion is not merely a crypto problem; it undermines competition in any market. Today, firms increasingly rely on algorithms to set prices, which can facilitate coordination among competitors, potentially leading to price-fixing cartels that harm both competition and consumers.

My latest paper, Detecting Algorithmic Collusion,  86 Ohio St. L. J. (forthcoming 2025), investigates algorithmic collusion by examining the same algorithms that enable cryptocurrencies like Bitcoin to verify their transactions in a decentralized fashion through consensus. In the U.S., collusion is prosecuted under Section 1 of the Sherman Act, which requires an agreement to collude. My study focuses on algorithms that enable computers to agree despite computers’ deviations from the algorithm’s instructions, thereby securing stable agreements. These algorithms are known as Byzantine agreement algorithms. My study extracts from these algorithms mechanisms that computers use to coordinate their behavior and reach consensus, as similar techniques might be used to collude by enabling, for example, competitors to agree on the same price.

Byzantine agreement algorithms stem from the Byzantine Generals Problem. In 1982, three computer scientists, Leslie Lamport, Robert Shostak, and Marshall Pease (LSP), described the problem of reaching an agreement with unreliable computers through an analogy they referred to the “Byzantine Generals Problem” (BGP).

“[S]everal divisions of the Byzantine army, which are camped outside an enemy city, each division commanded by its own general. The generals can communicate with one another only by messenger. After observing the enemy, they must decide upon a common plan of action. However, some of the generals may be traitors, trying to prevent the loyal generals from reaching an agreement on when to attack.”

This problem is studied in the context of distributed systems, which are any network of computers, such as the Bitcoin network, that work together to perform a common task by using algorithms.  The BGP is one of the most fundamental and studied problems in distributed systems, as even a single unreliable computer can prevent the system from reaching agreement and render it unworkable.

In their classic paper, Lamport, Shostak, and Pease developed the first solutions to this problem. They observed that the problem is unsolvable with three generals, when one is a traitor, unless the generals sign their messages with an unalterable signature; thus, cryptography in a computer context. Cryptography enables the solution of the BGP with three computers by using signed messages, which allow participants to detect if a computer is lying by sending a message that differs from the one it received.  In addition, Lamport, Shostak, and Pease found that the problem was solvable with four generals without using cryptography, using a majority value to reach an agreement, which in the Byzantine Generals problem framework is either “attack” or “retreat” from the enemy city.

These solutions laid the foundations for a substantial body of research in this field. Therefore, my article explores additional Byzantine agreement algorithms to identify recurring approaches for solving the BGP. These approaches include broadcasting, leader election, and private channels and are typically employed in combination to achieve consensus in distributed systems. Interestingly, these approaches show how there are many overlaps between the way computers reach agreements and companies collude. For instance, electing a leader is very common in the context of price fixing among competitors and is one of the main techniques used in Byzantine agreement algorithms to increase coordination among computers, which is done by introducing a single point of coordination—the leader.  Broadcasting implies sending a message to all computers as part of the network rather than having point-to-point communication. In the context of price-fixing, broadcasting recalls the role of public announcements that multiple studies argued can be adopted to effectively collude. Private channels—commonly used as a security measure—prevent malicious nodes from intercepting and altering messages and jeopardizing the agreement.

In summary, I have identified five mechanisms to solve the BGP: 1. Cryptography; 2. Minimum of four computers; 3. Broadcasting; 4. Leader elections; 5. Private channels. These mechanisms are important from a collusive context because U.S. courts use plus factors, operational criteria, to detect collusion. Collusion is illegal, and companies are unlikely to leave evidence of an explicit agreement. Plus factors support an inference of an agreement and presently include factors such as price parallelism and competitors communicating regularly or sharing confidential information. By identifying elements from algorithms that enable stable agreements, my study defines new plus factors, including cryptography, private channels, and a minimum of four computers to detect algorithmic collusion more effectively. These plus factors integrate and do not replace the current legal and economic plus factors. We need to consider that agreement algorithms, including Byzantine agreement algorithms, and the algorithmic plus factors are fundamental for the functioning of distributed systems, just like an agreement in a non-computer context is fundamental to engage in legal contracts and much more. This is why the new plus factors need to be considered in the specific context. For example, in the context of price fixing, they should be considered along with the existing plus factors, such as parallelism in price and a history of collusion among firms. In the context of cryptocurrencies like Bitcoin, miners may coordinate off-chain—outside the protocol’s formal consensus rules—and potentially collude in ways that undermine the system’s decentralization and security guarantees by using techniques, including private channels.

In a digital economy, computers can adopt more sophisticated techniques for reaching an agreement and potentially collude than those in the analog past. Courts and antitrust enforcers must modernize their oversight tools accordingly.

Giovanna Massarotto is a Lecturer at the University of Pennsylvania Carey Law School and an affiliate of the University of Pennsylvania Carey Law School’s Center for Technology, Innovation & Competition, Penn Program on Regulation, and the University College Centre for Blockchain Technologies (UCL CBT). The views and ideas expressed in this post are those of the author and do not necessarily represent those of the Wharton School or the Wharton Initiative on Financial Policy and Regulation.