This chapter describes the events that led to a fundamental change in our economic modeling assumptions. These changes represent the foundation of the methodologies that underlie the analysis and architecture that we are working hard to develop at the Ethereum research team (at least for the Casper and Sharding efforts). The design philosophy presented in this chapter (imho) strongly differentiates the work we’re doing at Ethereum from the work being done by every other project in the space.

Meet The Oligopoly

In December of 2014, Matthew Wampler-Doty (MWD) joined the Ethereum research team. In one of our first Skype calls, MWD and I got into an argument about economic modelling in an early sharding protocol. I wanted to exclusively consider the budget that a bribing adversary would have to spend to cause the failure of a protocol guarantee in a particular shard, when thinking about the security of that guarantee. MWD insisted that we assume that the distribution of deposit sizes in a shard was sampled from a Pareto distribution. We talked past each other, because the distribution of deposits does not necessarily affect the amount of deposits lost due to an attack. He accused me of making “strange linearity assumptions”, which is something I couldn’t understand through the bribing adversary model. This was my first hint that the concentration of wealth might be relevant to economic analysis of public blockchains.

In January 2015, Matthew Wampler-Doty, Jae Kwon, Ethan Buchman, Zackary Hess, Pink Penguin and I spent some time together in San Francisco. Our time together was kicked off by Cryptoeconomicon 1. Jae Kwon, Dominic Williams, Zack Hess, and I did a panel on proof-of-stake. I gave a presentation about cryptoeconomics as economic applied to achieving information security goals. MWD gave a talk where he showed that the problem of maximizing Ethereum miner revenue by choosing which transactions to include in blocks is (at least as hard as) the knapsack problem.

“Tendermint is two dudes!” Matthew Wampler-Doty excitedly told me, one evening. He explained that a cartel of Tendermint validators with more than 2/3 of the security deposits would form, because it does not require participation from the remaining validators to create finalized blocks (these “non-cartel validators” have less than 1/3 of security deposits). These less than 1/3 of nodes would be censored and eventually removed from the validator set. A new cartel with more than 2/3 of the (now smaller) set of security deposits would then form, and this process would continue until only [at most] 2 validators remain.

This argument struck a major cord. It fundamentally changed the way that I think about economic modelling and game theory in the public blockchain space. It was the first concrete move from efficient/competitive economic models to oligopolistic models. It changed the unit of analysis from individual validators to cartels of validators. It represented a shift from “ordinary” (independent choice) game theory to social choice/cooperative game theory.

This was a big change from the bribing adversary model. Instead of assuming that every node is willing and able to accept bribes, I instead assumed that profit-maximizing cartels would form, and that validators who are not in a cartel are not coordinating their strategy choices. I could then look at economic security in terms of how much money a cartel of a given size would lose when they undermine a protocol guarantee.

Our research team now had another usable model of economic security.

Unlike the bribing adversary, however, this model is exceptionally realistic. Cryptocurrency is incredibly concentrated. So is mining power. Oligopolistic competition is the norm in many “real-life” markets. Coordination between a small number of relatively wealthy validators is much easier than coordination between a large number of relatively poor validators. Cartels formation is completely expected, in our context.

So this is how I became committed to the design philosophy that motivates Casper, to this day:

Blockchain architecture is mechanism design for oligopolistic markets.

(When done correctly, at least…)

Thanks Matthew, your contributions have made a very significant and lasting impact on all of my work — you’re my hero!

A call to action

Taking a break from history for a moment, I’m going to take a moment to review blockchain projects in the space, identifying profit maximizing cartels that directly benefit from undermining protocol guarantees.

Cartels of 51% of the miners of any proof-of-work blockchain have a direct incentive to censor the non-cartel miners. This almost doubles their revenue from block rewards (after difficulty adjustment). This problem exists in Bitcoin, Ethereum, Dogecoin, and ZCash (to give the imo most notable examples).

Cartels of 51% of staked coins of any naive proof-of-stake protocol have precisely the same ability to directly benefit from censoring non-cartel members. NXT, PPC, and NEM — I’m thinking about you (among others).

Cartels of 67% of bonded coins of any consistency-favouring “traditional” consensus protocol have a similar direct incentive to censor non-cartel members, while 34% of bonded coins in these protocols have the ability to censor transactions by vetoing blocks (by preventing consensus/finality). Cosmos (Tendermint) and Polkadot — I’m looking directly at you.

Every single project in this space, as far as I can tell, has serious problems under cartel analysis. It is not a norm to use cooperative game theory, or even to use much game theory at all. Most of the projects in our space rely on an assumption that there are not more than some number of faulty nodes (or some percentage of faulty stake). Fault count assumptions are not appropriate for public blockchains, because public blockchains exist in an oligopolistic setting, where a very small number of miners or coin holders (or reputation holders, in more exotic architectures) control a vast majority of the weight in the consensus.

I want to call on all analysts and architects in the blockchain space to adopt oligopolistic market models and coordinated choice game theory as mainstays of their practice. They are absolutely realistic. If you don’t assume that there is a concentration of power, and that players coordinate their strategies, then you will be doing your clients a serious disservice. You’re leaving your clients to fend for themselves against the cartels.

I know it sounds hard to provide protocol guarantees in the context of these models, but this is our context. Difficulty of getting your software from where it is now to a place where cartels do not stand to benefit from screwing your clients is not an excuse for being negligent of your clients interests.

Over the remaining chapters of this history of Casper, I will document our progress defining Casper; a consensus protocol fit for an oligopolistic world.