tl;dr Given non-zero chance of losing deposits, we can’t assume people will participate as long as yield is positive. To quantify the threshold at which a validator may participate, we make an explicit participation constraint framework. Before diving into game theory, we explore and define the macroeconomic constraints and how that may affect the incentives for the entire validator set on average. Any reward and penalty shape optimization or security parameters that are not in the realm of this analysis has limited significance as this is a key driver of both the global constraints of the network as well as the the pro rata deposit yield as a function of total deposits.
takeaways:[~15%(±5%)] annualized net yield would be a compelling starting point for discussion. This will be bound by a[~0.5%] gross issuance rate, which bounds the“total deposit capacity” at 6.7% of market capitalization, which is about $2B today(at $30B cap). Any deposit level below that would increase the yield(e.g. $0.2B → 150% annualized net yield), providing strong incentives for joining the validator network.(Those parameters above can be tuned depending on our economic security needs).
What will it take to make it compelling to validate on Casper?
Context
A common failure mode in cryptoeconomic analyses will be to take for granted that people want to participate in your mechanism at all(especially while including draconian penalties for bad actors). The unexplored tradeoff there is that many honest/good validators may not be incentivized to validate at all due to the risk of losing part(or all) of their deposits.
This analysis in theoretical microeconomics is referred to as a participation constraint analysis. A participation constraint tries to measure if actors will benefit(or at least not be worse off) from participating in a given mechanism.
More specifically, for yield functions Y(p,TSF,TD) and N(p,TSF,TD)(for having voted or not in a checkpoint), this analysis explores dTDdYield and whether that is compelling enough for validators to participate.
In general, we should have an intuition for how enthusiastic will people be about validating. Out of a 100 miners or Ethereum users, how many people will be willing to validate? This will be a large driver of total deposits, the centralization level and even potentially the % of bad actors.
The rewards in excess of the participation constraint is the exact margin of safety a mechanism has to enforce additional security measures(i.e. penalties) for bad actors. The margin also compensates for the friction of getting started in a new process to begin with(i.e.“activation energy”). Therefore, even before beginning to shape the specific shapes of the reward and penalties for each type of situation and actors, we must engage in an macroeconomic analyses of a participation constraint for a given validator set(future work will explore game theory among a heterogenous set of validators with various levels of centralization). In other words, is the overall amount of rewards going to be worth the average cost of joining the network as a validator(i.e. risk and illiquidity)?
Framework
# constraint
(Net profit from participation) > (Opportunity Cost)
Opportunity cost is yield of comparable assets classes in risk & liquidity level.
[Activation energy is a proxy that captures the idea that given two asset classes with similar volatility and liquidity, people will prefer the well-known / more familiar asset class. It’s a proxy for all other risk outside of the traditional asset pricing(i.e.“PoS validation is a new process” rather than“PoS validation yields 8% returns”). Therefore the new asset class has to have excess returns to have parity.].
Source: Hal Varian, Intermediate Microeconomics
Method
Reverse engineering net profit, incremental issuance and“total deposit capacity”
Figure out what the risk of loss and illiquidity are for Casper validation.
Figure out what the opportunity cost for required return is for the given risk/liquidity profile
TODO: Figure out how much more we can provide as a premium(to get over the hump of other activation thresholds etc)
Determine the impact of that on the Ethereum economy will be(issuance level and margin of safety vs ideal threshold)
Opportunity Cost Range
Let’s assess opportunity cost to“reverse engineer” the appropriate yield range.
Opportunity cost is defined by the yield of an asset with comparable risk(chance of losses) and liquidity. Required returns go up as they have higher risk of loss and become more illiquid.
Cost of capital is a spectrum of risk and reward
Context
Framework
# constraint(Net profit from participation) > (Opportunity Cost)or# rational model(Net profit) - (opportunity cost) > 0or# behavioral model(Net profit) - (opportunity cost) - (activation energy) > 0Method
Opportunity Cost Range