Introduction
Blockchain protocols promise many innovations, from decentralized finance to supply chain tracking. However, as public blockchains grow, questions arise about fairly rewarding the many contributors that make these networks valuable. The hundreds of developers, validators, governance participants and users that comprise open protocols, need an alternative to traditional corporate structures to determine rewards and incentives.
Game theory provides conceptual tools for analyzing this challenge. Non-cooperative game theory studies settings where players make decisions independently and cannot negotiate binding agreements. In contrast, cooperative game theory allows groups of players to coordinate strategies and share payoffs as a team.
One key solution concept from cooperative theory is the Shapley value. Initially conceived for n-person cooperative games, Shapley values allocate payouts to each player based on their marginal contribution, averaged across all possible coalition subgroups. This approach satisfies intuitive fairness criteria while incentivizing team collaboration.
As we explore in this article, applying Shapley values to distribute protocol rewards could enable fair, performance-based incentives for open blockchain contributors. However, operationalizing this in a manipulation-resistant way poses research problems at the intersection of mechanism design, cryptography, and economics. If solved carefully, Shapley-style payouts may help growth and sustainability for Web3 protocols looking to compete with traditional technical solutions.
Shapley Values
Shapley values are a solution concept in the field of cooperative game theory that fairly assigns payouts amongst a group of individuals working together. The payouts are based on the marginal contribution of each group member; that is, the payout of the group with the individual included minus the payout of the group without the individual included. Intuitively, Shapley values represent the expected marginal contribution of a player to the game.
Shapley values also adhere to certain invariants. First, each player in the game should earn at least as much as they would from working individually. Players that have identical marginal contributions should receive equal payouts and tangentially, deadweight players with no payout. Finally, the sum of payoffs to each player should be equal to the total payoff generated when all players cooperate.
We can extend the concept of Shapley values to incorporate weights and coalitions. Adding weights to players allows the payoff vector to depend on more than just marginal contribution (e.g. a protocol can favour early adopters or token-holders). Separately, we can assume that players form pre-determined coalitions (smaller teams) and adjust the Shapley value to only account for orderings in which these players are working together.
Our Thesis
In order to apply the concept of Shapley values as a solution for distributing protocol rewards, it’s necessary to define a cooperative game beforehand. A game is defined by a set of players and a payoff function that can output a reward (“payoff”) for any subset of the players in the game. The calculation of Shapley values requires such a function to be defined ahead of time.
While Shapley values already have applications in machine learning and other data modeling fields, one of the big challenges in implementing its solution in an interactive setting like a blockchain protocol is defining the payoff function. The perfect solution would quantify the output of any group of players together even without knowing what would exactly happen if they worked together — however, this is extremely difficult, if not impossible, to do.
We propose as a different solution a function that pre-computes the payoff, with the payoff based not on user contributions but rather on a deterministic combination of the users' collective ratings. With this solution, we no longer face the challenge of quantifying group contributions ahead of time since users can calculate their predicted payoff beforehand. At the same time, since ratings can improve, users still have an incentive to put in their best effort to the protocol.
This report was commissioned by Mode, the Ethereum L2 building the onchain cooperative. To read the rest of our findings, visit their blog post here.
Shapley values are super underrated. The hard part here seems to be defining an objective function for a given protocol? We are exploring this in the treasury management context for Aera but that's necessarily a bit more narrow. Curious if you've tried this!