To the best of its abilities, the DoubleZero network abstracts connectivity away for end users. All else equal, a packet of information that travels from London to Frankfurt on a well-traveled line pays the same as a packet that travels to Sao Paolo on an infrequently-used line. But underneath the hood, connectivity matters greatly and the DoubleZero system aims to incentivize performance from it network contributors. Connections that have high throughput and low latency should be paid more than those that have low throughput and high latency. Connections between popular destinations should earn more than connections on less popular routes.
The rewards model is the key pillar that incentivizes value from network contributors, while shielding users from routing logic. At a high level, the DoubleZero protocol accumulates revenue from users, and distributes that pool to network contributors (net of rewards removed to prevent self-dealing attacks). The rewards model governs the distribution, and it does so based on the marginal and fair contribution of each network contributor to the network’s efficiency.
To do so, the rewards model operationalizes the concept of Shapley values from the field of cooperative game theory. This rewards a network contributor for its marginal contribution to a simple value function, under various counterfactual scenarios. Network contributors who generate lots of value, through provisioning low-latency and high-throughput connections along popular routes and under different combinations of present and absent peer contributors, are rewarded commensurately.
The methodology in this proposal focuses on value created under various counterfactual scenarios. That may not be immediately intuitive; and indeed a more natural approach is to pay out rewards simply on the basis of carried traffic. However, we believe that the carried traffic model — while simpler to understand — is insufficiently discriminating and thus does not incentivize long-term value.
To illustrate the point, consider a scenario with four links connecting cities A, B, and C. The red and green link connect A and B; a yellow link connects A and C; and a blue link connects B and C. Suppose the red link is more performant than the green link. Finally, each city wants to send 1 Gb of traffic to its clockwise neighbor. Under this topology and using the carried traffic model, the division of rewards is straightforward: the green link receives no rewards (as it carries no traffic) while each of the other links receives one-third of the rewards (as they each carry 1 Gb).
But do these rewards truly map to value created? Consider the world without each of the links sequentially. Should the red link drop out, the green link becomes much more important. Should the yellow or blue links drop out, users will care if the public internet pathway connecting those cities is meaningfully worse; but they will not care if the performance is comparable. This thought exercise illustrates that value is more complex, and these counterfactuals hint at a more robust notion of value.
Indeed, to augment the scenario, suppose the public internet pathway connecting each city has a one-way latency of 30ms. Suppose the red line is substantially more performant than the green line (with a latency of 10ms rather than 25ms); and that the blue line is more performant (20ms) than the yellow line (25ms). With this added information and under the lens of counterfactual scenarios, the division of rewards on the basis of traffic carried no longer seems optimal. The green link should get more than zero for its insurance value; the blue link should earn more rewards than the yellow link when benchmarked against the public internet alternative; and the red link should be rewarded for its very strong performance (over both the public internet and the green link counterfactual scenarios).
The carried traffic model could be modified with ad-hoc adjustments to distribute rewards for redundancy value, improved latency over the public internet and peers, etc. (For instance: we could mandate a line with no traffic but that provides insurance value to another line gets paid at 20% its rate if the first layer of insurance, 5% if the second layer of insurance, etc.) But this general approach would require substantial tuning of its many parameters. Moreover, this approach quickly erodes the simplicity of the carried traffic model anyways. By contrast, the Shapley value methodology handles these complexities simply and robustly.
Shapley values hail from the cooperative game theory, as a means of fairly distributing the gains of a joint endeavor amongst players, based on each player’s marginal contribution to different coalitions of other players. They satisfy key desirable properties like symmetry (players with equal contributions get equal rewards), dummy player (those who create no value get no reward), and additivity across both settings and value functions. Indeed, they were a major reason that their creator, Lloyd Shapley, won the Nobel Prize in Economics in 2012.
Operationally, Shapley values are generated by calculating the average marginal contribution to a payoff or value function of each contributor, across all possible combinations of other contributors (weighted by the probability of that combination occurring). To illustrate, suppose we want to compute the Shapley value for the green link. To do so, we would look at every combination of other contributions without the green link (e.g red only, red and blue, etc), and measure the marginal increase in the value function V when the green link is included in that coalition versus excluded. These marginal increases, weighted by a probability matrix, give the green link’s Shapley value.
To complete the exercise, we need to define the value function.
The value function is simple. Taking its inspiration from the “Increase Bandwidth and Reduce Latency” rallying cry, it is simply traffic times the negative latency of that traffic, summed over all traffic types (e.g. origin and destination).
$$ V = -\sum_i t_i l_i $$