Saito is an indirect mechanism: it implements incentives through signals generated by costly but observable behavior rather than through costless type reports. Because these action-generated signals cannot be reduced to cheap type messages without altering incentives, the direct-revelation reduction required by the Revelation Principle does not hold. As a result, classical impossibility results that depend on this reduction are not binding for routing-work mechanisms.
Given the importance of the distinction between direct and indirect mechanisms, this page reviews the historical development of implementation theory—from Hurwicz’s original formulation of mechanisms as general communication systems to the later shift toward direct revelation in Maskin and Myerson. Our goal is to show that Saito’s design aligns with standard implementation theory, even though the classical impossibility results built on direct mechanisms do not apply to routing-work systems.
Hurwicz’s foundational insight was that a mechanism is not merely an outcome rule but a communication system. The designer specifies a message space and an outcome function, and agents interact with the mechanism by sending signals drawn from this space. Crucially, Hurwicz imposed almost no restrictions on the nature of these signals. They might be direct reports of private preferences, but they could also be signals generated by behavior that leaves verifiable traces in the environment.
As the field developed, practitioners began informally distinguishing between two kinds of mechanisms. Direct mechanisms are those in which agents communicate only by reporting their private types, while indirect mechanisms are those that allow agents to take actions that generate observable information the mechanism can use. Hurwicz’s framework makes clear that both forms are legitimate; the distinction reflects modeling choices rather than limitations of the theory.
In much of the later literature, however, this distinction became obscured as the field restricted attention to the special case of direct mechanisms that accept only costless type reports. Within this restricted environment, Maskin and Myerson showed that many indirect mechanisms can be represented—in equilibrium—by equivalent direct mechanisms in which agents truthfully report their types. This reduction became formalized as the Revelation Principle, which provided a powerful tool for studying implementability, since any impossibility proven for the direct mechanism automatically applied to any indirect mechanism that could be reduced to it.
The convenience of this reduction came at a cost: it narrowed the mechanism space considerably. Many mechanisms—including Saito—cannot be converted into direct mechanisms without altering their incentive structure and therefore lie outside the domain of the impossibility proofs built on Maskin and Myerson’s work.
The Revelation Principle applies only under strict assumptions: that agents communicate solely through costless messages, that deviations are represented as alternative type reports, and that all strategically relevant behavior can be encoded in reports from agents to the mechanism. When these assumptions hold, any allocation rule implementable by an indirect mechanism has a direct-revelation counterpart in which truthful reporting is an equilibrium.
But routing-work mechanisms such as Saito violate each of these assumptions.
The first point of failure concerns the information conveyed by behavior. When nodes forward, withhold, or introduce transactions, they change observable features of the network—timing, flow, opportunity cost, and fee structure. These signals arise only because the underlying actions are costly. Replacing such behavior-generated evidence with costless reports removes the incentive consequences that make the signals credible. A direct mechanism cannot preserve incentives while substituting cheap talk for costly behavior.
The second point of failure concerns deviations. Direct mechanisms model every deviation as an alternative message about private type, but many deviations in routing work correspond to concrete behaviors—fabricating routes, withholding blocks, creating sybils—that are economically costly or topologically constrained. These behaviors cannot be represented as simple misreports. Because the deviation spaces differ, the strategic environment cannot be preserved under direct-revelation reduction.
A third point of failure arises from the richness of the underlying preference environment. Routing work implicitly solves a multi-good combinatorial allocation problem: participants have preferences over blockspace, time-to-inclusion, and various collusion or routing-sensitive goods. Any attempted reduction to a direct mechanism would require agents to report valuations over an exponentially large and highly structured space. In Saito, the presence of non-quasilinear preferences and infinitely granular time-based utility strengthens this problem: under Maskin’s framework, an agent seeking full strategic equivalence would need to report an infinite-dimensional preference map. Routing mechanisms avoid this impossibility by relying on action-generated revealed-preference signals rather than full type reports.
Taken together, these three problems show that routing-work mechanisms lie outside the domain in which the Revelation Principle applies. The assumptions necessary for direct-revelation reduction do not hold, and any attempt to enforce such a reduction would change the strategic environment rather than preserve it.
Once the Revelation Principle fails, a large number of impossibility results that assume the viability of direct-revelation reduction no longer apply. While we avoid detailed discussions of individual papers here, all of the following results require the direct-revelation framework and are therefore non-binding on routing-work mechanisms:
Myerson–Satterthwaite (1983): Bilateral Trade Impossibility
Depends on direct revelation, independent private values, and quasilinear utilities—assumptions violated in routing-work environments.
Green–Laffont (1979): Public-Goods Impossibility
Assumes costless misreports and prohibits the use of behavior-generated signals that routing work relies upon.
Gibbard–Satterthwaite (1973): Strategy-Proofness for Ordinal Social Choice
Applies only to mechanisms that take ordinal rankings as cheap-talk input; routing work does not operate on ordinal messages.
Bracha–Toueg (1985) and Dwork–Lynch–Stockmeyer (1988)
Byzantine impossibility results built on a message-only communication model, excluding the action-generated incentives central to routing work.
Each of these papers is discussed in greater detail elsewhere in the Wiki.