Analyzing the Economic Impact of Decentralization on Users

Aside from financial speculation, perhaps the dominant “real” use case of blockchain technology is as a currency for users with no viable alternative. While compelling applications, the economic case for such users is relatively straight-forward because the competing product³³3For example: a currency likely to be frozen by an authoritarian government, a hyperinflating currency, or a currency that can be tracked by law enforcement critical of your illicit activity is so dysfunctional that concerns about (say) Bitcoin’s transaction fees, volatility, and UI become very second-order. A classical pitch for decentralization therefore emphasizes simply that decentralized services make it more challenging for authoritarian leaders (and law enforcement) to deny access, and this pitch is plenty convincing in comparison to the (functionally non-existent) alternatives.

A modern discussion on blockchain technology, however, includes applications targeting users in developed economies with highly developed alternatives. For example, the pitch for stablecoins to users with a hyper-inflating local currency looks very different than to users with access to Venmo, Paypal, and credit cards. Consider also decentralized services such as file storage (for which centralized services such as Dropbox are a reasonable substitute), social networks (for which centralized services such as Facebook or Twitter are a reasonable substitute), or gaming (for which centralized gaming services produced by Riot or Blizzard are a reasonable substitute) – what would cause users to prefer decentralized services over highly-developed centralized alternatives?

A natural answer is that perhaps the decentralized service might somehow be “better” than the centralized competitor.⁴⁴4See here for an example of this pitch: https://a16zcrypto.com/posts/article/how-stablecoins-will-eat-payments/. But it is initially confusing how that might possibly arise as centralized services can optimally coordinate to lower internal costs, whereas decentralized services must additionally manage incentives/trust across distributed entities.

One well-understood source of inefficiency in centralized services is deadweight loss caused by a monopolist.⁵⁵5The holdup problem is another – see Section 1.3 for a brief discussion. That is, a decentralized service might plausibly be desirable to a highly-developed centralized alternative simply because the decentralized service results in different prices, and this can still be the case even if the centralized infrastructure is more efficient. Therefore it is natural to target domains with a “natural monopoly” aspect (such as social networks, payment systems, marketplaces, etc.).

Indeed, independently of any blockchain discussions, [48] highlights natural monopolies for digital services as a growing challenge, and further poses several possible approaches (each with drawbacks). One approach is described as follows: “An alternative approach to full-scale regulation consists in insulating a natural monopoly (or bottleneck or essential facility) segment, as became popular in the late twentieth century. This segment remains regulated and is constrained to provide a fair and nondiscriminatory access to competitors in segments that do not exhibit natural monopoly characteristics and therefore can sustain competition.”⁶⁶6[48] cites several examples: electricity markets might insulate the natural monopoly (the grid) and enable open competition on generation, or rail travel might insulate the natural monopoly (the tracks/stations) and enable open competition on train operation. A prevalent digital example is Local Loop Unbundling, where many countries insulate the natural monopoly (the “local loop” – physical copper wires servicing telecommunications) by requiring its owners to lease access at nondiscriminatory prices to service providers. One of two key drawbacks of this approach is as follows: “…one wants to break up the incumbent without destroying the benefits of network externalities. For example, breaking a social network into two or three social networks might not raise welfare.”⁷⁷7The second key challenge highlighted is identifying a core bottleneck to insulate. We argue in Section 4 that for many domains of interest, such a bottleneck can be identified and (in theory, at least) insulated. A final challenge highlighted is the actual process of unbundling an existing product, which is unrelated to our work.

One interpretation of Bitcoin is exactly through this lens, and [29] are the first to make this point.⁸⁸8“We model this novel economic structure and show that the BPS’s [Bitcoin Payment System’s] decentralized design offers a prototype of a payment system in which users are protected from monopoly harm even if the payment system were a monopoly…Standard economic arguments suggest that weak competition among monopolistic firms calls for regulation to mitigate monopoly harm. Under the BPS, users are protected from abuses of monopoly power even without competition from other payment systems. Thus, the BPS addresses potential antitrust concerns in a novel, even revolutionary, way.” Indeed, when viewed as a payment system, the natural monopoly segment is “ledger maintenance” (where a consistent record of transactions is maintained), while the user-facing “transaction processing” segment is not a natural monopoly. In the language of Bitcoin, substantial network effects arise from having consensus on a single consistent ledger, but minimal network effects arise from users transacting within the same block (or with the same miner). In the language of payment systems, substantial network effects arise from users transacting in the same “currency”, but minimal network effects arise from users using the same app to process those transactions.⁹⁹9The preceding sentence is necessarily clunky, as it is somewhat unnatural to imagine separating a centralized payment system into a back-end transaction processor (that stores data and moves money around, where network effects arise) and front-end transaction processor (that interfaces directly with users, and minimal network effects arise). One high-level contribution of the “Decentralized view” is as a lens to dis-integrate services without an obvious dis-integration. Perhaps shockingly, this insulation is maintained without regulation,¹⁰¹⁰10Our analysis does rely on Miners treating core aspects of the consensus protocol as exogenous, which bears conceptual similarity to regulation. and therefore provides a novel approach to insulating natural monopolies.

The preceding paragraph highlights blockchain-style decentralization an innovative approach to insulate natural monopolies from derivative services, but should we expect users to ultimately be better off? How would the answer depend on market primitives? Moreover, how do we even draw conclusions on users’ utility from decentralized services? Surprisingly few answers are known to questions like these, and surprisingly fewer frameworks are known to even approach them. The goal of this paper is therefore to provide a framework towards such questions in the core domain of distributed ledgers, with an emphasis on connecting users’ ultimate utility to properties of the decentralized ledger.

Our model is motivated by the concept of a ledger. Ultimately, the product consumed by an end-user is the ability to write information to the global ledger (which we call a Write).²¹²¹21In order to focus on the relevant market primitives, we do not explicitly model ledger maintenance, consensus, cryptography, privacy, or reading. The service purchased by an end-user gets their message onto the ledger, and in a manner that can be read by the desired recipients. That is, each end-user has a message they would like to write on the ledger, and purchases a Write to do so.

The entire value proposition of a global ledger is that there is ultimately a single consistent ledger. It is therefore crucial that some aspects of ledger maintenance are performed via a single entity/protocol/etc. (for example, centralized ledgers should maintain a single consistent back-end database. Decentralized ledgers should have a single protocol from which observers can conclude a single consistent ledger). Intuitively, these are operations that directly edit content in the ledger (and because there is a single consistent ledger, these operations must be carefully coordinated by a single entity/protocol/etc.). Other aspects of ledger maintenance can in principle be performed by competing entities (for example, end-users can in principle face different User Interfaces, pricing schemes, etc.). We abstract away precise details of the ledger maintenance process, and simply refer to operations that directly edit the single consistent ledger as Upstream (and refer to one unit of these operations as an Append), and those that could in principle be performed by competing entities Downstream.

It may help to have a few examples in mind. Imagine breaking a centralized ledger (i.e. Venmo) into its back-end database maintenance and front-end User Interface. The back-end database must ensure consistency on a single global ledger, and so is Upstream. Edits to the back-end database must be reliable and consistent (even if the database is replicated, distributed, etc.). One Append constitutes the resources necessary to add one entry to the back-end database (maintaing consistency, availability, etc.). The front-end User Interface is Downstream – the front-end UI interacts directly with consumers, and turns communication with end-users into a query to the Upstream back-end database. The front-end UI consumes Appends in order to produce Writes, and sells Writes to users. Note that, in principle, the centralized ledger could offer different front-end UIs to different consumers (with different pricing schemes, different communication protocols, different app layout, etc.) – doing so does not in principle interfere with the ability to maintain a single, consistent back-end database.

One could imagine instead a centralized back-end database that provides an API for third-party app access. The centralized back-end database again is a producer of Appends. Each third-party app is a consumer of Appends and a producer of Writes. End-users purchase Writes from a third-party app (who incurs costs both from interacting with the end-user, and from purchasing Appends). Again, each third-party app could in principle differ in pricing schemes, communication protocols, app layouts, etc., and purchase Appends from the same back-end database (that interacts with each third-party app in a manner that maintains a single consistent ledger).

One could also imagine a decentralized consensus protocol maintaining a decentralized ledger, allowing participation from “miners”, “stakers”, “proposers”, etc.²²²²22Throughout this paper, we adopt the language of Bitcoin and refer to these participants as miners. The decentralized protocol outlines a costly procedure by which miners receive Appends.²³²³23For example, Bitcoin miners receive Appends by repeated hashing (which costs electricity and hardware). Ethereum stakers receive Appends by locking up ETH in the Ethereum protocol (which costs capital). Each miner is a consumer of Appends (that they “purchase” by completing the costly procedure specified in the decentralized protocol), and a producer of Writes. End-users purchase Writes from a miner (who incurs costs both from interacting with the end-user, and “purchasing” an Append). The consensus protocol structures its “sale” of Appends so that all ledger updates contribute to a single consistent ledger.²⁴²⁴24That is, this paper assumes that the consensus protocol functions as intended. See Section 1.3 for a brief discussion on on related work surrounding this assumption.

The subsequent paragraphs formalize our model in the abstract – the running story provides intuition for each concept.

We consider two types of resources. The Downstream resource, Write, is consumed by end-users. The Upstream resource, Append, is required to produce Writes (in one-to-one ratio). Production of the Upstream resource is a natural monopoly, and therefore will be produced by a single entity/protocol. Production of the Downstream resource is not a natural monopoly, therefore we model a Downstream market with multiple competing participants.

There are two types of market participants. End-users are the ultimate consumers, who desire Writes. Each end-user wants a single Write, and has some value $v$ should they receive one. Downstream producers produce Writes, which necessitates consumption of Appends. The protocol (which is hard-coded and has no objective function or strategic decisions) produces Appends.

There is a continuum of end-users, with $D(p)$ denoting the mass of consumers with value at least $p$ for a Write.

We assume that $D(\cdot )$ provides finite revenue to a monopolist (that is, ). Our main results require a standard regularity assumption on $D(\cdot )$.

We model the interactions between the Upstream protocol, Downstream providers, and End-Users as a three-stage game. First, the Upstream protocol sets the dynamics for selling Appends to Downstream providers. Next, with this protocol fixed, Downstream providers set their strategies both for purchasing Appends and for selling Writes to End-Users. Finally, with these strategies fixed, End-Users set their strategies for purchasing Writes from Downstream providers.

Let DP denote the set of Downstream providers, EU denote the set of End-Users, and $P_i(\overrightarrow{a})$ denote the payoff to Player $i$ when the action profile is $\overrightarrow{a}$.

An End-User Equilibrium fixes some actions ${\overrightarrow{a}}_{\text{DP}}$ by the Downstream providers, and is a Nash Equilibrium of the End-User game induced by ${\overrightarrow{a}}_{\text{DP}}$ (with payoff $P_i({\overrightarrow{a}}_{\text{DP}};{\overrightarrow{a}}_{\text{EU}})$ to Player $i\in \text{EU}$ on action profile ${\overrightarrow{a}}_{\text{EU}}$).

A Downstream Equilibrium²⁵²⁵25We will sometimes simply call this an Equilibrium. specifies, for each possible action profile ${\overrightarrow{a}}_{\text{DP}}$ of the Downstream providers, an End-User Equilibrium $E({\overrightarrow{a}}_{\text{DP}})$ for the end-user game induced by ${\overrightarrow{a}}_{\text{DP}}$, and then (together with $E(\cdot )$) is a Nash Equilibrium among Downstream providers for the Downstream game induced by $E(\cdot )$ (which awards payoff $P_i({\overrightarrow{a}}_{\text{DP}},E({\overrightarrow{a}}_{\text{DP}}))$ to Player $i\in \text{DP}$ on action profile ${\overrightarrow{a}}_{\text{DP}}$). When $E(\cdot )$ is unique (or otherwise clear from context), we will abuse notation and simply refer to ${\overrightarrow{\alpha }}_{\text{DP}}$ as a Downstream Equilibrium. Moreover, we will also abuse notation and say that a Downstream Strategy ${\alpha }_i$ dominates ${\alpha }_i^{\prime }$ if ${\alpha }_i$ dominates ${\alpha }_i^{\prime }$ in the game among Downstream providers induced by $E(\cdot )$.

For a (not necessarily continuous) monotone non-increasing function $F(\cdot )$, we let $F^{-1}(y):=\{x|{lim}_{z\to x^{+}}F(z)\le y\le {lim}_{z\to x^{-}}F(z)\}$, $F_{inf}^{-1}(y)$ denote the infimum of $F^{-1}(y)$, and $F_{sup}^{-1}(y)$ denote the supremum of $F^{-1}(y)$. Observe that if $F(\cdot )$ is left-continuous, then $F(x)\ge y$ for any $x\in F^{-1}(y)$.²⁶²⁶26Because for any $x\in F^{-1}(y)$, $y\le {lim}_{z\to x^{-}}F(z)=F(x)$. If $F(\cdot )$ is continuous and strictly decreasing, we simplify notation and define $F^{-1}(y):=F_{inf}^{-1}(y)=F_{sup}^{-1}(y)$.

First-Price Auctions with Reserves are a common subgame in our market structures. With a continuum of bidders and a total supply of $Q$, a first-price auction with reserve $r$ concludes as follows. First, let $B(q)$ denote the mass of bidders who submit a bid at least as large as $q$.²⁷²⁷27Observe that $B(\cdot )$ is left-continuous. To see this, observe that all bidders who bid at least $b-\epsilon$ contribute to $B(b-\epsilon )$. So the bidders that contribute to $B(b-\epsilon )$ for all $\epsilon >0$ are exactly those who bid at least $b$ – the same bidders that contribute to $B(b)$. Next, if , then every bidder who submits a bid at least as large as $r$ wins and pays their bid. If $B(r)\ge Q$, then every bidder who submits a bid strictly exceeding $B_{sup}^{-1}(Q)$ wins and pays their bid, every bidder who submits a bid strictly below $B_{sup}^{-1}(Q)$ loses, a mass of $B(B_{sup}^{-1}(Q))-Q$ bidders who submit a bid of exactly $B_{sup}^{-1}(Q)$ lose and the remainder win and pay their bid (and in this case a total mass of $Q$ bidders win).²⁸²⁸28Recall that $B(B_{sup}^{-1}(Q))-Q\ge 0$ as $B$ is left-continuous.²⁹²⁹29All of our analysis holds no matter how ties are broken to select the winning bidders among those who bid $B(B_{sup}^{-1}(Q))$. Observe that every bid profile induces an effective price of $b:=max\{B_{sup}^{-1}(Q),r\}$ – every bidder who submits a bid exceeding $b$ certainly wins (and pays their bid) and every bidder who submits a bid below $b$ certainly loses.

Simultaneous First-Price Auctions are another common subgame in our market structures. Below we overview Simultaneous First-Price Auctions and technical lemmas helpful to understand our results – full analyses and proofs are in the full version.

For equilibria among bidders, fixing all $Q_i,r_i$, we establishes in the full version that all winning bidders pay the same price in equilibrium, and define the value of this as clearing price.

Downstream Equilibria in our market structures concern the behavior of sellers in Simultaneous First-Price Auctions (i.e. choosing a quantity $Q_i$ according by participating in the Upstream protocol, and setting a reserve $r_i$). We refer to the reserve-setting aspect as a price-setting equilibrium (noting that a Downstream Equilibrium must both induce a price-setting equilibrium for fixed $\overrightarrow{Q}$, and be a joint equilibrium when considering both investment and reserves).

A concept throughout our analyses is whether a seller clears their entire inventory, and whether they determine the price at which the bidding equilibrium clears.

Finally, Proposition 6 characterizes that all potential price-setting equilibria are either a “market-clearing equilibrium” where no seller is sufficiently large to profit from price-setting, or have a unique price-setter.

One key difference between the Distributed Ledger Model and traditional market structures is the presence of a non-strategic protocol. Specifically, the Upstream game is hard-coded in the Distributed Ledger Model rather than endogenously optimized by a profit-maximizing Monopolist. This distinction is key.³⁷³⁷37As noted above, it is certainly relevant to also study the meta-game by which protocol rules are formed, but the game induced by a fixed protocol would still be relevant for the entirety of Bitcoin’s existence. Additionally, the decision to fix the quantity $Q_A$ of Appends and run a Tullock contest is material, and meaningfully affects the analysis.³⁸³⁸38For example, conclusions would change if instead the protocol set a price $p_A$ for Appends and sold whatever is demanded, even if $p_A$ were determined exogenously. As previously noted, all blockchain protocols the authors are aware of run an Upstream Tullock contest, and it is not clear how to implement alternate Upstream market structures with a secure protocol. Finally, the decision to have a block reward (which directly rewards miners for purchasing Appends, even if they do not ultimately sell Writes) is material, although our analysis shows limited impact on end-users (see Section 3.3.3).

First, we map aspects of Bitcoin onto the Distributed Ledger Model. Assuming that the Bitcoin protocol functions as intended,³⁹³⁹39See Section 1.3 for a small subset of works describing manners by which the protocol may not function as intended. let us first describe the interaction between Miners and Protocol. In order to produce a valid block, Miners must solve a “proof-of-work cryptopuzzle.” Specifically, Miners trade one hash computation for one independent Bernoulli trial to create a valid block.⁴⁰⁴⁰40With extremely low probability of success – roughly $2^{-78}$ at the time of writing. Moreover, the success rate of each Bernoulli trial is dynamically adjusted by the Bitcoin protocol so that one block is created amongst the entire network every ten minutes. Each block provides 1 MB of space for the Miner to include transactions, and awards the miner a block reward (currently 3.125 BTC). So in our model, the interaction between Miners and Protocol captures the following aspect: Resource is hash computations. Each Miner $i$ has some cost $c_i^R$ to perform one hash computation.⁴¹⁴¹41This includes electricity, operational costs, amortized hardware costs, etc. Appends are units of space in a valid block, and Protocol has hard-coded that $Q_A$ = 1 MB per ten minutes are awarded in total and that each Miner receives a fraction of 1 MB blocks proportional to their hash computations (because the success probability of each hash dynamically adjusts to enforce a total quantity of 1 MB per ten minutes). Finally, the protocol hardcodes $B=3.125$ BTC per 10 minutes as the total block reward,⁴²⁴²42Note that this quantity halves every four years, as pre-specified by the Bitcoin protocol. which is also distributed proportionally to miners according to their hash computations.

Aside from its interaction with Miners, Protocol simply maintains consensus on the contents of the ledger. For example, Protocol verifies validity of contents of the ledger, resolves any conflicts using “Nakamoto consensus” [35], and widely disseminates the ledger itself. In particular, the protocol rules suffice to identify a unique consistent ledger to disseminate.

End-users get their transactions in a Bitcoin block by broadcasting to Miners. Each transaction includes a transaction fee, which is paid to whichever Miner includes that transaction in their block. Processing a transaction induces costs such as checking validity, and maintaining network connectivity (to hear about transactions in the first place), which are captured by $c^W$ in our model. Miners are typically revenue-maximizing, and typically fill their blocks with transactions paying the highest fees (and, to the best of the authors’ knowledge, typically without reserves). For a patient end-user, who wants their transaction in the Bitcoin ledger eventually but not necessarily immediately, each Miner is a potential seller running their own First-Price Auction, and the service offered by distinct miners is indistinguishable.

It is also worth highlighting which of these aspects are key to fit our model, and which are not. All permissionless distributed ledgers the authors are aware of run a Tullock Contest in some Resource. Some (including Bitcoin Cash, Litecoin, Ethereum Classic) also use hash computations as Resource (“proof-of-work”). Others (including Ethereum, Solana, Cardano) use locked capital as Resource (“proof-of-stake”).⁴³⁴³43That is, Miners are now called Stakers, who trade one unit of locked capital per Bernoulli trial. It is not material to our analysis which Resource is used, only that the Protocol ultimately awards block space proportional to that resource.

We note that [3] also model blockchain investment games as a Tullock contest, while other works [29] instead model it as perfect competition with free entry. We briefly note that free entry can also be captured arbitrarily well in our model by taking $n\to \mathrm{\infty }$ Miners with identical $c_i^R$ (see Theorem 11, for example).⁴⁴⁴⁴44Specifically, the final bullet concludes that the natural “market clearing equilibrium” becomes an equilibrium with sufficiently-many identical Miners.

On the other hand, it is crucial for our model to accurately capture end-users that they are patient and therefore equally happy to be included in any valid block. Impatient users (such as those primarily motivated by DeFi applications) are not captured by our model. Instead, impatient users view the particular block offered by the next Miner as the only resource of interest, and therefore that Miner faces no competition. Therefore, a Miner selling blockspace primarily to impatient users is instead a monopolist.

Additionally, observe that Miners(/Stakers) are free to use whatever “off-chain” auction they like in order to sell space in their created blocks, independent of whatever “on-chain” mechanism is hardcoded. For example, it is immaterial to our model that Bitcoin’s on-chain mechanism is pay-your-bid, whereas Ethereum’s is a posted-price mechanism, because Miners(/Stakers) in both protocols can run a first-price auction with reserve off-chain to determine which transactions are included in the first place. On the other hand, the fact that Ethereum’s EIP-1559 burns⁴⁵⁴⁵45That is, transactions included in an Ethereum pay a posted-price (set by the Ethereum protocol) that is destroyed, and not awarded to the miner. revenue from the posted-price mechanism is material, and can be captured in our model via $c^W$. That is, our model adopts the perspective of [24] that EIP-1559 is really specifying a Write cost per included transaction (the burned base fee) on each Proposer, and the Proposer is then free to run whatever off-chain auction they like to build their block (rather than that EIP-1559 specifies the auction that Proposers must run when facing users).

Finally, while all mainstream protocols the authors are aware of currently have a single Proposer at each time slot, some protocols are now experimenting with “Multiple Concurrent Proposer (MCP)” protocols. In these protocols, there is no longer a monopolist for each block slot. Instead, multiple Proposers have the opportunity to insert transactions. Interestingly, our model also captures MCP protocols with either patient or impatient users.⁴⁶⁴⁶46To be extra clear, our model verbatim captures an MCP protocol where the block space in each block is partitioned according to stake (i.e. a 10% staker gets 10% of every block). Most MCP proposals instead sample a discrete number of Proposers proportional to stake, and allow each such Proposer an equal fraction of the block. Our model does not capture this verbatim, as the sampling process would meaningfully complicate analysis, but it would be a natural direction for follow-up work to modify our model to capture these MCP protocols verbatim.

In summary, the Distributed Ledger Model captures key aspects of many mainstream blockchain protocols (they are Tullock contests, and the protocol can impact $c^W$), while not capturing others (such as impatient end-users, or blockchains with a heavy MEV ecosystem⁴⁷⁴⁷47In blockchains with a heavy MEV ecosystem, the process of turning Appends into Writes itself is cost-intensive and meaningfully asymmetric.). Indeed, this is in line with the motivation for our paper: Decentralization does not uniformly impact all users identically in all domains, and so our model necessarily picks one canonical domain of focus.

Throughout this section, we abuse notation and use $(\overrightarrow{q},\overrightarrow{r})$ to refer to the Downstream Equilibrium $(\overrightarrow{q},\overrightarrow{r})$ together with the mapping $E(\cdot )$ that takes $({\overrightarrow{q}}^{\prime },{\overrightarrow{r}}^{\prime })$ to the canonical End-User Equilibrium. We repeat the key takeaways of this section below:

• $\mathrm{■}$

  While Equilibria may not always exist, Proposition 8 establishes an upper bound on the price any Miner will set: any strategy that sets a price exceeding the monopoly reserve for $D(\cdot )$ is a dominated strategy.

• $\mathrm{■}$

  Theorem 10 characterizes all potential Equilibria. In particular, there exists a single $\overrightarrow{Q}$ such that Miner $i$ wins $Q_i$ Appends in all pure equilibria. From here, there is a unique “market-clearing” potential equilibrium (where each miner sets reserve at most $D^{-1}(Q_A)$), and for each $i$ a unique potential equilibrium where Miner $i$ is a price-setter.

• $\mathrm{■}$

  Theorem 11 provides necessary and sufficient conditions for the “market-clearing” potential equilibrium to be an equilibrium.⁴⁸⁴⁸48In addition, we extend the necessary and sufficient conditions for the “market-clearing” equilibrium (when they exists) to the scenario where different Miners having different cost per Write in the full version. Importantly, the condition depends only on $D(\cdot ),Q_A$, and ${max}_i\{Q_i\}$. That is, to the extent that a “measure of decentralization” impacts the ultimate price paid by end-users, the correct “measure of decentralization” is the market share of the largest miner.

• $\mathrm{■}$

  The magnitude of the block reward (or whether there is a block reward at all) does not impact $\overrightarrow{Q}$, nor any of the potential Equilibria identified by Theorem 10. But, a larger block reward makes Equilibria more likely to exist (see Proposition 12).