Random Proposer Mechanism

• Random Proposer Mechanism is defined as a family of methods that randomly allocates proposal rights in contexts like bilateral exchange and blockchain systems.
• The mechanism in bilateral exchange uses uniform randomization of proposer roles to guarantee an approximation ratio of about 3.15 for first-best gains from trade.
• In blockchain protocols, randomness-backed proposer selection underpins validator assignment and influences security, fairness, and MEV extraction mitigation.

“Random proposer mechanism” does not denote a single universally shared construction across the cited literature. In the bilateral-exchange literature, it denotes a simple mechanism in which one of the two agents is selected uniformly at random to make a take-it-or-leave-it price offer, and the resulting allocation is analyzed as an approximation to first-best gains from trade (Hartline et al., 8 Aug 2025). In blockchain research, by contrast, the phrase is most naturally associated with randomness-backed assignment of block-proposal rights, or with protocol components whose security depends on proposer unpredictability, even when no paper introduces a new mechanism under that exact name (Alpturer et al., 2024). Other literatures use proposer-side randomization differently, including per-vertex softmax proposals for maximum weighted matching and lottery-based delegation mechanisms (Alzuhair et al., 10 Jun 2026, Bechtel et al., 2020).

1. Bilateral exchange: the exact named mechanism

In the bilateral-exchange setting, the random proposer mechanism is studied in the standard Myerson–Satterthwaite environment with one buyer and one seller, independent private values, and quasi-linear utilities. A seller initially owns one indivisible good and has private cost $c$ for transferring it; a buyer has private value $v$ for receiving it. If trade occurs with probability $x(v,c)$, expected gains from trade are

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$

The first-best benchmark trades exactly when $v>c$, yielding

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$

Within this model, the mechanism is defined by uniformly randomizing proposer power: with probability $1/2$ the buyer proposes a take-it-or-leave-it price, and with probability $1/2$ the seller proposes a take-it-or-leave-it price. If the responder accepts, trade occurs at that price; otherwise no trade occurs. The cited theorem states that, for independent values and quasi-linear utilities, any Bayesian Nash equilibrium of the mechanism guarantees at least a $1/3.15$ fraction of first-best gains from trade, and the same paper gives a simple geometric proof of a factor-$4$ guarantee before refining it to recover the $v$0 ratio (Hartline et al., 8 Aug 2025).

A nearby but distinct bilateral-trade design is the random double auction. That mechanism does not randomize which side proposes. Instead, an intermediary publicly commits to charging a fixed commission fee and randomly drawing a spread from a uniform distribution; the buyer submits a bid and the seller submits an ask simultaneously, trade occurs if the bid-ask difference exceeds the realized spread, and the transaction price is the midpoint. The paper is explicit that this is a randomized double auction rather than a standard random proposer mechanism, even though both mechanisms use randomization in bilateral trade (Zhang, 2021).

2. Geometric analysis and approximation guarantees

The geometric analysis of the bilateral-trade mechanism fixes the buyer’s value $v$1 and writes seller cost as a nondecreasing quantile function $v$2 for $v$3, with $v$4. If the buyer offers price $v$5, seller acceptance probability is

$v$6

Conditional first-best gains from trade are represented as area: $v$7

The factor-$v$8 proof chooses

$v$9

and partitions $x(v,c)$0 into a left region $x(v,c)$1 and a right region $x(v,c)$2. The buyer’s utility from deviating to price $x(v,c)$3 is the rectangle

$x(v,c)$4

which covers at least half of $x(v,c)$5, so $x(v,c)$6. The seller’s quantile-doubling deviation

$x(v,c)$7

yields utility at least $x(v,c)$8. Since $x(v,c)$9,

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$0

Uniformly randomizing proposer power then gives

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$1

and hence

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$2

The sharper argument introduces a scaling parameter $\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$3. It yields the approximation ratio

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$4

optimized at approximately

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$5

which gives

$\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$6

reported as the $\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$7-approximation. The same paper emphasizes that this refines a geometric framework rather than improving the known numerical bound beyond $\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$8 (Hartline et al., 8 Aug 2025).

3. Blockchain interpretation: randomness-backed proposer assignment

In blockchain systems, “random proposer mechanism” most directly refers to a protocol in which block proposers are selected from a validator set using a pseudorandom seed. Ethereum is the clearest example in the cited material. Time is divided into epochs of $\mathbb{E}_{v,c}\!\left[(v-c)\,x(v,c)\right].$9 slots, each slot lasts $v>c$0 seconds, and the proposer list for an epoch is derived from a RANDAO-based seed. If slot $v>c$1 has no block, then

$v>c$2

If a block is proposed in slot $v>c$3, the proposer signs the epoch number $v>c$4, and

$v>c$5

The paper states Ethereum’s timing as

$v>c$6

so the RANDAO value at the end of epoch $v>c$7 determines the proposer list for epoch $v>c$8. Under the paper’s idealization, when the seed is uniformly random, proposers are modeled as independent draws proportional to stake. The same paper studies strategic withholding of tail-slot RANDAO contributions and defines $v>c$9 as the maximum fraction of rounds an adversary with stake fraction $$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$0 can propose. It reports, for example,

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$1

showing that the random proposer mechanism is slightly but provably biasable under optimal strategic manipulation (Alpturer et al., 2024).

The proposer-builder separation survey uses this randomness-backed scheduler as a background assumption rather than as an object of primary study. It treats proposers as validators selected to propose the next beacon block, states that sync committee rewards go to “512 randomly selected validators,” notes that participation depends in part on “RANDAO,” and argues that “potentially extractable value is relatively equitable (since proposition conditions are random).” The survey’s central point is that random assignment of proposal rights is not sufficient for reward equity once MEV extraction depends on builder sophistication, relay dependence, and order-flow asymmetries; PBS changes how selected proposers monetize their slots, not who gets selected (Koegler, 22 Jun 2025).

4. Randomness layers, alternatives, and proposer-constrained ordering

Several blockchain papers in the cited set are better understood as work on the randomness layer surrounding proposer assignment, or on alternatives to random proposer election, rather than as new random proposer mechanisms in the narrow sense.

“Commit-Reveal$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$2” is a randomness-generation protocol designed to mitigate last-revealer attacks in commit-reveal beacons. It uses two nested commitments per participant,

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$3

first reveals $$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$4, computes

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$5

then defines a reveal-order score

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$6

sorts participants by $$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$7, and finally derives

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$8

The paper motivates this as a randomness beacon for applications such as validator selection in Proof-of-Stake, not as a full proposer-selection protocol by itself (Lee et al., 4 Apr 2025).

“Don’t Mine, Wait in Line” argues that the usual PoS design—randomly choosing, on each round, one participant as consensus leader proportionally to stake—creates fairness problems when distributed randomness generation is biased or expensive. It proposes Robust Round Robin as an alternative: proposer candidates are selected deterministically from long-term identities by age order, while a lightweight random endorser committee preserves liveness. The paper’s explicit claim is that it replaces random proposer election as the primary scheduling mechanism rather than refining it (Ahmed-Rengers et al., 2018).

“Proof-of-randomness protocol for blockchain consensus” does present a direct randomized owner-selection procedure. Each node computes

$$\operatorname{FB} \;=\; \mathbb{E}_{v,c}\!\left[\max\{v-c,0\}\right].$$9

aggregates

$1/2$0

and then defines

$1/2$1

The node with minimal or maximal $1/2$2, depending on the agreed rule, becomes the block’s “owner,” which functionally coincides with the proposer for that round. This is a direct proposer lottery, although the paper leaves several security and deployment issues underspecified (Zhang et al., 2022).

A different strand constrains proposer power after proposer selection rather than randomizing the proposer. MEV-ACE assumes that “each slot has a designated block producer selected by the consensus protocol” and then locks the admissible transaction set, derives a delayed-randomness seed

$1/2$3

and uses that seed to generate a random permutation of admissible transactions. The paper is explicit that this is not random proposer selection, but a random transaction-ordering mechanism under a fixed proposer (Wang, 8 Apr 2026).

5. Other proposer-side randomization in optimization and delegation

Outside trade and blockchain, proposer terminology is used in more localized algorithmic senses. “Random Proposals” for maximum weighted matching studies a randomized vertex-driven proposal process. In each round and for each vertex $1/2$4, one neighbor $1/2$5 is sampled according to

$1/2$6

The proposed edge is accepted only if

$1/2$7

so a proposal replaces up to two matched edges when it yields a strict local improvement. With

$1/2$8

the algorithm returns a matching $1/2$9 satisfying

$1/2$0

Here the “proposer” is a vertex, not a bargaining agent or a block producer (Alzuhair et al., 10 Jun 2026).

Delegated stochastic probing studies the closest analogue to a randomized single-proposal mechanism in delegation settings. Its lottery mechanism allows the agent to propose a lottery $1/2$1 from a principal-approved menu $1/2$2, after which the principal samples an outcome $1/2$3. The paper proves that such randomized single-proposal mechanisms can outperform deterministic mechanisms on some instances but not in the worst case. In one family of examples, the best lottery mechanisms achieve

$1/2$4

of the principal’s nondelegated expected utility, whereas the best deterministic mechanisms achieve only

$1/2$5

in another family, both classes achieve only

$1/2$6

This is proposer-side randomization at the level of outcome recommendations rather than proposer identity (Bechtel et al., 2020).

6. Scope, misconceptions, and terminological boundaries

A recurring misconception is to treat all uses of “random proposer” as instances of one mechanism class. The cited literature suggests a sharper taxonomy. In bilateral exchange, the term names a specific mechanism: proposer identity is randomized uniformly between buyer and seller, and the object being proposed is a take-it-or-leave-it price (Hartline et al., 8 Aug 2025). In Ethereum and related blockchains, proposer randomness usually refers instead to the assignment of proposal rights through a protocol randomness beacon; papers on PBS often rely on that scheduler as background and then study how selected proposers outsource, monetize, or are constrained in their use of the slot (Koegler, 22 Jun 2025). In multiple-concurrent-proposer systems, randomness may govern transaction assignment to proposer lanes, proposer rank, or tie-breaking, while proposal rights are concurrent rather than exclusive. One paper on MCP MEV uses random transaction allocation to proposers and a stake-weighted VRF rank signal, and then shows that concurrency plus pre-ordering visibility creates same-tick duplicate steals, proposer-to-proposer auctions, and timing races; it proposes deterministic priority-DAG scheduling and duplicate-aware payouts as mitigations (Landers et al., 17 Nov 2025).

The distinction between “randomly selected proposer” and “known future proposer” is also economically decisive. In Ethereum PBS analysis, Flashback argues that future proposers in PoS Ethereum are decided ahead of time and can therefore be contacted by builders for future-block auctions. The paper’s point is precisely that once future proposer identities are known, mechanism design changes: reservation contracts and proposer precommitment become possible, whereas these opportunities disappear in a fully unknown-proposer environment (Mao et al., 2024).

Finally, some papers are only indirectly related to a random proposer mechanism in the narrow sense. Sedna assumes a multiple-concurrent-proposer blockchain and asks how users should disseminate transactions; it samples a subset of proposer lanes and sends addressed bundles of coded symbols, but it does not randomize proposal rights themselves (Ranchal-Pedrosa et al., 18 Dec 2025). This suggests that “random proposer mechanism” is best treated as a family resemblance term whose precise meaning depends on whether randomness governs proposer identity, proposal order, proposal content, or merely the dissemination path leading to proposal.