On the Incentive Compatibility of Block Propagation in Bitcoin

Abstract: Bitcoin is permissionless and does not rely on any central administrator, which gives it strong censorship resistance. At the same time, it is important to incentivize miners to behave in ways that align with the interests of the system as a whole. This paper asks whether miners are individually incentivized to propagate blocks, one of the most fundamental processes in Bitcoin. Miners collectively maintain the blockchain by generating blocks and disseminating them across the network. If miners have an incentive not to propagate some blocks, this would indicate a fundamental flaw in Bitcoin's incentive design. Although prior work has studied how propagation delays affect forks and mining rewards, it has not fully characterized miners' incentives to improve block propagation under different tie-breaking rules. To address this gap, we derive analytical reward expressions for each tie-breaking rule based on a blockchain network model that captures the effect of forks on mining fairness. These expressions explicitly characterize how block propagation delays, hashrate distribution, and tie-breaking rules jointly determine mining rewards. We then use them to analyze miners' incentives to improve block propagation. Our results show, for example, that miners have no mining-reward incentive to relay blocks generated by other miners. By contrast, under the first-seen rule, every non-majority miner is incentivized to receive other miners' blocks more quickly and to propagate its own blocks more quickly. Finally, we compare tie-breaking rules and identify a trade-off between propagation incentives and mining fairness. In particular, the first-seen rule provides the strongest incentives to reduce propagation delays, but it also worsens mining fairness the most.

• The paper demonstrates that Bitcoin block propagation fails to align miner incentives with network health, as miners lack rewards for relaying blocks.
• Analytical and simulation studies quantify how relay, inbound, and outbound delays under different tie-breaking rules affect miner profitability.
• The findings stress the need for incentive-aware protocol designs and reward mechanism revisions to enhance fairness and network security.

Incentive Compatibility of Block Propagation in Bitcoin

Introduction and Motivation

The paper "On the Incentive Compatibility of Block Propagation in Bitcoin" (2606.06860) critically examines the incentive structure underlying block propagation in Bitcoin's proof-of-work protocol. Given Bitcoin's permissionless and decentralized design, aligning individual miner incentives with the health of the protocol is paramount for maintaining security and fairness. While past literature has analyzed mining incentives in various settings, this work focuses on one of the protocol's most fundamental operations—block propagation—and explores whether current incentive mechanisms compel miners to disseminate blocks efficiently, especially under different tie-breaking rules for forks. The analysis leverages a formal network model of propagation delays and mining rewards, enabling precise characterization of incentive compatibility in block propagation.

Analytical Framework

The authors extend a round-based blockchain network model capturing propagation-induced forks and their effects on mining profit rates (MPR). Key variables include miner hashrate distribution $\alpha_i$, propagation delay matrices $T_{ij}$, and tie-breaking rules applied in the event of simultaneous chains with equal proof-of-work. Three classes of block propagation delays are distinguished:

• Relay delays: Propagation of another miner's block between two other miners.
• Inbound delays: Time for another miner's block to arrive at the focal miner.
• Outbound delays: Time for a focal miner's own block to reach other miners.

The model is expressed under three canonical tie-breaking rules: first-seen (miners extend the chain they receive first), random, and last-generated (miners build on the chain containing the most recently generated block). Analytical approximations under small delay assumptions and propagation-based triangle inequalities yield closed-form expressions for each miner’s expected reward as a function of network topology and tie-breaking policy.

Numerical Validation

The analytical expressions are validated using simulation-based experiments leveraging the SimBlock simulator, instantiated with empirically grounded network and hashrate configurations. The formulas accurately track model-based mining reward calculations across a broad range of fork rates, including scenarios with higher-than-observed real-world fork rates. Maximum observed relative errors are bounded (typically below 5%, with worst-case conservative bounds well below 20%), establishing the practical applicability of the analytical framework for incentive and fairness analysis in realistic large-scale blockchain settings.

Incentive Analysis of Propagation Behavior

A central finding is that under all considered tie-breaking rules, miners have no individual mining-reward incentive to relay blocks generated by other miners; in fact, reducing relay delays benefits rival miners rather than the focal miner. This negatively impacts the system-level propagation which, if left purely to self-interest, can degrade network robustness and security.

For inbound and outbound delays, the incentive landscape is rule- and hashrate-dependent:

• First-seen rule: All miners with less than 50% hashrate are incentivized to reduce both inbound and outbound delays. The incentive vanishes for majority miners, who in some cases are incentivized to delay both the reception and propagation of blocks.
• Random rule: Incentives are weaker and thresholded by the relative hashrate share.
• Last-generated rule: Only miners with less than 50% hashrate have outbound delay reduction incentives; inbound incentives are only present if the sender miner's hashrate exceeds the receiver's.

Thus, propagation-facilitating actions (such as efficient relaying) are almost never privately optimal, while inbound and outbound optimizations are only partially compatible with the network’s collective interest.

Strategic Block Propagation

The theoretical findings are operationalized into explicit miner strategies:

• Relay-Delay Strategy: Rational miners benefit from not relaying others’ blocks. A system of non-relaying, miner-rational agents is a Nash equilibrium in the absence of exogenous incentives or protocol enforcement.
• Inbound- and Outbound-Delay Manipulation: Miners can profit, under certain conditions, by artificially delaying their own block propagation (outbound) or the acceptance of incoming blocks (inbound). The equilibrium structure shows that only miners above specific hashrate thresholds (e.g., majority miners) will manipulate delays under standard tie-breaking rules.

These results extend to real-world mining costs and rewards, affirming that the lack of incentive compatibility holds under practical constraints and not just in idealized reward models.

Tie-Breaking Rules: Trade-offs and Design Implications

The comparison of tie-breaking rules reveals a fundamental trade-off:

• First-seen confers the strongest propagation incentives for non-majority miners but tightly couples mining profitability to propagation performance, amplifying rich-get-richer (RGR) effects in the presence of asymmetric network advantages.
• Random rule offers less propagation incentive, but reduces the RGR feedback from network disparities and mitigates certain strategic mining vulnerabilities.
• Last-generated provides intermediate outbound incentives and further dampens RGR amplification from inbound disadvantages, but at the cost of even weaker inbound propagation incentives.

No rule is universally optimal: maximizing propagation efficiency exacerbates fairness concerns, while improving fairness diminishes intrinsic propagation incentives, especially among non-majority participants.

Limitations

The analysis assumes homogeneous miner behavior at the pool level and constant network parameters; intra-pool propagation dynamics and parameter non-stationarity are identified as important directions for further work. The first-seen analytical approximation also relies on a benign-network triangle inequality, which may not hold under adversarial eclipse attacks. Direct simulation of long-run rewards in large-scale settings remains computationally out of reach, although not central to the analytic findings.

Conclusion

This work establishes, both analytically and empirically, that block propagation in Bitcoin is not fully incentive compatible under standard mining reward mechanisms. Miners’ rational behavior, in absence of explicit protocol mandates or side payments, leads to under-provision of relay services and strategic delay in sending/receiving blocks, with direct implications for network robustness, security, and fairness. Tie-breaking rules profoundly shape the incentive landscape, mediating the trade-off between propagation improvement and fair reward allocation. These findings underscore the necessity of incentive-aware protocol design, potentially incorporating extrinsic rewards for relaying or revised tie-breaking mechanisms, to align network-level objectives with individual miner incentives. This analytical framework provides a foundation for future theoretical and applied work bridging blockchain network engineering, economic mechanism design, and distributed protocol analysis.