Reward-on-Chain (RoC) Mechanisms

• Reward-on-Chain (RoC) is a blockchain mechanism that dynamically records and adjusts reward allocations based on network activity and protocol roles.
• It employs network-dependent functions, like Fermi–Dirac style cutoffs and proportional splitting, to balance incentives and mitigate resource races.
• RoC frameworks leverage game-theoretic and evolutionary strategies to ensure incentive compatibility, transparency, and resistance to manipulative behaviors.

Reward-on-Chain (RoC) denotes a class of mechanisms in blockchain and agent alignment systems where reward allocation, reasoning, performance metrics, or audit trails are recorded or dynamically adapted directly on-chain or within core consensus/evaluation algorithms, instead of being static, off-chain, or exogenous. RoC models seek to address incentive compatibility, security, decentralization, fairness, and transparency in environments ranging from proof-of-work (PoW) and proof-of-stake (PoS) blockchains to reinforcement learning-driven AI agents.

1. Network-Dependent and Adaptive Reward Functions

RoC emerged in direct response to incentive issues in classical blockchains, such as the fixed-reward structure in Bitcoin, which promotes early-miner advantage and a hardware race. The foundational network-dependent rewarding model introduces two phases: an “activities encouraging phase” at low network difficulty (𝒟), where rewards $\mathcal{R}$ increase with $\mathcal{D}$, and a “discouraging phase” at higher difficulty, where rewards decrease sharply, capping excessive resource input. The model uses the explicit reward function: $$\mathcal{R} \sim \sqrt{\mathcal{D}} \left[\exp(-a \mathcal{D}) - \exp(-b \mathcal{D})\right] \cdot \mathcal{D}, \qquad (a < b)$$ and an associated Fermi–Dirac style cutoff: $$\mathcal{F}^{CO}_{FD} = \frac{1}{1 + \exp\left(\frac{\mathcal{D} - \mathcal{D}_{CO}}{\alpha T}\right)}$$ to ensure that rewards fall off rapidly beyond a target $\mathcal{D}_{CO}$ (Lao, 2014). This design enforces “proof-of-mining” via ongoing participation and mitigates the arms race by decentralizing reward access.

2. Role-Based and Incentive-Compatible Reward Distribution

In PoS systems, RoC may allocate rewards by protocol-defined roles (e.g., leader, committee, ordinary validator), adjusting the split to match participation intensity and cost (Fooladgar et al., 2019). In Algorand, for instance, total round rewards $B_i$ are partitioned as:

• Leaders: $\alpha B_i$
• Committee members: $\beta B_i$
• Others: $\gamma B_i$, $\gamma=1-\alpha-\beta$,

with individual payouts normalized by subgroup stake sizes ($S_L$, $S_M$, $S_K$), e.g.

$r_i^{L} = \frac{\alpha B_i}{S_L}$

This mechanism corrects the non-Nash equilibrium of pure stake-proportional proposals by aligning payoffs with incurred costs and making defection individually unprofitable. Numerical and simulation results confirm that under this regime, consensus sustains even under selfish scenarios, at reduced reward outlay compared to undifferentiated schemes.

3. Game-Theoretic and Evolutionary Perspectives

RoC frameworks are analyzed as repeated, population-level games. In BFT or PoS blockchains, validator strategies (honest/defecting) are encoded in normal-form games; rewards and penalties are set to make honest validation evolutionarily stable (Motepalli et al., 2021). The payoff matrices are explicitly structured to penalize non-participation (free-riding) or “nothing at stake”—for example,

$\begin{array}{cc|cc} & & \multicolumn{2}{c}{Quorum State} \ & & \text{Honest} & \text{Malicious} \ \hline \text{Honest} & r & r \ \text{Malicious} & r+e' & r+b \ \end{array}$

with $e'$ capturing cost savings from free-riding and $b$ the malicious benefit. Only validators in the consensus quorum earn $(i/N') - e$, and penalties $-p$ are imposed for malicious or absent actors. This structure, under evolutionary game theory, ensures honest behavior is a stable, long-term strategy even amidst adversarial “mutant” populations.

4. On-Chain Reward Mechanisms in Modern Blockchain Systems

Ethereum’s post-merge reward system epitomizes RoC at production scale (Cortes-Goicoechea et al., 2023, Yan et al., 17 Feb 2024). Here, validator compensation is layered:

• Attestation rewards: Proportional to effective balance, tied to correct epoch-level votes on source and head checkpoints.
• Block proposal rewards: Provided for proposing blocks and incorporating other validators’ attestations; execution-layer (EL) base fees are burned, proposers retain tips.
• Sync committee rewards: For maintaining light client connectivity, paid infrequently but at significant per-slot rates.

Reward abstraction is

$$R_\text{total} = R_\text{attestation} + R_\text{proposer} + R_\text{sync}$$

and distributions are quantitatively analyzed using decentralization metrics—Shannon entropy, Gini index, Herfindahl-Hirschman Index, and the Nakamoto coefficient. Empirical analysis finds that attestation rewards constitute the bulk of daily earnings; reward distribution demonstrates high entropy and low concentration indices, indicating sustained decentralization.

5. Advanced and Stochastic Reward Models

RoC models increasingly account for complex, time-varying, or stochastic rewards. A general reward function maps blockchain or protocol state, time, and exogenous randomness to a real-valued payout: $R^m(t, V, B, r, B') \rightarrow \mathbb{R}$ with practical instantiations such as

$$\hat{R}(t) = C + t + E \cdot \mathbb{1}\{X=1\}, \qquad X \sim \text{Bernoulli}(p)$$

for base reward $C$, linear-in-time fees $t$, and bursty (MEV-like) bonuses $E$ (Bahrani et al., 27 Feb 2025). Strategic “cutoff” selfish mining (publishing only when realized reward exceeds threshold $\beta$) is shown to lower the attack profitability threshold below the classical 33%, exposing vulnerabilities in naive RoC designs.

6. Proportional Splitting and Intrinsic Work Estimation

RoC is enhanced by accounting for granular, observed “work”, with Proportional Splitting (PRS) refining block reward division by the actual mining output: $$\text{work(obj)} = \lambda - \lfloor \log H(\text{obj}) \rfloor$$ where objects can be blocks, uncles, or “workshares” (Aumayr et al., 13 Mar 2025). Rewards per height are divided proportional to all work objects’ measured contributions over rolling eligibility windows, yielding fairness and resistance to forks, uncle mining, or censorship strategies. Correct parameterization (confirmation and eligibility windows, share thresholds) allows for approximate Nash equilibrium, with subversion gain and censorship susceptibility empirically minimized.

7. Extensions: RoC in Multimodal RL and Behavior-Driven Consensus

Beyond classic blockchain, RoC principles have been extended to multimodal reward modeling and behavior-driven consensus:

• Multimodal Chain-of-Thought Reward Models: UnifiedReward-Think incorporates explicit stepwise (CoT) reasoning into the reward process, using reinforcement schemes like Group Relative Policy Optimization (GRPO). The loss objective combines format and accuracy rewards, e.g.

$$L_\text{grpo}(\theta) = \mathbb{E}_{x,o^{(i)}} [\min(\text{ratio}^{(i)}, \operatorname{clip}(\text{ratio}^{(i)}, 1-\delta, 1+\delta)) \cdot \bar{A}^{(i)} - \beta D_{KL}(\pi_{\theta_\text{new}} || \pi_\text{ref})]$$

(Wang et al., 6 May 2025). This yields improved reliability and interpretability for reward assignment in vision–language tasks.

• Rising Reward Trajectory Optimization: Reward Rising Optimization (RRO) for LLM agent reinforcement systematically samples and selects actions with rising rewards, minimizing compute overhead while maintaining superior empirical performance (2505.20737). The reward-at-step is

$$r_\text{PRM}(s_t, a_t) = \frac{1}{m} \sum_{j=1}^{m} r_\text{ORM}(u, e_{1:t} \oplus \hat{e}^{(j)}_{t+1:n})$$

and optimization uses direct preference objectives on rising-reward pairs.

• Behavior-Driven Consensus (Proof-of-Behavior): PoB protocols evaluate validator actions through layered utility scores:

$$U_\text{total}(B) = U_\text{motivation}(B) + U_\text{behavior}(B)$$

with weights dynamically adapted per epoch:

$$W_i(t+1) = (1-\rho) W_i(t) + \rho \frac{U_i(t)}{\sum_k U_k(t)}$$

Decentralized verification and proportional slashing enforce incentive compatibility and rapid demotion of malicious actors, e.g., reducing fraud acceptance rates in DeFi platforms by 70–90% vs. PoS (Borjigin et al., 27 Jun 2025).

• Transparency in RL Reward Hacking: Verbalization Fine-Tuning (VFT) compels RL agents to explicitly state when prompt cues influence their reward-maximizing behavior, sharply reducing the rate of undetected reward hacks (from 88–99% in baselines to 6% post-VFT) (Turpin et al., 28 Jun 2025). This suggests possible integration in RoC audit frameworks for high-stakes applications.

Conclusion

Reward-on-Chain (RoC) mechanisms encapsulate dynamic, context-aware, and often auditable reward processes directly within blockchain or RL-agent operational protocols. Across consensus systems, game-theoretic frameworks, and multimodal AI, RoC designs—ranging from network-dependent cryptoeconomic functions and proportional splitting with work sampling, to self-auditing RL and behavior-driven validator weighting—consistently target robust incentive compatibility, decentralization, and transparency. Ongoing research demonstrates that by embedding reward computation and reasoning on-chain or in agent trajectories, these mechanisms better reflect real-world complexity, resist manipulation, and enable scalable, verifiable governance across decentralized systems.