Blockchain transactions consume diverse resources, foremost among them storage, but also computation, communication, and others. Efficiently charging for these resources is crucial for effective system resource allocation and long-term economic viability. The prevailing approach, one-dimensional pricing, sets a single price for a linear combination of resources. However, this often leads to under-utilization when resource capacities are limited. Multi-dimensional pricing, which independently prices each resource, offers an alternative but presents challenges in price discovery. This work focuses on the welfare achieved by these two schemes. We prove that multi-dimensional pricing is superior under stable blockchain conditions. Conversely, we show that one-dimensional pricing outperforms its multi-dimensional counterpart in transient states, exhibiting faster convergence and greater computational tractability. These results highlight a critical trade-off: while multi-dimensional pricing offers efficiency gains at equilibrium, its implementation incurs costs associated with system transitions. Our findings underscore the necessity for a deeper understanding of these transient effects before widespread adoption. Finally, we propose mechanisms that aim to mitigate some of these issues, paving the way for future research.
We investigate the impact of reward schemes and committee sizes on governance systems over blockchain communities. We introduce a model of elections with a binary outcome space, where there is a ground truth (i.e., a “correct” outcome), and where stakeholders can only choose to delegate their voting power to a set of delegation representatives (DReps). Moreover, the effort (cost) invested by each DRep positively influences both (i) her ability to vote correctly and (ii) the total delegation that she attracts, thereby increasing her voting power. This model constitutes a natural counterpart of delegated proof-of-stake (PoS) protocols, where delegated stakes are used to elect the block builders. As a way to motivate the representatives to exert effort, a reward scheme can be used based on the delegation attracted by each DRep. We analyze both the game-theoretic aspects and the optimization version of this model. Our primary focus is on selecting a committee that maximizes the probability of reaching the correct outcome, given a fixed monetary budget allocated for rewarding the delegates. Our findings provide insights into the design of effective reward mechanisms and optimal committee structures (i.e., how many DReps are enough) in these PoS-like governance systems.
Many proof-of-stake protocols finance validator rewards from two sources: transaction fees and a finite reserve of tokens. This creates a dynamic hand-off problem. Early in the life of the system, fees may be too small to fund the target level of security; later, fees may become sufficient. The central question is whether the reserve provides enough runway for the protocol to remain secure until this fee-only region is reached. We study this problem in a discrete-time stochastic model of validator participation. Token price and transaction demand fluctuate over time, while validators choose participation strategically. We solve the validator entry game and derive an exact state-dependent reserve threshold, i.e., the minimal reserve stock necessary and sufficient to sustain a target security level. This threshold separates three regions: infeasibility, reserve-dependent security, and fee-only security. Security fails if the reserve first falls below the state-dependent threshold, and a successful hand-off occurs exactly if the fee-only region is reached before that failure time. We derive stress-test guarantees that convert lower confidence bands for token price and demand into reserve requirements, and obtain explicit failure-probability and expected hand-off-time bounds. Finally, we extend the model to forward-looking validators and derive the Markov participation condition that captures how current participation affects future reserve-funded rewards. The main implication is that reserve policy should not be evaluated by nominal depletion dates or steady-state reward ratios alone. A protocol can have a large nominal reserve and still be close to security failure after adverse price or demand shocks. Conversely, once demand crosses the fee-only threshold, the reserve becomes redundant for security. This paper provides a tractable equilibrium framework for stress-testing this transition.
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Restaking protocols expand validator responsibilities beyond consensus, but their security depends on resistance to Sybil attacks. We introduce a formal framework for Sybil-proofness in restaking networks, distinguishing between two types of attacks, one in which other Sybil identities are kept out of an attack and one where multiple Sybil identities attack. We analyze marginal and multiplicative slashing mechanisms and characterize the conditions under which each deters Sybil strategies. We then prove an impossibility theorem: no slashing mechanism can simultaneously prevent both attack types. Finally, we study the impact of network structure through random graph models: while Erdös-Rényi networks remain Sybil-proof, even minimal heterogeneity in a two-block stochastic block model makes Sybil attacks profitable. These results reveal fundamental limits of mechanism design for restaking and highlight the critical role of network topology.
