We study the amount of maximal extractable value (MEV) captured by validators, as a function of searcher competition, in blockchains with competitive block building markets such as Ethereum. We argue that the core is a suitable solution concept in this context that makes robust predictions that are independent of implementation details or specific mechanisms chosen. We characterize how much value validators extract in the core and quantify the surplus share of validators as a function of searcher competition. Searchers can obtain at most the marginal value increase of the winning block relative to the best block that can be built without their bundles. Dually this gives a lower bound on the value extracted by the validator. If arbitrages are easy to find and many searchers find similar bundles, the validator gets paid all value almost surely, while searchers can capture most value if there is little searcher competition per arbitrage. For the case of passive block-proposers we study, moreover, mechanisms that implement core allocations in dominant strategies and find that for submodular value, there is a unique dominant-strategy incentive compatible core-selecting mechanism that gives each searcher exactly their marginal value contribution to the winning block. We validate our theoretical prediction empirically with aggregate bundle data and find a significant positive relation between the number of submitted backruns for the same opportunity and the median value captured by the proposer from the opportunity.

翻译：本研究探讨了在具有竞争性区块构建市场（如以太坊）的区块链中，验证者捕获的最大可提取价值（MEV）与搜索者竞争程度之间的关系。我们认为，核解概念在此背景下是合适的解决方案，它能做出稳健的预测，且独立于具体实现细节或所选机制。我们刻画了验证者在核解中提取的价值量，并将验证者的盈余份额量化为搜索者竞争的函数。搜索者最多只能获得获胜区块相对于不含其交易包的次优区块的边际价值增量。这反过来为验证者提取的价值提供了下界。如果套利机会易于发现且多个搜索者提交相似的交易包，验证者几乎必然获得全部价值；而若每个套利机会面临的搜索者竞争较弱，搜索者则可能捕获大部分价值。针对所研究的被动区块提议者场景，我们进一步探讨了在占优策略中实现核分配配置的机制，并发现对于次模价值函数，存在唯一的占优策略激励相容核选择机制，该机制使每位搜索者恰好获得其对获胜区块的边际价值贡献。我们通过汇总交易包数据对理论预测进行实证验证，发现针对同一机会提交的尾随交易数量与提议者从该机会获取的价值中位数之间存在显著的正相关关系。