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Centralization in maximal extractable value (MEV) markets is a significant concern for blockchain systems, as persistent concentration of economic power can weaken competition, reduce openness, and undermine the decentralization goals of permissionless protocols. While much of the existing analysis has focused on builders, validators, and block-building markets, this paper studies centralization from the perspective of searcher competition. We develop a heterogeneous model in which searchers differ in opportunity coverage and execution efficiency, and we analyze how auction design affects fairness, decentralization, and security among searchers competing for the same MEV opportunity. To evaluate searcher competition, we introduce two metrics: a Shapley-weighted Jain fairness index, which measures whether rewards are proportional to searchers' marginal contributions, and an expected-reward Herfindahl-Hirschman Index (HHI), which measures concentration in long-run searcher rewards. Using these metrics, we first analyze the standard first-price, winner-take-all auction as a benchmark. Our analysis shows that, under searcher heterogeneity, first-price competition can reward rank dominance rather than marginal contribution, leading to concentrated rewards and weaker contribution-adjusted fairness. Motivated by these limitations, we propose an entry-filtered Shapley-capped auction mechanism that distributes searcher rewards more fairly and broadly among admitted high-quality submissions. Designing such a mechanism in a permissionless blockchain environment is challenging: searchers may create Sybil identities by submitting copied or degraded versions of the same execution strategy, and validators may collude with searchers to increase joint payoff. We address these concerns through Bayesian security constraints for copied-code Sybil deviations and validator-searcher coalition deviations, and show that suitable parameter choices make the Shapley-capped mechanism secure against both. We complement the theoretical analysis with numerical benchmarks and Ethereum on-chain data. The theoretical benchmarks show that the proposed mechanism is especially effective in centralized opportunity classes, where first-price competition concentrates rewards among a small set of searchers. They further indicate that the proposed mechanism is a potential improvement over first-price competition in empirically motivated opportunity types.