Blockchain systems must navigate a fundamental tradeoff between rewarding capable participants for performance and preserving a sufficiently decentralized distribution of stake. We study this tradeoff through algorithmic reward policies in dynamic blockchain environments with publicly known capability types and evolving token stakes. We analyze two settings. First, under full participation, we study virtual-stake policies that combine type and stake in winner selection. We show that fixed virtual-stake rules exhibit strong path dependence, and that this limitation extends to broader winner-selection rules based on virtual stake; when the type weight varies over time, the winner distribution asymptotically approaches either stake-proportional or type-proportional selection. Second, we study a repeated participation game in which agents may abstain, rewards update stake, and token value depends on the decentralization of the participating stake. We characterize stage equilibria under myopic behavior. In this environment, strongly performance-favoring winner-take-most policies can drive the system to minimum decentralization under myopic play. We then identify policies that preserve participation or decentralization only by departing from strict performance-first reward design. In particular, our analysis identifies three benchmarks: policies that spread winner eligibility across the top-$k$ types, policies that simulate lookahead, and broad-sharing reward rules. Each mitigates failures of performance-first designs with different tradeoffs in participation, robustness, and performance priority. Overall, our results suggest that winner selection alone does not robustly resolve the capability-stake tradeoff: sustaining decentralization requires reward rules that react explicitly to concentration, even when this entails sacrificing some immediate performance advantage.

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