Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort. Yet persistent disparities across race, gender, and class challenge this ideal. Some attribute these gaps to structural inequality; others to individual choice. We develop a game-theoretic model in which candidates from different socioeconomic groups differ in their perceived post-selection value--shaped by social context and, increasingly, by AI-powered tools offering personalized career or salary guidance. Each candidate strategically chooses effort, balancing its cost against expected reward; effort translates into observable merit, and selection is based solely on merit. We characterize the unique Nash equilibrium in the large-agent limit and derive explicit formulas showing how valuation disparities and institutional selectivity jointly determine effort, representation, social welfare, and utility. We further propose a cost-sensitive optimization framework that quantifies how modifying selectivity or perceived value can reduce disparities without compromising institutional goals. Our analysis reveals a perception-driven bias: when perceptions of post-selection value differ across groups, these differences translate into rational differences in effort, propagating disparities backward through otherwise "fair" selection processes. While the model is static, it captures one stage of a broader feedback cycle linking perceptions, incentives, and outcome--bridging rational-choice and structural explanations of inequality by showing how techno-social environments shape individual incentives in meritocratic systems.

翻译：从招生到招聘，精英选拔制度旨在公正地奖励技能与努力。然而，种族、性别和阶级间持续存在的差异挑战着这一理想。有人将这些差距归因于结构性不平等，有人则归因于个人选择。我们建立了一个博弈论模型，其中来自不同社会经济群体的候选人在感知的选拔后价值上存在差异——这种差异由社会背景塑造，并日益受到提供个性化职业或薪资指导的人工智能工具影响。每位候选人策略性地选择努力程度，在努力成本与预期回报之间进行权衡；努力转化为可观察的绩效，而选拔仅基于绩效。我们在大量参与者极限下刻画了唯一的纳什均衡，并推导出显式公式，展示了价值差异与机构选拔标准如何共同决定努力程度、代表性、社会福利及效用。我们进一步提出了一个成本敏感的优化框架，用于量化如何通过调整选拔标准或感知价值来减少差异，同时不损害机构目标。我们的分析揭示了一种感知驱动的偏见：当不同群体对选拔后价值的感知存在差异时，这些差异会转化为努力程度的理性差异，从而通过原本“公平”的选拔过程反向加剧差距。尽管模型是静态的，但它捕捉了连接感知、激励与结果的更广泛反馈循环中的一个阶段——通过展示技术社会环境如何塑造精英制度中的个人激励，弥合了理性选择与结构性不平等解释之间的鸿沟。