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We develop a dynamic model of board decision-making akin to dynamic voting models in the political economy literature. We show a board could retain a policy all directors agree is worse than an available alternative. Thus, directors may retain a CEO they agree is bad—deadlocked boards lead to entrenched CEOs. We explore how to compose boards and appoint directors to mitigate deadlock. We find board diversity and long director tenure can exacerbate deadlock. We rationalize why CEOs and incumbent directors have power to appoint new directors: to avoid deadlock. Our model speaks to short-termism, staggered boards, and proxy access.