Self-reference and the acyclicity of rational choice

Guided by an analogy between the logic of truth and the logic of a rationally choosing agent, I propose for the latter a principle of acyclicity, which blocks paradoxical self-referring reasoning. Certain decision-theoretic paradoxes are used to illustrate what can happen when acyclicity is violated. The principle, however, is argued for directly on grounds of coherence. Among its consequences are certain decision-theoretic rules, as well as a guiding line for setting Bayesian prior probabilities. From this perspective I discuss in the last two sections Prisoner's Dilemma and Newcomb's Paradox.