A Robust Resolution of Newcomb's Paradox

Newcomb's problem is viewed as a dynamic game with an agent and a superior being as players. Depending on whether or not a risk-neutral agent's belief about the move order exceeds a threshold, one obtains the one-box outcome or the two-box outcome, respectively. The findings are extended to an agent with arbitrary increasing utility, featuring in general two thresholds. All solutions require only minimal assumptions about the being's payoffs and the being is always sure to predict the agent's choice in equilibrium. All Nash equilibria are subgame-perfect except for risk-seeking agents where for intermediate beliefs the being may be unable to ensure perfect prediction without relying on noncredible threats. Lastly, analogies of Newcomb's problem to the commitment problem on a continuum are discussed