Abstract
A Robust Resolution of Newcomb's Paradox
Highlights
Suppose a “superior being” claims to be able to predict an agent’s action and, conditional on this prediction, influence his payoffs in a simple game of choice
For Newcomb’s problem, we show that because of rational expectations the probability of the being’s making correct predictions is endogenously determined in equilibrium and must be 100 %, provided
We show that the existence of a subgame-perfect Nash equilibrium with perfect prediction, where x1(p) =
Summary
Suppose a “superior being” claims to be able to predict an agent’s action and, conditional on this prediction, influence his payoffs in a simple game of choice. Newcomb in 1960 (Gardner 1973) and published by Nozick (1969), is referred to as Newcomb’s paradox because for both of the agent’s feasible actions a priori reasonable justifications have been advanced (see Gardner 1974) Taking both boxes (the “two-box strategy”) seems plausible because of the following dominance argument: no matter what box II contains, adding the reward of box I increases the agent’s payoff. If the belief p belongs to the agent’s private information, the being can devise a mechanism that leads to full information revelation, guarantees perfect prediction, and implements the (first-best) one-box strategy, given the two additional assumptions that the agent’s belief is always strictly positive and that the agent believes the being may be able to inflict a negative payoff to discourage deviations which never occur in equilibrium. Faced with a risk-seeking agent of intermediate belief, the being cannot maintain a zero prediction error in equilibrium without relying on noncredible threats
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