Newcomb's Problem

1. Introduction

Newcomb’s Problem is a thought experiment in decision theory that appears to pit two widely accepted patterns of reasoning against each other. It presents a simple choice between taking one box or two boxes, under conditions where a highly reliable predictor has already anticipated what the agent will do and has set the payoffs accordingly. The puzzle is frequently described as a paradox, because seemingly orthodox principles can be marshalled to defend both incompatible options.

At its core, the problem is used to probe what it is for an action to be rational in circumstances where an agent’s choice is tightly correlated with events that lie in the past or are otherwise beyond the agent’s causal control. It thereby functions as a test case for rival theories of rational choice, especially Evidential Decision Theory (EDT) and Causal Decision Theory (CDT), as well as for more recent policy-based and functional approaches.

In philosophical practice, Newcomb’s Problem is typically employed as an intuition pump: a structured scenario designed to elicit and challenge intuitive judgments about what one should do. These judgments are then used to motivate or criticize formal decision rules, assumptions about causation and correlation, and conceptions of free will and predictability.

The problem has become a standard example in discussions of:

• How to incorporate predictive information into rational choice
• Whether rational agents should follow dominance reasoning or expected utility when the two seem to diverge
• How to model choices in the presence of extremely accurate predictors

Because no consensus has emerged about the “correct” response, Newcomb’s Problem continues to serve as a central reference point in contemporary debates about rationality and decision-making.

2. Origin and Attribution

The puzzle is named after William Newcomb, a physicist at the Lawrence Livermore Laboratory, who first proposed the problem informally in the 1960s. Newcomb did not publish a formal presentation, and surviving accounts of his original formulation derive from recollections and secondary reports rather than a canonical text.

The problem entered the philosophical literature primarily through Robert Nozick, who presented and analyzed it in:

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“Newcomb’s Problem and Two Principles of Choice,”
in Essays in Honor of Carl G. Hempel (1969 draft; 1970 publication; reprinted in Essays in Philosophical Explanation, 1974)

Nozick credits Newcomb explicitly and emphasizes that the scenario had circulated within scientific and philosophical circles before appearing in print.

Key attributions and milestones can be summarized as follows:

Subsequent authors, such as David Lewis, Allan Gibbard, William L. Harper, and Richard Jeffrey, developed formal treatments that anchored the problem within precise frameworks of evidential and causal decision theories. While Newcomb is generally acknowledged as the originator of the intuitive setup, Nozick is widely regarded as the figure who fixed the standard formulation and framed its central philosophical significance.

3. Historical and Intellectual Context

Newcomb’s Problem emerged during a period in which formal decision theory, Bayesian probability, and game theory were being actively refined and integrated into analytic philosophy. The late 1950s and 1960s saw influential work on expected utility, subjective probability, and rational choice, including developments by Leonard Savage, Frank Ramsey, and others. Philosophers and economists were increasingly interested in using formal models to capture everyday and scientific reasoning about uncertain outcomes.

Within this context, several intellectual currents set the stage for Newcomb’s Problem:

The problem also coincided with heightened interest in the philosophy of science, particularly in understanding prediction and explanation in physics. Newcomb, working in a scientific environment, proposed a scenario involving an almost infallible predictor, which resonated with debates about what highly accurate prediction would imply for human freedom and responsibility.

When Nozick introduced the problem, analytic philosophy was receptive to thought experiments that could expose tensions between intuitive judgments and formal principles. Newcomb’s Problem quickly became entangled with broader discussions about:

• Whether rationality is fundamentally about maximizing expected utility given one’s evidence
• Whether rationality must respect causal structure and temporal order
• How to reconcile subjective choice with objective laws and regularities

Thus, the problem is best understood as arising at the crossroads of formal decision theory, metaphysical worries about determinism, and a broader methodological reliance on thought experiments to clarify concepts of rational action.

4. The Argument Stated

Newcomb’s Problem presents an argument that appears to yield two incompatible prescriptions for what a rational agent should do. The scenario can be expressed in a compact decision-theoretic form.

4.1 Basic Setup

• There are two boxes: A (transparent, containing $1,000) and B (opaque, containing either $1,000,000 or $0).
• A highly reliable predictor has already predicted whether the agent will:
  1. Take only box B (one-boxing), or
  2. Take both boxes A and B (two-boxing).
• If the predictor predicted one-boxing, it placed $1,000,000 in B; if it predicted two-boxing, it left B empty.
• The prediction and box-filling are completed before the agent chooses, and the agent knows all these facts and the predictor’s strong track record.

4.2 Two Lines of Reasoning

From this setup, two seemingly sound lines of reasoning emerge:

1. Dominance-style reasoning:
   Holding the contents of the boxes fixed, two-boxing yields $1,000 more than one-boxing in each possible case:

   • If B is empty, two-boxing yields $1,000 vs. $0.
   • If B is full, two-boxing yields $1,001,000 vs. $1,000,000.
     By the Dominance Principle, two-boxing appears rational.

2. Expected-utility / evidential reasoning:
   Given the predictor’s reliability, choosing one-box is very strong evidence that B is full, while choosing two-box is strong evidence that B is empty. Calculating expected payoffs conditional on each act appears to favor one-boxing, often by a wide margin.

4.3 Structural Tension

The argument thus has the following schematic structure:

The puzzle lies in reconciling or adjudicating between these lines of reasoning without discarding seemingly plausible principles of rational choice.

5. Detailed Scenario and Variants

5.1 Canonical Scenario

The canonical version of Newcomb’s Problem specifies:

• Box A: Transparent, visibly containing $1,000.
• Box B: Opaque, containing $1,000,000 if the predictor predicted one-boxing, and $0 otherwise.
• Predictor reliability: Often stipulated as nearly perfect (e.g., 99.9% or higher), sometimes idealized as infallible.
• Temporal order: The predictor makes its prediction and fills the boxes before the agent sees them and chooses.
• Knowledge conditions: The agent knows the rules, the predictor’s reliability, and that the contents of the boxes are already fixed at decision time.

5.2 Payoff and Reliability Variants

Philosophers have explored how altering monetary amounts or reliability affects intuitions:

Some argue that lowering predictor reliability makes the case less paradoxical, as expected-utility calculations become less extreme, potentially softening the conflict between dominance and evidential reasoning.

5.3 Predictive Mechanism Variants

The scenario is also varied by changing how the predictor operates:

• Physical simulation: The predictor has a perfect model of the agent’s brain.
• Statistical prediction: The predictor has extensive data on similar agents.
• Deterministic lawlike prediction: The predictor uses fundamental physical laws.

These details influence discussions about causation and free will, but the standard puzzle typically abstracts away from the specific mechanism, focusing only on very high reliability.

5.4 Structural and Narrative Variants

More elaborate variants preserve the essential structure—choice plus prediction—while altering presentation:

• “Newcomb with a twist” cases introduce additional options or side bets.
• Multiple-player versions model many agents facing the same predictor.
• Iterated versions repeat the game, raising issues about learning and strategy over time.

Despite these modifications, variants retain the core feature: an agent’s current act is strongly correlated with a past prediction that set payoffs, thereby generating the tension in rational choice.

6. Logical and Decision-Theoretic Structure

Newcomb’s Problem is frequently formalized using the tools of choice theory and probability theory, in order to clarify exactly where competing analyses diverge.

6.1 States, Acts, and Outcomes

A typical representation specifies:

• States of the world:

  • S₁: Predictor predicted one-boxing and placed $1,000,000 in B.
  • S₂: Predictor predicted two-boxing and left B empty.

• Acts:

  • O: One-box (take only B).
  • T: Two-box (take A and B).

• Outcomes (utility in dollars, ignoring risk attitudes):

6.2 Probability Assignments

The key structural feature is that the probabilities of states are not independent of the act, at least from the agent’s evidential perspective. Informally:

• ( P(S₁ \mid O) ) is very high (if you one-box, that is excellent evidence the predictor predicted one-boxing).
• ( P(S₁ \mid T) ) is very low (if you two-box, that is strong evidence the predictor predicted two-boxing).

Decision theories differ in whether they use:

• Conditional probabilities (P(S_i \mid \text{Act})) (EDT-style), or
• Counterfactual probabilities (P(S_i \Box!!\rightarrow \text{Act})) (CDT-style), where the latter treat the predictor’s past action as fixed across alternatives.

6.3 Dominance and Expected Utility

On a standard, act-independent state space, dominance is defined purely in terms of outcome comparisons across states. In Newcomb’s Problem, the payoff table appears to show T (two-boxing) weakly dominating O (one-boxing) if one treats the states as fixed and independent of the act.

By contrast, expected utility is computed by weighting payoffs by probabilities, but here there is a choice between:

• Treating probabilities as evidentially conditioned on acts, or
• Treating probabilities as reflecting causal counterfactuals.

This generates two different expected-utility calculations, corresponding to the evidential and causal perspectives, and yields the formal underpinning for the conflicting recommendations.

7. Evidential vs Causal Decision Theory

Newcomb’s Problem is often used as a canonical illustration of the contrast between Evidential Decision Theory (EDT) and Causal Decision Theory (CDT).

7.1 Evidential Decision Theory (EDT)

EDT evaluates actions by considering them as evidence about which state of the world obtains and then maximizing expected utility conditional on the action. Formally, for each act (A), EDT computes:

[ EU_{EDT}(A) = \sum_i P(S_i \mid A) \cdot U(\text{Outcome}(A, S_i)). ]

Applied to Newcomb’s Problem, EDT typically takes:

• (P(S₁ \mid O)) (predictor predicted one-box) to be very high,
• (P(S₁ \mid T)) (predictor predicted one-box) to be very low.

Because the payoff in S₁ is much greater than in S₂, EDT computations generally favor one-boxing. Proponents argue that it is rational to choose the act that is good news about what has already been done by the predictor.

7.2 Causal Decision Theory (CDT)

CDT evaluates actions by their causal consequences, using counterfactuals or causal models. For each act (A), CDT evaluates:

[ EU_{CDT}(A) = \sum_i P(S_i) \cdot U(\text{Outcome}(A \Box!!\rightarrow S_i)), ]

where the probabilities (P(S_i)) concern how likely each state is, holding fixed that the act was different. CDT typically represents the predictor’s past action as causally independent of the present choice, so that the distribution over states does not change across acts.

Under this representation, CDT finds that two-boxing yields at least $1,000 more than one-boxing in each state, so it recommends two-boxing.

7.3 Comparison in the Newcomb Setting

A schematic comparison is:

Newcomb’s Problem thus functions as a test case where EDT and CDT appear to generate conflicting verdicts, raising questions about which notion of expected utility is appropriate for rational action in predictive contexts.

8. Premises and Key Assumptions Examined

Philosophical discussions of Newcomb’s Problem frequently turn on scrutinizing its underlying assumptions. Different interpretations and responses often arise from differing views about how these assumptions should be understood.

8.1 Predictor Reliability

A central premise is that the predictor is extremely reliable. Some formulations treat the predictor as nearly infallible; others assign a very high but imperfect reliability. This raises several questions:

• Is such reliability empirically or conceptually plausible?
• Does assuming near-infallibility commit one to strong forms of determinism?
• Does the argument remain compelling if reliability is lowered, and if so, to what threshold?

Critics sometimes maintain that intuitions about rational choice are distorted by what they regard as an unrealistic or incoherent idealization of prediction.

8.2 Independence and Causal Structure

Another key assumption concerns the causal independence of the agent’s choice from the predictor’s earlier action. Many formulations stipulate that:

• The predictor has already acted.
• The contents of the boxes are now fixed and cannot be changed.

This appears to preclude any direct causal influence from choice to box contents. However, the strong correlation between choice and contents (via prediction) suggests that the agent’s act is nonetheless highly informative about the boxes. Debates focus on whether this is:

• A purely evidential link, or
• A symptom of a deeper causal or lawlike connection.

8.3 Knowledge and Common Knowledge

The argument presupposes that:

• The agent knows the rules and the predictor’s track record.
• The agent trusts the relevant background information.

Some discussions explore whether:

• Mistrust or uncertainty about the setup would rationalize two-boxing even for EDT.
• Perfect common knowledge of the setup is coherent or necessary for the paradox.

8.4 Representation of States

A more technical assumption concerns how states of the world are carved up:

• Does the state space include the agent’s decision?
• Are states defined prior to choice, or do they incorporate the agent’s policy?

Different resolutions sometimes rely on modifying the state–act–outcome framework, arguing either that traditional state descriptions are misleading here or that the paradox depends on a problematic representation of the decision situation.

9. Dominance Reasoning and the Case for Two-Boxing

Dominance reasoning is one of the main supports for two-boxing in Newcomb’s Problem. The basic idea is that one course of action is never worse and sometimes better than another across all relevant states.

9.1 The Dominance Argument

Using the standard payoff matrix and treating the contents of the boxes as fixed at decision time:

On this representation:

• In the “B full” state, T yields $1,001,000 vs. O’s $1,000,000.
• In the “B empty” state, T yields $1,000 vs. O’s $0.

Thus, T weakly dominates O. The Dominance Principle states that if one act yields at least as much utility in every possible state and strictly more in at least one, then rationality requires choosing that act. Under this framing, two-boxing appears to be the only rational option.

9.2 Justifications for Dominance

Proponents argue that:

• Dominance reasoning is local: it compares outcomes state by state, without requiring controversial probabilistic or causal assumptions.
• It seems to capture an intuitive idea: choosing an act that is worse in some possible case and no better in any case seems irrational.
• Many standard decision problems (e.g., money pumps, Dutch books) are resolved by eliminating dominated strategies.

Applied to Newcomb’s Problem, dominance advocates maintain that, because the prediction and box-filling are already completed, the agent cannot causally affect the state they are in. The only remaining question is which act yields the higher payoff given that fixed state.

9.3 Critiques of Dominance in This Context

Critics contend that dominance reasoning may be misapplied here because the states are not independent of the act in the evidential or lawlike sense. They argue that adopting a policy of two-boxing changes the probability distribution over states in a way that is not captured by the simple dominance comparison. Nonetheless, defenders of two-boxing typically hold that the dominance principle, interpreted causally, accurately reflects what rational choice should be when past events are beyond one’s control.

10. Expected Utility Reasoning and the Case for One-Boxing

The main argument for one-boxing is grounded in expected utility (EU) reasoning that treats the agent’s action as highly informative about what the predictor has already done.

10.1 Conditional Expected Utilities

If the predictor’s reliability is extremely high, one can assign probabilities such that:

• (P(\text{B full} \mid \text{one-box}) \approx 0.99) or higher,
• (P(\text{B full} \mid \text{two-box}) \approx 0.01) or lower.

Using these conditional probabilities, the expected utilities (in dollars) are:

[ EU(\text{one-box}) \approx 0.99 \cdot 1{,}000{,}000 + 0.01 \cdot 0 \approx 990{,}000 ]

[ EU(\text{two-box}) \approx 0.01 \cdot 1{,}001{,}000 + 0.99 \cdot 1{,}000 \approx 11{,}010 + 990 \approx 12{,}000 ]

On these numbers, one-boxing yields a dramatically higher expected payoff.

10.2 Evidential Justification

Proponents argue that rational agents should maximize expected utility relative to their beliefs. Since the action of one-boxing is extremely strong evidence that the predictor predicted one-boxing and filled B, it is rational to choose the action that, by one’s own lights, is correlated with the better outcome. On this view:

• Actions should be evaluated as information-bearing events.
• Ignoring such powerful evidence because it is not causally downstream of the act is said to violate Bayesian rationality, which emphasizes coherent updating on all relevant information.

10.3 Robustness and Variants

Supporters of the one-boxing argument often note that:

• As long as the predictor is more likely than not to be correct, expected-utility calculations can favor one-boxing for sufficiently large stakes in B relative to A.
• Varying payoffs and reliabilities shows how the expected-utility advantage of one-boxing depends on these parameters, but for standard values (e.g., $1,000 vs $1,000,000 and very high reliability), one-boxing is clearly favored in EU terms.

Thus, the expected utility case for one-boxing rests on treating the act as a reliable indicator of the already-determined state of the world, and then choosing the act that is, from the agent’s perspective, associated with the better-prospect world.

11. Alternative Decision Theories and Policy-Based Approaches

Beyond EDT and CDT, several alternative frameworks have been proposed to address Newcomb’s Problem and similar cases.

11.1 Functional Decision Theory (FDT) and Related Views

Functional Decision Theory (FDT) and closely related ideas (e.g., Timeless Decision Theory) evaluate acts by considering the output of the decision function implemented by the agent. The guiding idea is:

• If the predictor bases its actions on a simulation or model of the agent’s decision procedure, then the predictor’s action and the agent’s choice are logically correlated.
• The correct question is: “Which decision function, if implemented in me (and predicted by the predictor), would lead to the best overall outcomes?”

In Newcomb’s Problem, FDT-style agents tend to:

• Choose to be the kind of agent who one-boxes, because predictors will then have filled B.
• Emphasize policy or function selection rather than one-off causal influence.

11.2 Policy-Based and Updateless Approaches

Policy-based decision theories recommend choosing a policy for types of situations, rather than a single act for the specific information set one is in. Updateless Decision Theory (UDT) is an example, where agents:

• Select a policy before receiving detailed observational data.
• Commit to follow that policy even after they learn specific information.

In Newcomb-like setups, policy-based agents typically endorse being predictably one-boxing, because such a policy induces predictors to place the million in B.

11.3 Coordination and Multi-Agent Analogues

Some theorists frame Newcomb’s Problem as analogous to a coordination or precommitment problem:

• Agents are, in effect, “coordinating” with their own predicted behavior.
• Policy-based frameworks capture the benefits of credibly committing to patterns of action that others (or predictors) will anticipate.

11.4 Summary Comparison

These alternative theories aim to preserve some causal intuitions while explaining why being predictably one-boxing might be rational when powerful predictors or logical correlations are present.

12. Standard Objections and Replies

Debate over Newcomb’s Problem has generated a range of objections, along with corresponding responses. Several have become standard in the literature.

12.1 Objection: The Predictor Is Impossible or Incoherent

Some critics challenge the coherence of near-infallible prediction of human choices, especially in contexts where agents are fully informed about the prediction setup. They argue that this appears to conflict with:

• Free will or the ability to choose otherwise.
• The possibility of agents deliberately acting contrary to predicted behavior.

Replies often suggest that:

• The scenario can be interpreted as idealized but coherent, similar to frictionless planes in physics.
• Deterministic or highly lawlike universes may allow extremely reliable prediction without contradiction.
• Even if perfect prediction is impossible, high reliability suffices to make the puzzle philosophically interesting.

12.2 Objection: Dominance Should Clearly Decide the Case

Another objection maintains that the dominance principle is obviously correct and that any reasoning that violates it must be flawed. From this standpoint:

• Two-boxing strictly dominates one-boxing, given fixed box contents.
• One-boxing is said to confuse correlation with causation.

Replies from evidential and alternative theorists counter that:

• The apparent dominance depends on a state specification that hides important probabilistic or logical dependencies.
• When those dependencies are recognized, dominance is either inapplicable or must be reformulated to account for them.

12.3 Objection: Expected Utility Maximization Has Been Misapplied

Critics of one-boxing sometimes argue that expected utility has been misused:

• They contend that EU theory should be applied to causal consequences of actions, not to merely evidential correlations.
• Under a causal interpretation, they maintain, two-boxing maximizes expected utility.

Defenders of EDF-style reasoning respond that:

• Bayesian decision theory, as traditionally formulated, uses conditional probabilities given acts, not explicitly causal probabilities.
• Ignoring the predictive information embedded in one’s own choice seems to leave valuable evidence unused.

12.4 Objection: The Problem Is a Framing Illusion

Some philosophers suggest that the paradox arises from ambiguous framing:

• The description simultaneously encourages thinking of choice as causally efficacious (via prediction) and as causally inert (box contents fixed).
• Once the causal structure is properly represented—e.g., in a causal decision graph or influence diagram—the conflict between principles may disappear.

Replies vary. Some accept the deflationary view, taking Newcomb’s Problem as illustrating the importance of explicit causal modeling. Others maintain that even with careful modeling, there remains a substantive question about how rationality should treat predictive correlations that are not straightforwardly causal.

13. Connections to Free Will, Prediction, and Causation

Newcomb’s Problem intersects with classic philosophical debates about free will, predictability, and causation, because it depicts agents whose choices are strongly anticipated by a highly reliable predictor.

13.1 Free Will and Determinism

The scenario raises questions such as:

• If an agent’s choice can be accurately predicted in advance, does the agent still have genuine alternatives?
• Is the agent morally responsible for a choice that was highly predictable, or even determined, by prior conditions?

Compatibilists may view reliable prediction as compatible with free choice, whereas incompatibilists may see the setup as undermining genuine freedom. Newcomb’s Problem thus provides a concrete, decision-theoretic context in which to examine abstract debates about determinism and autonomy.

13.2 Nature of Prediction

The problem highlights different conceptions of what prediction involves:

• Physical or computational prediction (e.g., brain simulations).
• Statistical prediction based on extensive data and regularities.
• Lawlike determination, in which the future is fixed by prior states and laws.

How one interprets the predictor can influence whether the correlation between choice and box contents is seen as causal, merely evidential, or logically necessary.

13.3 Causation and Temporal Asymmetry

Newcomb’s Problem confronts standard intuitions about causal direction:

• The agent’s choice happens after the predictor’s action.
• Nevertheless, the choice is strongly associated with what the predictor has already done.

This leads to questions about:

• Whether rational choice should care only about forward-looking causal influence, as CDT suggests.
• Whether backward-looking correlations can matter for rational deliberation.
• How to represent temporal asymmetries in causal and decision-theoretic models.

Some proposals regard the agent’s decision as part of a larger causal or logical structure in which the predictor’s action and the agent’s choice are jointly determined by underlying factors, blurring the simple picture of unilateral causal influence from past to future.

14. Applications in Economics, AI, and Rationality Debates

Beyond its role in philosophy, Newcomb’s Problem has been used as a conceptual tool in several applied domains.

14.1 Economics and Rational Choice Theory

In economics, the puzzle has been used to:

• Illustrate tensions between dominance and expected utility principles.
• Discuss dynamic consistency and the role of commitment in strategic interactions.
• Explore how agents should respond when other actors (e.g., markets, regulators) can anticipate their behavior.

While not a standard economic model, Newcomb-like reasoning appears in discussions of reputation, time inconsistency, and credible commitment.

14.2 Artificial Intelligence and AI Safety

In artificial intelligence, Newcomb’s Problem is prominent in debates about agent design and alignment:

• When AI systems interact with other agents or predictors (including humans), their decisions may be anticipated and planned around.
• Designers must decide whether AI agents should follow causal, evidential, or policy-based decision rules in settings with powerful predictors or simulators.

Newcomb-like scenarios are particularly salient in AI safety and multi-agent contexts, where the behavior of one system may be modeled or simulated by another. Some AI researchers use these thought experiments to argue for non-standard decision theories (e.g., FDT, UDT) for advanced agents.

14.3 Rationality and Human Decision-Making

In broader rationality debates, the problem is invoked to:

• Test intuitive judgments about rational choice under prediction.
• Examine whether standard norms of rationality should be context-sensitive to the presence of predictors.
• Study disagreement among agents about what is rational, given shared information.

Psychologists and behavioral economists sometimes use Newcomb-type scenarios to investigate how people reason about correlation vs causation, though empirical work typically uses simplified or approximate versions of the setup.

Overall, Newcomb’s Problem provides a stylized framework for analyzing situations where being predictable has strategic implications, making it relevant to theoretical and applied work in multiple disciplines.

15. Legacy and Historical Significance

Since its introduction in the late 1960s, Newcomb’s Problem has become a standard tool in the philosophical and decision-theoretic canon.

15.1 Influence on Decision Theory

The puzzle has played a significant role in:

• Motivating the explicit distinction between Evidential Decision Theory and Causal Decision Theory.
• Inspiring the development of alternative decision theories—including policy-based and functional approaches—designed to handle predictive and correlated decision problems.
• Encouraging formal treatments of causal structure in decision models, using tools such as causal graphs and counterfactual semantics.

Work by David Lewis, Allan Gibbard, William L. Harper, Richard Jeffrey, James Joyce, Brian Skyrms, Hilary Greaves, and others has used Newcomb’s Problem as a central test case.

15.2 Role in Philosophical Methodology

Newcomb’s Problem exemplifies the use of thought experiments to probe foundational concepts:

• It shows how apparently plausible principles can conflict in carefully constructed cases.
• It has been used in teaching and research to illustrate the importance of precise modeling of information, causation, and rationality.

The problem is frequently cited in textbooks and reference works, including the Stanford Encyclopedia of Philosophy, as a paradigm of a decision-theoretic paradox.

15.3 Continuing Debates

Despite decades of analysis, no universally accepted resolution has emerged. The problem continues to:

• Generate new proposals for decision theories and modeling techniques.
• Serve as a touchstone in debates about free will, determinism, and predictability.
• Inform discussions in AI and economics about how to think of rational action under sophisticated forms of forecasting and simulation.

In this way, Newcomb’s Problem has secured a lasting place in the history of philosophy and decision theory as a case that continually challenges and refines conceptions of rational choice.