Editing Newcomb's paradox (section)

==Game-theory strategies==
In his 1969 article, Nozick noted that "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."<ref name="Wolpert" /> The problem continues to divide philosophers today.<ref>{{cite news |last1=Bellos |first1=Alex |title=Newcomb's problem divides philosophers. Which side are you on? |url=https://www.theguardian.com/science/alexs-adventures-in-numberland/2016/nov/28/newcombs-problem-divides-philosophers-which-side-are-you-on |access-date=13 April 2018 |work=The Guardian |date=28 November 2016 |language=en}}</ref><ref>Bourget, D., Chalmers, D. J. (2014). "What do philosophers believe?" Philosophical Studies, 170(3), 465–500.</ref> In a 2020 survey, a modest plurality of professional philosophers chose to take both boxes (39.0% versus 31.2%).<ref>{{cite web | url=https://survey2020.philpeople.org/survey/results/4886 | title=PhilPapers Survey 2020 }}</ref>

[[Game theory]] offers two strategies for this game that rely on different principles: the [[expected utility hypothesis|expected utility]] principle and the [[strategic dominance]] principle. The problem is considered a paradox because two seemingly logical analyses yield conflicting answers regarding which choice maximizes the player's payout.
* Considering the expected utility when the probability of the predictor being right is certain or near-certain, the player should choose box B. This choice statistically maximizes the player's winnings, resulting in approximately $1,000,000 per game.
* Under the dominance principle, the player should choose the strategy that is ''always'' better; choosing both boxes A and B will ''always'' yield $1,000 more than only choosing B. However, the expected utility of "always $1,000 more than B" depends on the statistical payout of the game; when the predictor's prediction is almost certain or certain, choosing both A and B sets player's winnings at $1,000 per game.

[[David Wolpert]] and [[Gregory Benford]] point out that paradoxes arise when not all relevant details of a problem are specified, and there is more than one "intuitively obvious" way to fill in those missing details. They suggest that, in Newcomb's paradox, the debate over which strategy is 'obviously correct' stems from the fact that interpreting the problem details differently can lead to two distinct noncooperative games. Each strategy is optimal for one interpretation of the game but not the other. They then derive the optimal strategies for both of the games, which turn out to be independent of the predictor's infallibility, questions of [[causality]], determinism, and free will.<ref name="Wolpert" />