According to some views of reality, some objects are fundamental and other objects depend for their existence upon these fundamental objects. In this article, I argue that we have reason to reject these views.

Philosophy and Phenomenological Research, Volume 104, Issue 2, Page 505-510, March 2022.

This paper introduces a new equilibrium concept for normal form games called dependency equilibrium; it is defined, exemplified, and compared with Nash and correlated equilibria in Sections 2–4. Its philosophical motive is to rationalize cooperation in the one shot prisoners' dilemma. A brief discussion of its meaningfulness in Section 5 concludes the paper. †To contact the author, please write to: Department of Philosophy, University of Konstanz, 78457 Konstanz, Germany; e-mail: [email protected].

I present a game-theoretic way to understand the situation describing Newcomb’s Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoners Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a one-shot (...) game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick’s set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible – depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor’s accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena. (shrink)

Newcomb's problem supposedly involves your choosing one or else two boxes in circumstances in which a predictor has made a prediction of how many boxes you will choose. We argue that the circumstances which allegedly define Newcomb's problem generate a previously unnoticed regress which shows that Newcomb's problem is insoluble because it is ill-formed. Those who favor, as we do, a ``no-box'' reply to Newcomb's problem typically claim either that the problem's solution is underdetermined or else that it is overdetermined. (...) We are no-boxers of the first kind, but the underdetermination we identify is more radical than any previously identified: it blocks the very set-up of the problem and not just potential solutions to the problem once it has been set up. The defect is subtle, but it cripples every genuine version of the problem, regardless of variations in such things as the predictor's degree of reliability, the basis on which the prediction is made, or the amount of money in each box. The regress shows that, surprisingly enough, no one can understand Newcomb's problem, and so no one can possibly solve it. (shrink)

This paper reviews six attempts to give cooperative solutions to Prisoners Dilemmas: symmetry (agents are in identical situations, so should choose the same way, so should both choose cooperation because that’s better for each), mechanism (each agent should delegate the decision to a machine which will choose cooperation for them provided the other does likewise), inducement (the agents should make a side bet which pays off only upon both cooperating), resolution (each agent should resolve to cooperate, then act on the (...) resolution), alternative principle (rationality requires not dominance reasoning and so defecting, but constrained maximization or resolution compliance or “sophisticated” choosing, and so cooperation), and preference revision (each agent should acquire conditional preferences to cooperate, then cooperate provided the other agent has acquired similar preferences). It distinguishes one-stage from two-stage games, as well as endogenously available solutions (ones available to agents in the circumstances of the game merely due to the nature of rationality) from solutions requiring exogenous devices. It contrasts Edward McClennen’s endogenous solution, which is some combination of resolution and alternative principle solution, with David Gauthier’s endogenous alternative principle solution. It argues that all have problems, ones best solved by the endogenous preference revision solution defended by Duncan MacIntosh. (shrink)

Several recent commentators have suggested that for fully rational agents who find themselves in iterated prisoner's dilemmas of indefinite length, co-operation is the rational strategy. Their argument is that these fully rational agents can be taught, through the co-operative actions of other agents, to bypass the dominant move of noncooperation and co-operate instead. The proponents of the “teaching strategy” seem to have ignored the compelling argument of Jordan Howard Sobel. While the teaching argument may work for agents who are less (...) than purely rational, Sobel has pointed out that hyperrational utility maximizers cannot be taught; they reason deductively, not inductively, as the “teaching argument” requires. (shrink)

According to David Lewis, the prisoner's dilemma (PD) and Newcomb's problem (NP) are really just one dilemma in two different forms (Lewis 1979). Lewis's argument for this conclusion is ingenious and has been widely accepted. However, it is flawed. As this paper shows, the considerations that Lewis brings to bear to show that the game he starts with is an NP equally show that the game is not a PD.

The paper is essentially a short version Spohn "Strategic Rationality" which emphasizes in particular how the ideas developed there may be used to shed new light on the iterated prisoner's dilemma (and on iterated Newcomb's problem).

The paper attempts to rationalize cooperation in the one-shot prisoners' dilemma (PD). It starts by introducing (and preliminarily investigating) a new kind of equilibrium (differing from Aumann's correlated equilibria) according to which the players' actions may be correlated (sect. 2). In PD the Pareto-optimal among these equilibria is joint cooperation. Since these equilibria seem to contradict causal preconceptions, the paper continues with a standard analysis of the causal structure of decision situations (sect. 3). The analysis then raises to a reflexive (...) point of view according to which the agent integrates his own present and future decision situations into the causal picture of his situation (sect. 4). This reflexive structure is first applied to the toxin puzzle and then to Newcomb's problem, showing a way to rationalize drinking the toxin and taking only one box with-out assuming causal mystery (sect. 5). The latter result is finally extended to a rationalization of cooperation in PD (sect. 6). (shrink)

The paper argues that the standard decision theoretic account of strategies and their rationality or optimality is much too narrow, that strategies should rather condition future action to future decision situations (a point of view already developed in my Grundlagen der Entscheidungstheorie, sect. 4.4), that practical deliberation must therefore essentially rely on a relation of superiority and inferiority between possible future decision situations, that all this allows to substantially broaden the theory of practical rationality, that a long list of points (...) attended to in the literature can be subsumed under the broadened perspective (including a novel view on the iterated prisoner's dilemma and on iterated Newcomb's problem, which, however, is revised in Spohn (2003) "Dependency Equilibria and the Causal Structure of Decision and Game Situation"), and that the task to complete and systematize this list indeed forms a fruitful research programme. (shrink)