Abstract
Can rational agents coordinate in simultaneous interactions? According to standard game theory they cannot, even if there is a uniquely best way of doing so. To solve this problem we propose an argument in favor of ‘belief-less reasoning’, a mode of inference that leads to converge on the optimal solution ignoring the beliefs of the other players. We argue that belief-less reasoning is supported by a commonsensical Principle of Relevant Information that every theory of rational decision must satisfy. We show that this principle can be used to justify (some versions of) team reasoning, as well as other schemes of practical reasoning that do not involve sophisticated meta-representation.
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Notes
Although we are assuming the impossibility of communication, sending messages would not change the strategic nature of the problem in a significant way unless it is supported by social norms that modify the payoffs of the game (classic statements of this view can be found in Lewis, 1969 and Aumann, 1990). Communication may of course be used to create a focal point, but the interpretation of the message would constitute a higher-order coordination game, and the equilibrium selection problem would remain intact from a purely logical point of view.
Hi-lo has been named differently by different authors. Early discussions can be found in Schelling (1960), Hodgson (1967) and Lewis (1969). The ‘Hi-lo’ label was introduced by Michael Bacharach, who is mostly responsible for the current revival of interest in this game (see in particular Bacharach 2006).
In a Nash equilibrium the strategy of each player is a best response to the strategy of every other player—or, equivalently, no player has a unilateral incentive to deviate. An outcome is Pareto optimal (or efficient) if and only if it is not (Pareto-)dominated by any other outcome, that is, if there is no other outcome that is better for some players and is not worse for any of them.
Harsanyi and Selten for example propose payoff dominance only as a temporary solution to the problem of equilibrium selection, until a more satisfactory one is found Harsanyi and Selten (1988: 357–9).
If some players have a ‘brute propensity’ to choose the obvious strategy (H, in this case), then any other player with slightly more sophisticated cognitive capacities has an incentive to converge on the Pareto-optimal outcome.
See the discussion in Browne (2018), who also criticizes Hurley’s attempt to use mind-reading as a regress stopper.
Another strategy is to argue that group identification is justified by normative considerations (such as commitments—cf. e.g. Gilbert 1990, Gauthier 2013). Units of agency, again, cannot be rationally chosen.
See Guala (2020).
It has been argued, in fact, that ‘team reasoning is simply a matter of using certain patterns of inference’ (Pacherie, 2013: 1834). Since we are not interested in exegetical issues we remain neutral on what counts as ‘genuine’ team reasoning, and highlight the similarities between argumentative patterns that display collectivistic and individualistic premises to various degrees.
Whether common knowledge of rationality holds in real-life situations is an issue that must be settled empirically, of course. But, to repeat, we are primarily interested in normative issues here.
For example: if Jack believes (mistakenly) that the quickest way to reach the top of the Empire State Building is to take the elevator, but the elevator is broken and he gets stuck for two hours, he cannot be accused of irrationality—he did what he had to do, given the available information.
Not even the prisoner’s dilemma: dilemmas of cooperation and mixed-motive games more generally, as we explain below, elicit conflicting intuitions that pull in opposite direction.
It may be argued that some famous attempts to justify cooperation in prisoner’s dilemma games are misapplications of belief-less reasoning (e.g. Davis, 1977). To make this point adequately, however, would require a separate paper.
This point can be generalized to other theories that have been proposed to explain cooperative behaviour: a pair of players may successfully cooperate if they care about equality or fairness for example (e.g. Bolton & Ockenfels 2000; Fehr & Schmidt 1999; Rabin 1993) or if they are sensitive to social norms (Bicchieri 2006). These approaches presuppose, as it is well known, the transformation of the prisoner’s dilemma into a Hi-lo type of game, and this transformation lies outside the realm of practical reasoning.
Although the mixed-strategy equilibrium is symmetric, it is not Pareto-dominant either (it is inferior to SS).
If there is some other non-equilibrium outcome that is also Pareto optimal, then a belief-less reasoner would be unable to identify the profile of strategies that is ‘best for me and for you’, as stated in premise 2* of the BR* scheme (Sect. 5). This is essentially the same issue that prevents its application to the game of Chicken. We are grateful to a referee for pointing this out.
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Acknowledgements
Versions of this paper have been presented at the universities of Firenze, Caserta, Leeds, San Raffaele, and at a conference of the Italian Society of Economists. We are grateful to the members of these audiences for their feedback, and especially to Bob Sugden, Natalie Gold, Luis Bermudez, Ivan Moscati, and various anonymous referees for detailed written comments. This research was funded by the Department of Philosophy “Piero Martinetti” of the University of Milan under the Project “Departments of Excellence 2018-2022” awarded by the Ministry of Education, University and Research (MIUR).
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Colombo, C., Guala, F. Rational Coordination Without Beliefs. Erkenn 88, 3163–3178 (2023). https://doi.org/10.1007/s10670-021-00496-5
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DOI: https://doi.org/10.1007/s10670-021-00496-5