Coordination without meta-representation

ABSTRACT

Meta-representation does not always facilitate social interaction. We illustrate this claim focusing on the case of coordination, and conjecture that people coordinate using a mode of reasoning that does not require the representation of others’ beliefs. We compare this sort of belief-less reasoning with theories that appeal to limited meta-representation, and present evidence indicating that people employ both – with meta-representation being used less frequently in coordinative than in competitive tasks.

KEYWORDS:

• Coordination
• meta-representation
• Hi-lo
• team reasoning
• Level-k theory

Acknowledgments

This research was realized at the PhiLab and 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). We are grateful to various referees and to seminar participants at the University of Warwick for their comments on a previous version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed here

Notes

1. Sellars (1956), Davidson (1963), Dennett (1971), Churchland (1981), and Fodor (1987), and Lewis (1994) are among the philosophers who have held this view.

2. See e.g., Davidson (1980), Lewis (1974), Pettit (1991), and Rosenberg (1992).

3. To say something is, of course, one form of action.

4. Many scholars, moreover, have argued that the first step to solve a problem of free riding – such as the prisoner’s dilemma – is to turn it into a coordination game (see e.g., Binmore, 2005; Bicchieri, 2006; as well as Peterson, 2015 for a recent overview). If they are right, problems of coordination must play a pivotal role in any general theory of human sociality.

5. For experimental corroboration of Schelling’s insight, see e.g., Bardsl Bardsley et al. (2010), Isoni et al. (2014).

6. Discussions of Hi-lo can be found in Schelling (1960), Hodgson (1967), and Gauthier (1975). The contemporary debate owes a lot to Bacharach’s (2006) detailed analysis.

7. An equilibrium, in the jargon of game theory, is a profile of actions (one for each player) that are best-responses to each another. Another way to put it is that in equilibrium no one has an incentive to change her action unilaterally. For simplicity we will ignore randomized behavior and focus on equilibria in ‘pure’ strategies.

8. For an insightful discussion of implicit vs. explicit interpretations of folk psychology, see Bermùdez (2005).

9. According to an influential line of research, the main function of belief-desire attribution is not to predict or explain behavior at all. Its main function is to justify behavior, by reconstructing agents’ reasons for doing what they did. This insight can be traced back to Bruner (1990), and has been recently developed by McGeer (1996, 2007), Hutto (2008), Zawidzki (2008, 2013), Andrews (2012, 2015), among others.

10. Gergely and Csibra distinguish goals (states of the world that are caused by behavior) from desires and intentions (mental states that cause behavior). If they are right, then teleological reasoning may be an entirely non-mentalistic process, which exploits purely behavioral patterns and does not involve the attribution of subjective mental states. This interpretation is currently controversial: some psychologists are willing to attribute mind-reading skills to infants before eighteen months and in some cases as early as six months of age (Baillargeon et al., 2016). In this case, it would be appropriate to speak of a ‘rationality principle’, rather than merely of an efficiency principle: predictions would be based on a capacity to identify goal representations rather than mere states of affairs.

11. There are subtle differences between Level-k and a ‘Cognitive Hierarchy’ theory (Camerer et al., 2004), which however do not matter for our purposes. For simplicity in this paper we will refer mainly to Level-k theory, although what we say can be generalized to Cognitive Hierarchy theory.

12. Sugden (1993, 2000, 2003), Bacharach (2006), Gold and Sugden (2007).

13. See also Guala (2018, 2020).

14. The experimental procedures described in this paper were approved by the Research Ethics Committee of the University of Milan on June 24th, 2019. The data that support the findings of this study are openly available in figshare at http://doi.org/10.6084/m9.figshare.14545995.

15. To check for possible unintended effects of the colors (Red in theory might be more salient than Blue, or vice versa) we switched them in half of the experimental sessions. The choice of colors does not make any difference statistically.

16. The subjects of course might have wondered whether the other knew what was going on, so a priori we cannot be certain that we have achieved full experimental control on subjects’ beliefs. When we asked about it in a post-experimental questionnaire, however, the majority of subjects said that they did not think that the other subject had been informed. Questionnaire data are summarized and discussed in Appendix B.

17. The principle of insufficient reason prescribes that, in the absence of relevant information, a rational agent should assign equal probabilities to the occurrence of mutually exclusive possible events.

18. An outcome is Pareto-efficient or Pareto-optimal if and only if no alternative outcome is available that would make at least one individual better off and no other individual worse off.

19. For the sake of clarity, we shall continue to use the label ‘Blue’ for the equilibrium and the label ‘Red’ for the disequilibrium strategy, even though in half of the experimental sessions the colors were switched for control purposes (see footnote 15 above).

20. The Level-k literature is not entirely consistent on this matter: in some papers L₀ players are modeled as behaving randomly, while in others as choosing the salient option (if there is one). In practice it does not make a difference when we analyze the Hi-lo game in Study 1, since L₁ would respond to L₀ by choosing H (Red) in any case. Lacking a uniform convention, here we stipulate that L₀ behaves randomly. The choices of players at L₂ and above are anchored by L₁.

21. As mentioned earlier, we cannot discriminate between L₂ and L₃ reasoners in the case of P_A, which might explain the apparent asymmetry between the two players.

22. The answers were coded independently by each experimenter. Controversial cases were adjudicated jointly, but amounted to less than 10% of the observations.

23. A few subjects wrote that they hadn’t considered this possibility, but now realized that the other player might have known about the payoff switch. We interpreted these answers as ‘No’, since we are ultimately interested in what the subjects thought at the moment of decision-making.

24. 26% of subjects completed the task wrongly and 12% did not complete the task.

25. This fact should not surprise anyone who has taught game theory in class.

26. We only had a small number of STEM students in our sample, however (15 out of 96).

Additional information

Funding

This work was supported by the Ministero dell’Istruzione, dell’Università e della Ricerca [Ministero dell’Istruzione, dell’Università e della Ricerca Dipartimenti di Eccellenza 2018-2022].

Notes on contributors

Camilla Colombo

Camilla Colombo is a post-doctoral fellow at Scuola IMT Alti Studi- Lucca, where she works on the project “From Models to Decisions”. She obtained her PhD in Philosophy at the London School of Economics in 2019, and her main research interests are the cognitive and theoretical foundations of decision theory, practical ethics and bioethics.

Francesco Guala

Francesco Guala is a philosopher and experimental economist interested primarily in the foundations and the methodology of social science. He is the author of many articles in scientific and philosophical journals, and of two monographs, The Methodology of Experimental Economics (Cambridge, 2005) and Understanding Institutions (Princeton, 2016).