Abstract
The paper begins by providing a game-theoretic reconstruction of Gilbert’s (1989) philosophical critique of Lewis (1969) on the role of salience in selecting conventions. Gilbert’s insight is reformulated thus: Nash equilibrium is insufficiently powerful as a solution concept to rationalize conventions for unboundedly rational agents if conventions are solutions to the kinds of games Lewis supposes. Both refinements to NE and appeals to bounded rationality can plug this gap, but lack generality. As Binmore (this issue) argues, evolutive game theory readily explains the origin of conventional behavior, but that is not Lewis’s project. Gilbert’s critique is generalized by reference to Bacharach’s (2006) work on team reasoning in games. The paper then argues that although Lewis’s account of the rationalization of conventions is shown by the reconstruction of Gilbert’s critique to be incomplete, Gilbert is wrong to conclude that classical (‘eductive’) game theory lacks the resources to explain conformity to conventions among people. A game-theoretic account of the dynamics of socialization, based on Ross’s (2005, 2006) idea of ‘game determination’, rationalizes choices of conventional strategies in overlapping generations contexts, provided agents are products of evolutionary selection and know that other players are also such products.
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Notes
It may be objected that the problem with SE reasoning identified above stems from a non-natural feature of deductive logic, that contradictions imply all propositions. This objection would be beside the point because SE reasoning is not a plausible model of strategic psychology; it’s offered as a solution to the logical problem with defining SPE given simultaneous moves.
Postema says this applies to Schelling’s account as well. I think this is mistaken. Schelling was ahead of his time, and couldn’t be expected to be clear with respect to Binmore’s distinction. I read him, along with the even greater genius Hume, as anticipating Binmore on this point. This is also Binmore’s reading.
It seems to me that in this case we would surely want to say, pace both Lewis and Gilbert (for different reasons), that i and j are operating a (foolish) convention—what else could explain their sub-optimal behavior?
As Dan Dennett would say.
Let me be clear about the scope of the ‘might’ here. Bacharach offers a selectionist account of the relevant framing effects, so it follows that he must think these effects could be modeled using evolutive game theory. I don’t know, however, whether Binmore would agree that these framing effects are plausibly truly general. My point is just that if Binmore were convinced of the generality of the effects, this would be a way in which he could flesh out his claim that evolutive game theory is the right resource for modeling the origins of conventions.
An anonymous referee objects that this point is irrelevant to the assessment of the viability of team reasoning models. So it is, for the reason indicated in the concluding paragraph of Sect. 3. However, the point I am making here is different: it is implausible to think that game theory incorporates any commitment to what kind of empirical entity an agent is other than: something whose behavior over some interval relevant to some useful model can be rationalized by a consistent utility function.
I say ‘misleadingly’ here because what gets discussed under this label in most of the polemical literature to which I allude is in fact not methodological but ontological individualism—that is, social atomism.
Different cultures draw the line between the mandated and the free preferences of people in widely varying places; but all draw it.
Yet a third interpretation of impulsive behavior models the agent as an expected utility maximizer who encounters exogenous temptations that are costly to avoid; see Gul and Pesendorfer (2001, 2005). This helps to confirm, by negative example, the tight logical relation between matching and self-signaling; in Gul and Pesendorfer’s model we find neither.
I have not followed Gold and Sugden’s way of representing this, which is as a 3-person game between two stages of Joe and Joe-as-a-whole. This conceptually baroque way of writing down the game is not necessary for their analysis.
An anonymous referee suggests a nice way of putting this point: “Team reasoning is the psychological uniform in which socialization casts our preferences.”
That is, all agents enter society at once.
This is a point of difference between me and Bacharach (or, at least, Bacharach as interpreted by Gold and Sugden). I have endorsed Bacharach’s key insight that people frame games that Lewis models as Pure Coordination games as Hi-lo games. But Bacharach thinks this shows that game theory incorporates a dubious metaphysical individualism into its axioms. On my account, not one axiom of game theory calls for weakening: unamended evolutive game theory explains why some determining games converge on conventions, and unamended eductive game theory rationalizes individual agents’ choices to play some determined games according to conventions.
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Acknowledgments
I would like to thank Luca Tummolini and an anonymous referee for very helpful comments on an earlier draft of this paper.
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Ross, D. Classical Game Theory, Socialization and the Rationalization of Conventions. Topoi 27, 57–72 (2008). https://doi.org/10.1007/s11245-008-9028-1
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DOI: https://doi.org/10.1007/s11245-008-9028-1