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Is Language a Game?

Published online by Cambridge University Press:  01 January 2020

Joseph Heath
Affiliation:
University of Toronto, Toronto, ON, Canada M5S 1A1

Extract

Recent developments in game theory have shown that the mathematical models of action so widely admired in the study of economics are in fact only particular instantiations of a more general theoretical framework. In the same way that Aristotelian logic was ‘translated’ into the more general and expressive language of predicate logic, the basic action theoretic underpinnings of modern economics have now been articulated within the more comprehensive language of game theory. But precisely because of its greater generality and expressive power, game theory has again revived the temptation to apply formal models of action to every domain of social life. This movement has been fuelled by some notable successes. Game theory has provided useful insights into the logic of collective action in the theory of public goods, and strategic models of voting have illustrated important aspects of institutional decision-making. But this extension of formal models into every area of social interaction has also encountered significant difficulties, despite the fact that contemporary decision theory has weakened its basic assumptions to the point where it teeters constantly on the brink of vacuity.

Type
Research Article
Copyright
Copyright © The Authors 1996

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References

1 See Parsons, Talcott and Shils, Edward eds., Toward a General Theory of Action (New York: Harper & Row 1951)Google Scholar.

2 See Hollis, Martin and Sugden, RobertRationality in Action,Mind 102 (1993) 135CrossRefGoogle Scholar.

3 The locus classicus of this view is Parsons, Talcott The Structure of” Social Action, 2 vols. (New York: Free Press 1968)Google Scholar.

4 Nash, JohnNoncooperative Games,Annals of Mathematics 54 (1951) 279-95 at 286CrossRefGoogle Scholar; see also Eatwell, John et al., eds., The New Palgrave: Game Theory (New York: W.W. Norton 1989), 95CrossRefGoogle Scholar.

5 The exceptions are analyses that employ axiomatic bargaining models or assume coalitions. Both of these techniques tend to be avoided because it is generally acknowledged that they lack microfoundations.

6 For example, standard textbooks on game theory like Fudenberg, Drew and Tirole, Jean Game Theory (Cambridge, MA: The MIT Press 1991)Google Scholar, do not deal with cooperative game theory at all.

7 Nash, 295

8 See, e.g., Ordeshook, Peter C. Game Theory and Political Theory (Cambridge: Cambridge University Press 1986), 303-4CrossRefGoogle Scholar, or Austen-Smith, DavidStrategic Models of Talk in Political Decision Making,International Political Science Review 13 (1992) 4558CrossRefGoogle Scholar.

9 Jakko Hintikka's ‘game-theoretic semantics’ are not relevant to this discussion, since he does not try to model communication as a move within a game. Instead, he uses game theory to represent the verification conditions for certain types of sentences. See, for instance, ‘Language-Games for Quantifiers’ in Logic, Language-Games and Information (Oxford: Clarendon Press 1973).

10 Here I follow Savage, Leonard J. The Foundations of Statistics (New York: John Wiley & Sons 1954)Google Scholar, except that he takes beliefs for granted.

11 The clearest presentation of this derivation remains Luce, R. Duncan and Raiffa, Howard Games and Decisions (New York: John Wiley & Sons 1957), 1239Google Scholar.

12 As Neumann, John von and Morgenstern, Oskar put it, ‘Every participant can determine the variables which describe his own actions, but not those of the others. Nevertheless, those “alien” variables cannot, from his point of view, be described by statistical assumptions. This is because the others are guided, just as he himself, by rational principles’ (The Theory of Gamcs and Economic Behavior, 2nd ed. [Princeton: Princeton University Press 1947], 11)Google Scholar. Thus the traditional ‘Robinson Crusoe’ model of instrumental rationality ‘is of much more limited value to economic theory than has been assumed even by the most radical critics’ (12).

13 See Fudenberg, and Tirole, Game Theory, 2936Google Scholar, or Myerson, Roger Game Theory: Analysis of Conflict (Cambridge, MA: Harvard University Press 1991), 136-40Google Scholar. Note that the only general solution concepts are backward induction based, i.e., they start with an outcome and reason back to the required actions. This can be very counterintuitive, and should therefore always be kept in mind.

14 See ‘Of Speech’ in Leviathan (Cambridge: Cambridge University Press 1991), 24-30. For historical analysis see Taylor, CharlesTheories of Meaning,’ in Human Agency and Language: Philosophical Papers I (Cambridge: Cambridge University Press 1985)CrossRefGoogle Scholar.

15 Grice, H.P.Meaning,Philosophical Review 66 (1957) 377-88CrossRefGoogle Scholar. Reprinted in Grice, H.P. Studies in the Way of Words (Cambridge, MA: Harvard University Press 1989)Google Scholar.

16 I think this should be non-controversial. Nevertheless, it should be noted that a prima facie consequence of this claim is that Davidson's, Donald program for a unified theory of meaning and action cannot be carried through as he intends, since he (somewhat inexplicably) limits the action-theoretic component to simple decision theory. See ‘The Structure and Content of Truth,The Journal of Philosophy 87 (1990) 279328CrossRefGoogle Scholar.

17 Lewis, David Convention (Cambridge, MA: Harvard University Press 1969)Google Scholar

18 This is the psychological’ solution developed by Schelling, Thomas in The Strategy of Conflict (Cambridge, MA: Harvard University Press 1960)Google Scholar.

19 Most obviously, the game-theoretic segment does not handle compositionality.

20 In this paper, I follow the convention of using male pronouns to refer to odd players and female pronouns for even.

21 Kreps, David M. and Wilson, RobertSequential Equilibria’ in Econometrica 50 (1982) 871-89 at 871CrossRefGoogle Scholar.

22 Harsanyi, JohnGames with Incomplete Information Played by “Bayesian” Players,’ 3 parts, Management Science 14 (1967-68) 159-82, 320-34, 486-502CrossRefGoogle Scholar. The idea, roughly, is to take the single game of incomplete information and represent it as a set of different games of complete information, where not all players know which game is being played. In a similar way, one might represent the vagueness of a predicate as a probability distribution over the set of acceptable sharpenings.

23 For a clear presentation of the model, see Bunks, Jeffrey S. and Sobel, JoelEquilibrium Selection in Signalling Games,Econometrica 55 (1988) 647-61CrossRefGoogle Scholar, or Crawford, Vincent P. and Sobel, JoelStrategic Information Transmission,Econometrica 50 (1982) 1431-51CrossRefGoogle Scholar.

24 Lewis uses an example that involves Paul Revere hanging lanterns in the belfry (Convention, 122-3). The structure of the game shown in Figure 3 is the same, except that it has only two messages instead of three. We could easily add more types to the above game, e.g., pillars and beams, but it would make Figure 3 even less intelligible.

25 This type of game tree diagram can be hard to read at first. The origin is in the center, and nature starts the game by moving up or down, thereby determining player 1 ‘s type. From either l.a or 1.b, player I then moves left by shouting ‘block’ or moves right by shouting ‘slab.’ If Player 2 hears ‘block’ then she is at information set 2.a, and is at 2.b if she hears ‘slab.’ She then passes either a block or a slab, ending the game.

26 Lewis adds a clever mechanism for determining whether the utterance is an assertion or an imperative, which need not concern us here (Convention, 144).

27 Hardin, Russell in his Collective Action (Baltimore: Johns Hopkins University Press 1980), 163Google Scholar, misunderstands Lewis to be suggesting that linguistic conventions arise in a repeated game (in which case the folk theorem would apply and each game would have an infinite number of equilibria). Lewis's claim is only that past plays of the game determine the salient outcome, they are not part of the equilibrium. This is what allows us to learn the meaning of a message by watching others play the language game.

28 Myerson, Game Theory, 373-4Google Scholar

29 Farrell, JosephMeaning and Credibility in Cheap-Talk Games,Games and Economic Behavior 5 (1993) 514-31, §1CrossRefGoogle Scholar

30 Crawford and Sobel, 1450

31 Bennett, Jonathan has suggested a modification that would allow beliefs to be treated as outcomes in non-cooperative games, ‘The Meaning-Nominalist Strategy,Foundations of Language 10 (1973) 141-68Google Scholar. He expands the category of actions to what he calls doings. These include the ‘act’ of belief-acquisition, and so it becomes possible to treat beliefs as outcomes. But this modification creates enormous tension with the utility-maximizing conception of practical reason. If beliefs were outcomes, they would have to be associated with payoffs for both players. If the agent faced with doing a belief-acquisition did so on the basis of these payoffs it would effectively condone ‘wishful thinking’ and thus spell the end of belief rationality. But if the belief-outcome is still determined belief-rationally, and the payoff is relevant only to the sender, then R no longer has any strategy. Without a strategy, there is nothing for R's beliefs to be consistent with, nothing for S's strategy to be in equilibrium with, and thus no end to the regress of anticipations.

32 Lewis, 160

33 Farrell, ‘Meaning and Credibility in Cheap-Talk Games’

34 The only problem with neologisms is that they multiply the set of equilibria enormously, e.g., R could take ‘pillar’ to reveal type need-a-block, and then there would be all sorts of new equilibria in which S randomized in various ways between ‘block’ and ‘pillar’ every time he was of type need-a-block. But other than creating this annoying proliferation of equilibria, neologisms do not create fundamental problems for any of the traditional non-cooperative solution concepts.

35 This analysis may seem counterintuitive. For more extensive discussion, see Farrell, §7.

36 See, e.g., Myerson, Roger B.Credible Negotiation Statements and Coherent Plans,’ in Journal of Economic Theory 48 (1989) 264303 at 287CrossRefGoogle Scholar.

37 See Aumann, RobertAgreeing to Disagree,Annals of Statistics 4 (1976) 1236-9CrossRefGoogle Scholar.

38 Myerson, ‘Credible Negotiation Statements and Coherent Plans,’ 266Google Scholar

39 Alexander, Jeffrey Theoretical Logic in Sociology, 4 vols. (Berkeley: University of California Press 1982-4)Google Scholar

40 Habermas, Jürgen The Theory of Communication Action, 2 vols. (Boston: Beacon Press 1984, 1987)Google Scholar. He develops a similar analysis for imperatives and expressives at 273-337.

41 See, for example, chapter one of Goffman's, Erving Behaviour in public places (New York: The Free Press 1963)Google Scholar, or Garfinkel, HaroldThe Rational Properties of Scientific and Common Sense Activities,’ in Studies in Ethnomethodology (Cambridge: Polity Press 1984)Google Scholar.

42 This is, as far as I can tell, Elster's, Jon current position. See The Cementt of Society (Cambridge: Cambridge University Press 1989)CrossRefGoogle Scholar.

43 I would like to thank Joel Anderson, David Davies, James Johnson, Thomas McCarthy, and referees for the Canadian Journal of Philosophy for detailed comments and criticisms, as well as the Social Sciences and Humanities Research Council of Canada for financial assistance.

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