An interview with robert aumann
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736 SERGIU HART A: A lot of game theory has to do with relationships among different objects. I talked about this in my 1995 “birthday” lecture, and it is also in the Introduction to my Collected Papers [vi]. Science is often characterized as a quest for truth, where truth is something absolute, which exists outside of the observer. But I view science more as a quest for understanding, where the understanding is that of the observer, the scien- tist. Such understanding is best gained by studying relations—relations between different ideas, relations between different phenomena; relations between ideas and phenomena. Rather than asking “How does this phenomenon work?” we ask, “How does this phenomenon resemble others with which we are familiar?” Rather than asking “Does this idea make sense?” we ask, “How does this idea resemble other ideas?” Indeed, the idea of relationship is fundamental to game theory. Disciplines like economics or political science use disparate models to analyze monopoly, oligopoly, perfect competition, public goods, elections, coalition formation, and so on. In contrast, game theory uses the same tools in all these applications. The nucleolus yields the competitive solution in large markets [16], the homogeneous weights in parliaments (cf. Peleg), and the Talmudic solution in bankruptcy games [46]. The fundamental notion of Nash equilibrium, which a priori reflects the behavior of consciously maximizing agents, is the same as an equilibrium of populations that reproduce blindly without regard to maximizing anything. The great American naturalist and explorer John Muir said, “When you look closely at anything in the universe, you find it hitched to everything else.” Though Muir was talking about the natural universe, this applies also to scientific ideas— how we understand our universe.
reasonableness or correctness of assumptions and axioms. That is wrongheaded. I have never been so interested in assumptions. I am interested in conclusions. Assumptions don’t have to be correct; conclusions have to be correct. That is put very strongly, maybe more than I really feel, but I want to be provocative. When Newton introduced the idea of gravity, he was laughed at, because there was no rope with which the sun was pulling the earth; gravity is a laughable idea, a crazy assumption, it still sounds crazy today. When I was a child I was told about it. It did not make any sense then, and it doesn’t now; but it does yield the right answer. In science one never looks at assumptions; one looks at conclusions. It does not interest me whether this or that axiom of utility theory, of the Shapley value, of Nash bargaining is or is not compelling. What interests me is whether the conclusions are compelling, whether they yield interesting insights, whether one can build useful theory from them, whether they are testable. Nowhere else in science does one directly test assumptions; a theory stands or falls by the validity of the conclusions, not of the assumptions. INTERVIEW WITH ROBERT AUMANN 737 H: Would you like to say something about the ethical neutrality of game theory? A: Ethical neutrality means that game theorists don’t necessarily advocate carrying out the normative prescriptions of game theory. Game theory is about selfishness. Just like I suggested studying war, game theory studies selfishness. Obviously, studying war is not the same as advocating war; similarly, studying self- ishness is not the same as advocating selfishness. Bacteriologists do not advocate disease, they study it. Game theory says nothing about whether the “rational” way is morally or ethically right. It just says what rational—self-interested—entities will do; not what they “should” do, ethically speaking. If we want a better world, we had better pay attention to where rational incentives lead.
SCIENTIFIC PUBLICATIONS OF ROBERT AUMANN BOOKS [i] Values of Non-Atomic Games, with Lloyd S. Shapley. Princeton, NJ: Princeton University Press, 1974, xi + 333.
[ii] Game Theory (in Hebrew), with Yair Tauman and Shmuel Zamir. Tel Aviv: Everyman’s Uni- versity, 1981. Vol. 1: 211, Vol. 2: 203. [iii] Lectures on Game Theory, Boulder, CO: Underground Classics in Economics, Westview Press, 1989, ix
+ 120. [iv] Handbook of Game Theory with Economic Applications, coedited with Sergiu Hart. Amsterdam: Elsevier. Vol. 1, 1992, xxvi + 733, Vol. 2, 1994, xxviii + 787, Vol. 3, 2002, xxx + 858. [v] Repeated Games with Incomplete Information, with Michael Maschler. Cambridge, MA: MIT Press, 1995, xvii + 342. [vi] Collected Papers, Vol. 1, xi + 786, Vol. 2, xiii + 792, Cambridge, MA: MIT Press, 2000. ARTICLES [1] Asphericity of alternating knots. Annals of Mathematics 64 (1956), 374–392. [2] The coefficients in an allocation problem, with Joseph B. Kruskal. Naval Research Logistics
[3] Assigning quantitative values to qualitative factors in the naval electronics problem, with Joseph B. Kruskal. Naval Research Logistics Quarterly 6 (1959), 1–16. [4] Acceptable points in general cooperative n-person games. In A.W. Tucker and R.D. Luce (eds.), Contributions to the Theory of Games IV, Annals of Mathematics Study 40, pp. 287–324. Princeton, NJ: Princeton University Press, 1959. [5] Von Neumann–Morgenstern solutions to cooperative games without side payments, with Bezalel Peleg. Bulletin of the American Mathematical Society 66 (1960), 173–179. [6] Acceptable points in games of perfect information. Pacific Journal of Mathematics 10 (1960), 381–417.
[7] A characterization of game structures of perfect information. Bulletin of the Research Council of Israel 9F (1960), 43–44. [8] Spaces of measurable transformations. Bulletin of the American Mathematical Society 66 (1960), 301–304.
738 SERGIU HART [9] Linearity of unrestrictedly transferable utilities. Naval Research Logistics Quarterly 7 (1960), 281–284.
[10] The core of a cooperative game without side payments. Transactions of the American Mathe- matical Society 98 (1961), 539–552. [11] Borel structures for function spaces. Illinois Journal of Mathematics 5 (1961), 614–630. [12] Almost strictly competitive games. Journal of the Society for Industrial and Applied Mathematics 9 (1961), 544–550. [13] (a) Utility theory without the completeness axiom. Econometrica 30 (1962), 445–462. (b) Utility theory without the completeness axiom: a correction. Econometrica 32 (1964), 210– 212. [14] A definition of subjective probability, with Frank J. Anscombe. Annals of Mathematical Statistics 34 (1963), 199–205. [15] On choosing a function at random. In F.W. Wright (ed.), Ergodic Theory, pp. 1–20. New Orleans, LA: Academic Press, 1963. [16] Markets with a continuum of traders. Econometrica 32 (1964), 39–50. [17] The bargaining set for cooperative games, with Michael Maschler. In M. Dresher, L.S. Shapley, and A.W. Tucker (eds.), Advances in Game Theory, Annals of Mathematics Study 52, pp. 443–476. Princeton, NJ: Princeton University Press, 1964. [18] Mixed and behavior strategies in infinite extensive games. In M. Dresher, L.S. Shapley, and A.W. Tucker (eds.), Advances in Game Theory, Annals of Mathematics Study 52, pp. 627–650. Princeton, NJ: Princeton University Press, 1964. [19] Subjective programming. In M.W. Shelly and G.I. Bryan (eds.), Human Judgments and Opti-
[20] A variational problem arising in economics, with Micha Perles. Journal of Mathematical Analysis and Applications 11 (1965), 488–503. [21] Integrals of set-valued functions. Journal of Mathematical Analysis and Applications 12 (1965), 1–12. [22] A method of computing the kernel of n-person games, with Bezalel Peleg and Pinchas Rabi- nowitz. Mathematics of Computation 19 (1965), 531–551. [23] Existence of competitive equilibria in markets with a continuum of traders. Econometrica 34 (1966), 1–17. [24] A survey of cooperative games without side payments. In M. Shubik (ed.), Essays in Mathemat- ical Economics in Honor of Oskar Morgenstern, pp. 3–27. Princeton, NJ: Princeton University Press, 1967. [25] Random measure preserving transformations. In L.M. LeCam and J. Neyman (eds.), Proceedings
pp. 321–326. Berkeley: University of California Press, 1967. [26] Measurable utility and the measurable choice theorem. In La Decision, pp. 15–26. Paris: Editions du Centre National de la Recherche Scientifique, 1969. [27] Some thoughts on the minimax principle, with Michael Maschler. Management Science 18 (1972), P-54–P-63. [28] Disadvantageous monopolies. Journal of Economic Theory 6 (1973), 1–11. [29] Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1 (1974), 67–96. [30] A note on Gale’s example, with Bezalel Peleg. Journal of Mathematical Economics 1 (1974), 209–211. [31] Cooperative games with coalition structures, with Jacques Dr`eze. International Journal of Game Theory 4 (1975), 217–237. [32] Values of markets with a continuum of traders. Econometrica 43 (1975), 611–646. [33] An elementary proof that integration preserves uppersemicontinuity. Journal of Mathematical
[34] Agreeing to disagree. Annals of Statistics 4 (1976), 1236–1239. INTERVIEW WITH ROBERT AUMANN 739 [35] Orderable set functions and continuity III: orderability and absolute continuity, with Uri Rothblum. SIAM Journal on Control and Optimization 15 (1977), 156–162. [36] The St. Petersburg paradox: a discussion of some recent comments. Journal of Economic Theory 14 (1977), 443–445. [37] Power and taxes, with Mordecai Kurz. Econometrica 45 (1977), 1137–1161. [38] Power and taxes in a multi-commodity economy, with Mordecai Kurz. Israel Journal of Mathe-
[39] Core and value for a public goods economy: an example, with Roy J. Gardner and Robert W. Rosenthal. Journal of Economic Theory 15 (1977), 363–365. [40] On the rate of convergence of the core. International Economic Review 19 (1979), 349–357. [41] Recent developments in the theory of the Shapley value. In O. Lehto (ed.), Proceedings of the
Scientiarum Fennica, 1980. [42] Survey of repeated games. In V. B¨ohm (ed.), Essays in Game Theory and Mathematical
senschaftsverlag, pp. 11–42. Mannheim: Bibliographisches Institut, 1981. [43] Approximate purification of mixed strategies, with Yitzhak Katznelson, Roy Radner, Robert W. Rosenthal, and Benjamin Weiss. Mathematics of Operations Research 8 (1983), 327– 341. [44] Voting for public goods, with Mordecai Kurz and Abraham Neyman. Review of Economic Studies 50 (1983), 677–694. [45] An axiomatization of the non-transferable utility value. Econometrica 53 (1985), 599–612. [46] Game-theoretic analysis of a bankruptcy problem from the Talmud, with Michael Maschler.
[47] What Is game theory trying to accomplish? In K. Arrow and S. Honkapohja (eds.), Frontiers of Economics, pp. 28–76. Oxford: Basil Blackwell, 1985. [48] On the non-transferable utility value: a comment on the Roth–Shafer Examples. Econometrica 53 (1985), 667–677. [49] Rejoinder. Econometrica 54 (1986), 985–989. [50] Bi-convexity and bi-martingales, with Sergiu Hart. Israel Journal of Mathematics 54 (1986), 159– 180.
[51] Values of markets with satiation or fixed prices, with Jacques Dr`eze. Econometrica 54 (1986), 1271–1318. [52] Power and public goods, with Modecai Kurz and Abraham Neyman. Journal of Economic Theory 42 (1987), 108–127. [53] Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55 (1987), 1– 18.
[54] Value, symmetry, and equal treatment: a comment on Scafuri and Yannelis. Econometrica 55 (1987), 1461–1464. [55] Game theory. In J. Eatwell, M. Milgate, and P. Newman (eds.), The New Palgrave, A Dictionary
[56] Endogenous formation of links between players and of coalitions: an application of the Shapley value, with Roger Myerson. In A.E. Roth (ed.), The Shapley Value: Essays in Honor of Lloyd S.
[57] Cooperation and bounded recall, with Sylvain Sorin. Games and Economic Behavior 1 (1989), 5–39. [58] CORE as a macrocosm of game-theoretic research, 1967–1987. In B. Cornet and H. Tulkens (eds.), Contributions to Operations Research and Economics: The Twentieth Anniversary of CORE, pp. 5–16. Cambridge and London: The MIT Press, 1989. [59] Nash equilibria are not self-enforcing. In J.J. Gabszewicz, J.-F. Richard, and L. Wolsey (eds.), Economic Decision Making: Games, Econometrics and Optimisation (Essays in Honor of Jacques Dr`eze), pp. 201–206. Amsterdam: Elsevier Science Publishers, 1990. 740 SERGIU HART [60] Irrationality in game theory. In P. Dasgupta, D. Gale, O. Hart, and E. Maskin (eds.), Economic
London: MIT Press, 1992. [61] Long-term competition: a game-theoretic analysis, with Lloyd S. Shapley. In N. Megiddo (ed.),
[62] The Shapley value. In J.-F. Mertens and S. Sorin (eds.), Game-Theoretic Methods in General Equilibrium Analysis, pp. 61–66. Dordrecht: Kluwer Academic Publishers, 1994. [63] Economic applications of the Shapley value. In J.-F. Mertens and S. Sorin (eds.), Game-Theoretic Methods in General Equilibrium Analysis, pp. 121–133. Dordrecht: Kluwer Academic Publish- ers, 1994. [64] Backward induction and common knowledge of rationality. Games and Economic Behavior 8 (1995), 6–19. [65] Epistemic conditions for Nash equilibrium, with Adam Brandenburger. Econometrica 63 (1995), 1161–1180. [66] Reply to Binmore. Games and Economic Behavior 17 (1996), 138–146. [67] Reply to Margalit and Yaari. In K.J. Arrow, E. Colombatto, M. Perlman, and C. Schmidt (eds.), The Rational Foundations of Economic Equilibrium, pp. 106–107. London and Basingstoke: Macmillan, 1996. [68] Reply to Binmore and Samuelson. In K.J. Arrow, E. Colombatto, M. Perlman, and C. Schmidt (eds.), The Rational Foundations of Economic Equilibrium, pp. 130–131. London and Basingstoke: Macmillan, 1996. [69] The absent-minded driver, with Sergiu Hart and Motty Perry. Games and Economic Behavior 20 (1997), 102–116. [70] The forgetful passenger, with Sergiu Hart and Motty Perry. Games and Economic Behavior 20 (1997), 117–120. [71] Rationality and bounded rationality. Games and Economic Behavior 21 (1997), 2–14. [72] On the centipede game. Games and Economic Behavior 23 (1998), 97–105. [73] Common priors: a reply to Gul. Econometrica 66 (1998), 929–938. [74] Interactive epistemology I: knowledge. International Journal of Game Theory 28 (1999), 263– 300.
[75] Interactive epistemology II: probability. International Journal of Game Theory 28 (1999), 301– 314.
[76] Species survival and evolutionary stability in sustainable habitats, with Werner G¨uth. Journal of Evolutionary Economics 10 (2000), 437–447. [77] The rationale for measurability. In G. Debreu, W. Neuefeind, and W. Trockel, Economics Essays, A Festschrift for Werner Hildenbrand, pp. 5–7. Berlin: Springer, 2001. [78] Harsanyi’s sweater. Games and Economic Behavior 36 (2001), 7–8. [79] Incomplete information, with Aviad Heifetz. In R.J. Aumann and S. Hart (eds.), Handbook of
[80] Risk aversion in the Talmud. Economic Theory 21 (2003), 233–239. [81] Presidential address. Games and Economic Behavior 45 (2003), 2–14. [82] Long cheap talk, with Sergiu Hart. Econometrica 71 (2003), 1619–1660. OTHER [83] Letter to Leonard Savage, 8 January 1971. In J.H. Dr`eze, Essays on Economic Decisions under Uncertainty, pp. 76–78. Cambridge: Cambridge University Press, 1987. [84] On the state of the art in game theory, an interview. W. Albers, W. G¨uth, P. Hammerstein, B. Moldovanu, and E. van Damme (eds.), Understanding Strategic Interaction (Essays in Honor of Reinhard Selten). Berlin: Springer, 1997, pp. 8–34. Reprinted in Games and Economic Behavior 24 (1998), 181–210. Yüklə 2,96 Mb. Dostları ilə paylaş:
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