An interview with

H: The uncertainty about the court’s decision may be viewed also as a chance device—which may lead to a Pareto improvement. Like mutual insurance.

A: Well, okay, that is theoretically correct. Still, it is farfetched. In general, uncertainty is a dampening factor.

In brief, for these two reasons—introducing uncertainty into the economy and into the polity, and its undemocratic nature—judicial activism is to be deplored.

* * *

H: Another topic you wanted to talk about is war.

A: Barry O’Neill, the game theory political scientist, gave a lecture here a few months ago. Something he said in the lecture—that war has been with us for thousands of years—set me thinking. It really is true that there is almost nothing as ever-present in the history of mankind as war. Since the dawn of history we have had constant wars. War and religion, those are the two things that are ever-present with us. A tremendous amount of energy is devoted on the part of a very large number of well-meaning people to the project of preventing war, settling conflicts peacefully, ending wars, and so on. Given the fact that war is so, so prevalent, both in time and in space, all over the world, perhaps much of the effort of preventing or stopping war is misdirected. Much of this effort is directed at solving specific conflicts. What can we do to reach a compromise between the Irish Catholics in the Republic of Ireland and the Protestants in North Ireland? What can we do to resolve the conflict between the Hindus in India and the Moslems in Pakistan? What can we do to resolve the conflict between the Jews and the Arabs in the Middle East? One always gets into the particulars of these conflicts and neglects the more basic problems that present themselves by the very fact that we have had wars continuously. War is only apparently based on specific conflicts. There appears to be something in the way human nature is constituted—or if not human nature, then the way we run our institutions—that allows war and in fact makes it inevitable. Just looking at history, given the constancy of war, we should perhaps shift gears and ask ourselves what it is that causes war. Rather than establishing peace institutes, peace initiatives, institutions for studying and promoting peace, we should have institutions for studying war. Not with an immediate view to preventing war. Such a view can come later, but first we should understand the phenomenon.

It’s like fighting cancer. One way is to ask, given a certain kind of cancer, what can we do to cure it? Chemotherapy? Radiation? Surgery? Let’s do statistical studies that indicate which is more effective. That’s one way of dealing with cancer, and it’s an important way. Another way is simply to ask, what is cancer? How does it work? Never mind curing it. First let’s understand it. How does it get started, how does it spread? How fast? What are the basic properties of cells that go awry when a person gets cancer? Just study it. Once one understands it one can perhaps hope to overcome it. But before you understand it, your hope to overcome it is limited.

H: So, the standard approach to war and peace is to view it as a black box. We do not know how it operates, so we try ad hoc solutions. You are saying that this is not a good approach. One should instead try to go inside the black box: to understand the roots of conflict—not just deal with symptoms.

A: Yes. Violent conflict may be very difficult to overcome. A relevant game-theoretic idea is that, in general, neither side really knows the disagreement level, the “reservation price.” It’s like the Harsanyi–Selten bargaining model with incomplete information, where neither side knows the reservation price of the other. The optimum strategy in such a situation may be to go all the way and threaten. If the buyer thinks that the seller’s reservation price is low, he will make a low offer, even if he is in fact willing to pay much more. Similarly for the seller. So conflict may result even when the reservation prices of the two sides are compatible. When this conflict is a strike, then it is bad enough, but when it’s a war, then it is much worse. This kind of model suggests that conflict may be inevitable, or that you need different institutions in order to avoid it. If in fact it is inevitable in that sense, we should understand that. One big mistake is to say that war is irrational.

H: It’s like saying that strikes are irrational.

A: Yes, and that racial discrimination is irrational (cf. Arrow). We take all the ills of the world and dismiss them by calling them irrational. They are not necessarily irrational. Though it hurts, they may be rational. Saying that war is irrational may be a big mistake. If it is rational, once we understand that it is, we can at least somehow address the problem. If we simply dismiss it as irrational we can’t address the problem.

H: Exactly as in strikes, the only way to transmit to the other side how important this thing is to you may be to go to war.

A: Yes. In fact Bob Wilson discussed this in his Morgenstern lecture here in ’94—just after a protracted strike of the professors in Israel.

H: Here in Israel, we unfortunately have constant wars and conflicts. One of the “round tables” of the Rationality Center—where people throw ideas at each other very informally—was on international conflicts. You presented there some nice game-theoretic insights.

A: One of them was the blackmailer’s paradox. Ann and Bob must divide a hundred dollars. It is not an ultimatum game; they can discuss it freely. Ann says to Bob, look, I want ninety of those one hundred. Take it or leave it; I will not walk out of this room with less than ninety dollars. Bob says, come on, that’s crazy. We have a hundred dollars. Let’s split fifty-fifty. Ann says, no. Ann—“the blackmailer”—is perhaps acting irrationally. But Bob, if he is rational, will accept the ten dollars, and that’s the end.

H: The question is whether she can commit herself to the ninety. Because if not, then of course Bob will say, you know what, fifty-fifty. Now you take it or leave it. For this to work, Ann must commit herself credibly.

A: In other words, it’s not enough for her just to say it. She has to make it credible; and then Bob will rationally accept the ten. The difficulty with this is that perhaps Bob, too, can credibly commit to accepting no less than ninety. So we have a paradox: once Ann credibly commits herself to accepting no less than ninety, Bob is rationally motivated to take the ten. But then Ann is rationally motivated to make such a commitment. But Bob could also make such a commitment; and if both make the commitment, it is not rational, because then nobody gets anything.

This is the blackmailer’s paradox. It is recognized in game theory, therefore, that it is perhaps not so rational for the guy on the receiving end of the threat to accept it.

What is the application of this to the situation we have here in Israel? Let me tell you this true story. A high-ranking officer once came to my office at the Center for Rationality and discussed with me the situation with Syria and the Golan Heights. This was a hot topic at the time. He explained to me that the Syrians consider land holy, and they will not give up one inch. When he told me that, I told him about the blackmailer’s paradox. I said to him that the Syrians’ use of the term “holy,” land being holy, is a form of commitment. In fact, they must really convince themselves that it’s holy, and they do. Just like in the blackmailer’s paradox, we could say that it’s holy; but we can’t convince ourselves that it is. One of our troubles is that the term “holy” is nonexistent in our practical, day-to-day vocabulary. It exists only in religious circles. We accept holiness in other people and we are not willing to promote it on our own side. The result is that we are at a disadvantage because the other side can invoke holiness, but we have ruled it out from our arsenal of tools.

H: On the other hand, we do have such a tool: security considerations. That is the “holy” issue in Israel. We say that security considerations dictate that we must have control of the mountains that control the Sea of Galilee. There is no way that anything else will be acceptable. Throughout the years of Israel’s existence security considerations have been a kind of holiness, a binding commitment to ourselves. The question is whether it is as strong as the holiness of the land on the other side.

A: It is less strong.

H: Maybe that explains why there is no peace with Syria.

A: You know, the negotiations that Rabin held with the Syrians in the early nineties blew up over a few meters. I really don’t understand why they blew up, because Rabin was willing to give almost everything away. Hills, everything.

Without suggesting solutions, it is just a little bit of an insight into how game-theoretic analysis can help us to understand what is going on, in this country in particular, and in international conflicts in general.

* * *

H: Next, what about what you refer to as “connections”?

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 scientist. 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.

* * *

H: How about the issue of assumptions vs. conclusions?

A: There is a lot of discussion in economic theory and in game theory about the 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.

* * *

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 selfishness 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.

H: That’s a very good conclusion to this fascinating interview. Thank you.

A: And thank you, Sergiu, for your part in this wonderful interview.
SCIENTIFIC PUBLICATIONS OF ROBERT AUMANN
BOOKS

[i] Values of Non-Atomic Games, Princeton, NJ: Princeton University Press, 1974 (with Lloyd S. Shapley), xi + 333.

[ii] Game Theory (in Hebrew), Vol. 1: 211, Vol. 2: 203, Tel Aviv: Everyman’s University, 1981 (with Yair Tauman and Shmuel Zamir).

[iii] Lectures on Game Theory, Boulder, CO: Underground Classics in Economics, Westview Press, 1989, ix + 120.

[iv] Handbook of Game Theory with economic applications, Vol. 1, 1992, xxvi + 733, Vol. 2, 1994, xxviii + 787, Vol. 3, 2002, xxx + 858, Amsterdam: Elsevier (coedited with Sergiu Hart).

[v] Repeated Games with Incomplete Information, Cambridge, MA: MIT Press, 1995, xvii + 342 (with Michael Maschler).

[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. Naval Research Logistics Quarterly 5 (1958), 111–123 (with Joseph B. Kruskal).

[3] Assigning Quantitative Values to Qualitative Factors in the Naval Electronics Problem. Naval Research Logistics Quarterly 6 (1959), 1–16 (with Joseph B. Kruskal).

[4] Acceptable Points in General Cooperative n-Person Games. In A. W. Tucker & 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. Bulletin of the American Mathematical Society 66 (1960), 173–179 (with Bezalel Peleg).

[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.

[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 Mathematical 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. Annals of Mathematical Statistics 34 (1963), 199–205 (with Frank J. Anscombe).

[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. In M. Dresher, L. S. Shapley & A. W. Tucker (eds.), Advances in Game Theory, Annals of Mathematics Study 52, pp. 443–476. Princeton, NJ: Princeton University Press, 1964 (with Michael Maschler).

[18] Mixed and Behavior Strategies in Infinite Extensive Games. In M. Dresher, L. S. Shapley & 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 & G. I. Bryan (eds.), Human Judgments and Optimality, pp. 217-242. New York, NY: John Wiley and Sons, 1964.

[20] A Variational Problem Arising in Economics. Journal of Mathematical Analysis and Applications 11 (1965), 488–503 (with Micha Perles).

[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. Mathematics of Computation 19 (1965), 531–551 (with Bezalel Peleg and Pinchas Rabinowitz).

[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 Mathematical Economics in Honor of Oskar Morgenstern, pp. 3–27. Princeton, NJ: Princeton University Press, 1967.

[25] Random Measure Preserving Transformations. In L. M. LeCam & J. Neyman (eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, Part 2, pp. 321–326. Berkeley, CA: 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. Management Science 18 (1972), P-54–P-63 (with Michael Maschler).

[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. Journal of Mathematical Economics 1 (1974), 209–211 (with Bezalel Peleg).

[31] Cooperative Games with Coalition Structures. International Journal of Game Theory 4 (1975), 217–237 (with Jacques Drèze).

[32] Values of Markets with a Continuum of Traders. Econometrica 43 (1975), 611–646.

[33] An Elementary Proof that Integration Preserves Uppersemi-continuity. Journal of Mathematical Economics 3 (1976), 15–18.

[34] Agreeing to Disagree. Annals of Statistics 4 (1976), 1236–1239.

[35] Orderable Set Functions and Continuity III: Orderability and Absolute Continuity. SIAM Journal on Control and Optimization 15 (1977), 156–162 (with Uri Rothblum).

[36] The St. Petersburg Paradox: A Discussion of some Recent Comments. Journal of Economic Theory 14 (1977), 443–445.

[37] Power and Taxes. Econometrica 45 (1977), 1137–1161 (with Mordecai Kurz).

[38] Power and Taxes in a Multi-Commodity Economy. Israel Journal of Mathematics 27 (1977), 185–234 (with Mordecai Kurz).

[39] Core and Value for a Public Goods Economy: An Example. Journal of Economic Theory 15 (1977), 363–365 (with Roy J. Gardner and Robert W. Rosenthal).

[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 International Congress of Mathematicians, Helsinki, 1978, pp. 995–1003. Helsinki: Academia Scientiarum Fennica, 1980.

[42] Survey of Repeated Games. In V. Böhm (ed.), Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern, Vol. 4 of Gesellschaft, Recht, Wirtschaft, Wissen-schaftsverlag, pp. 11–42. Mannheim: Bibliographisches Institut, 1981.

[43] Approximate Purification of Mixed Strategies. Mathematics of Operations Research 8 (1983), 327–341 (with Yitzhak Katznelson, Roy Radner, Robert W. Rosenthal and Benjamin Weiss).

[44] Voting for Public Goods. Review of Economic Studies 50 (1983), 677–694 (with Mordecai Kurz and Abraham Neyman).

[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. Journal of Economic Theory 36 (1985), 195–213 (with Michael Maschler).

[47] What Is Game Theory Trying to Accomplish? In K. Arrow & 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. Israel Journal of Mathematics 54 (1986), 159–180 (with Sergiu Hart).

[51] Values of Markets with Satiation or Fixed Prices. Econometrica 54 (1986), 1271–1318 (with Jacques Drèze).

[52] Power and Public Goods. Journal of Economic Theory 42 (1987), 108–127 (with Modecai Kurz and Abraham Neyman).

[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 & P. Newman (eds.), The New Palgrave, A Dictionary of Economics, Vol. 2, pp. 460–482. London & Basingstoke: Macmillan, 1987.

[56] Endogenous Formation of Links between Players and of Coalitions: An Application of the Shapley Value. In A. E. Roth (ed.), The Shapley Value: Essays in Honor of Lloyd S. Shapley, pp. 175–191. Cambridge: Cambridge University Press, 1988 (with Roger Myerson).

[57] Cooperation and Bounded Recall. Games and Economic Behavior 1 (1989), 5–39 (with Sylvain Sorin).

[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 & L. Wolsey (eds.), Economic Decision Making: Games, Econometrics and Optimisation (Essays in honor of Jacques Drèze), pp. 201–206. Amsterdam: Elsevier Science Publishers, 1990.

[60] Irrationality in Game Theory. In P. Dasgupta, D. Gale, O. Hart & E. Maskin (eds.), Economic Analysis of Markets and Games (Essays in Honor of Frank Hahn), pp. 214–227. Cambridge and London: MIT Press, 1992.

[61] Long-Term Competition: A Game-Theoretic Analysis. In N. Megiddo (ed.), Essays in Game Theory in Honor of Michael Maschler, pp. 1–15. New York: Springer, 1994 (with Lloyd S. Shapley).

[62] The Shapley Value. In J.-F. Mertens & 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 & S. Sorin (eds.), Game-Theoretic Methods in General Equilibrium Analysis, pp. 121–133. Dordrecht: Kluwer Academic Publishers, 1994.

[64] Backward Induction and Common Knowledge of Rationality. Games and Economic Behavior 8 (1995), 6–19.

[65] Epistemic Conditions for Nash Equilibrium. Econometrica 63 (1995), 1161–1180 (with Adam Brandenburger).

[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 & 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 & C. Schmidt (eds.), The Rational Foundations of Economic Equilibrium, pp. 130–131. London and Basingstoke: Macmillan, 1996.

[69] The Absent-Minded Driver. Games and Economic Behavior 20 (1997), 102–116 (with Sergiu Hart and Motty Perry).

[70] The Forgetful Passenger. Games and Economic Behavior 20 (1997), 117–120 (with Sergiu Hart and Motty Perry).

[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. Journal of Evolutionary Economics 10 (2000), 437–447 (with Werner Güth).

[77] The Rationale for Measurability. In G. Debreu, W. Neuefeind & 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. In R. J. Aumann and S. Hart (eds.), Handbook of Game Theory with economic applications, Vol. 3, pp. 1665–1686. Amsterdam: Elsevier, 2002 (with Aviad Heifetz).

[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. Econometrica 71 (2003), 1619–1660 (with Sergiu Hart).
OTHER
[83] Letter to Leonard Savage, 8 January 1971. In J. H. Drèze, Essays on Economic Decisions under Uncertainty. Cambridge: Cambridge University Press, 1987, pp. 76–78.

[84] On the State of the Art in Game Theory, an Interview. W. Albers, W. Güth, P. Hammerstein, B. Moldovanu, and E. van Damme (eds.). Berlin: Springer, 1997, pp.8–34. Reprinted in Games and Economic Behavior 24 (1998), 181–210.

 To appear in Macroeconomic Dynamics. A shortened version is available at http://www.ma.huji.ac.il/hart/abs/aumann.html.

^ Center for the Study of Rationality, Department of Economics, and Department of Mathematics, The Hebrew University of Jerusalem, Feldman Building, Givat Ram Campus, 91904 Jerusalem, Israel.

E-mail: [e-mail] Web page: http://www.ma.huji.ac.il/hart