On the state of the art in game theory: An interview with Robert Aumann

Games and Economic Behavior

Volumn 24, Issue 1-2, 1998, Pages 181-210

  Van Damme, Eric ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012268635     PISSN: 08998256     EISSN: None     Source Type: Journal    
DOI: 10.1006/game.1997.0612     Document Type: Review

References (71)

1. In Frontiers of Economics (K. Arrow and S. Honkapohja, Eds.), Oxford: Basil Blackwell, 1985, pp. 28-76.
2. Genesis 1, 2. "Tohu" is sometimes translated as "formless." It seems to me that the idea of "form" is in the mind of the observer; there can be no form without an observer.
3. See P. Milgrom, Auction Theory for Privatization, Oxford: Oxford University Press (forthcoming).
4. R. Wilson, (1992) "Strategic Analysis of Auctions," in Handbook of Game Theory, Vol. 1, (R. Aumann and S. Hart, Eds.) Amsterdam: Elsevier, pp. 227-279.
5. "The Value of Information in a Sealed Bid Auction," Journal of Mathematical Economics 10 (1982), 105-114; see also R. Engelbrecht-Wiggins, P. Milgrom, and R. Weber (1983), "Competitive Bidding and Proprietary Information," Journal of Mathematical Economics 11, 161-169.
6. "The Value of Information in a Sealed Bid Auction," Journal of Mathematical Economics 10 (1982), 105-114; see also R. Engelbrecht-Wiggins, P. Milgrom, and R. Weber (1983), "Competitive Bidding and Proprietary Information," Journal of Mathematical Economics 11, 161-169.
7. "An Empirical Study of an Auction with Asymmetric Information," American Economic Review 78 (1988), 865-883.
8. D. Gale and L. Shapley (1962), "College Admissions and the Stability of Marriage," American Mathematical Monthly 69, 9-15.
9. A. Roth (1984), "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy 92, 991-1016.
10. See A. Roth and M. Sotomayor (1990), Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monograph Series, Cambridge: Cambridge University Press; A. Roth (1991), "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review 81, 415-440; and A. Roth and X. Xing (1994), "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Interactions," American Economic Review 84, 992-1004.
11. See A. Roth and M. Sotomayor (1990), Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monograph Series, Cambridge: Cambridge University Press; A. Roth (1991), "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review 81, 415-440; and A. Roth and X. Xing (1994), "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Interactions," American Economic Review 84, 992-1004.
12. See A. Roth and M. Sotomayor (1990), Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Econometric Society Monograph Series, Cambridge: Cambridge University Press; A. Roth (1991), "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review 81, 415-440; and A. Roth and X. Xing (1994), "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Interactions," American Economic Review 84, 992-1004.
13. See, e.g., G. Debreu and H. Scarf (1963), "A Limit Theorem on the Core of a Market," International Economic Review 4, 235-246; R. Aumann (1964), "Markets with a Continuum of Traders," Econometrica 32, 39-50; R. Aumann and L. Shapley (1974), Values of Non-Atomic Games, Princeton: Princeton University Press; and P. Champsaur (1975), "Cooperation versus Competition," Journal of Economic Theory 11, 394-417.
14. See, e.g., G. Debreu and H. Scarf (1963), "A Limit Theorem on the Core of a Market," International Economic Review 4, 235-246; R. Aumann (1964), "Markets with a Continuum of Traders," Econometrica 32, 39-50; R. Aumann and L. Shapley (1974), Values of Non-Atomic Games, Princeton: Princeton University Press; and P. Champsaur (1975), "Cooperation versus Competition," Journal of Economic Theory 11, 394-417.
15. See, e.g., G. Debreu and H. Scarf (1963), "A Limit Theorem on the Core of a Market," International Economic Review 4, 235-246; R. Aumann (1964), "Markets with a Continuum of Traders," Econometrica 32, 39-50; R. Aumann and L. Shapley (1974), Values of Non-Atomic Games, Princeton: Princeton University Press; and P. Champsaur (1975), "Cooperation versus Competition," Journal of Economic Theory 11, 394-417.
16. See, e.g., G. Debreu and H. Scarf (1963), "A Limit Theorem on the Core of a Market," International Economic Review 4, 235-246; R. Aumann (1964), "Markets with a Continuum of Traders," Econometrica 32, 39-50; R. Aumann and L. Shapley (1974), Values of Non-Atomic Games, Princeton: Princeton University Press; and P. Champsaur (1975), "Cooperation versus Competition," Journal of Economic Theory 11, 394-417.
17. R. Aumann and J. Kruskal (1959), "Assigning Quantitative Values to Qualitative Factors in the Naval Electronics Problem," Naval Research Logistics Quarterly 6, 1-16.
18. P. Hammerstein and S. Riechert (1988), "Payoffs and Strategies in Territorial Contests: ESS Analysis of Two Ecotypes of the Spider Agelenopsis Aperta," Evolutionary Ecology 2, 115-138.
19. R. Aumann and M. Maschler (1985), "Game Theoretic Analysis of a Bankruptcy Problem from the Talmud," Journal of Economic Theory 36, 195-213.
20. See, e.g., D. Kreps and J. Sobel (1994), "Signalling," in Handbook of Game Theory, Vol. 2 (R. Aumann and S. Hart, Eds.), Amsterdam: Elsevier, pp. 849-867.
21. See, e.g., J. Kennan and R. Wilson (1993), "Bargaining with Private Information," Journal of Economic Literature 31, 45-104; and R. Wilson (1994), "Negotiation with Private Information: Litigation and Strikes," Nancy L. Schwartz Lecture, J. L. Kellogg School of Management, Evanston, IL: Northwestern University.
22. See, e.g., J. Kennan and R. Wilson (1993), "Bargaining with Private Information," Journal of Economic Literature 31, 45-104; and R. Wilson (1994), "Negotiation with Private Information: Litigation and Strikes," Nancy L. Schwartz Lecture, J. L. Kellogg School of Management, Evanston, IL: Northwestern University.
23. J.-F. Mertens (1989), "Stable Equilibria - A Reformulation, Part I: Definition and Basic Properties," Mathematics of Operations Research 14, 575-625; and J.-F. Mertens (1989), "Stable Equilibria - A Reformulation, Part II: Discussion of the Definition and Further Results," Mathematics of Operations Research 16, 694-753.
24. J.-F. Mertens (1989), "Stable Equilibria - A Reformulation, Part I: Definition and Basic Properties," Mathematics of Operations Research 14, 575-625; and J.-F. Mertens (1989), "Stable Equilibria - A Reformulation, Part II: Discussion of the Definition and Further Results," Mathematics of Operations Research 16, 694-753.
25. S. Govindan and R. Wilson (1996), "A Sufficient Condition for the Invariance of Essential Components," Duke Journal of Mathematics 81, 39-46; see also R. Wilson (1992), "Computing Simply Stable Equilibria," Econometrica, 60, 1039-1070.
26. S. Govindan and R. Wilson (1996), "A Sufficient Condition for the Invariance of Essential Components," Duke Journal of Mathematics 81, 39-46; see also R. Wilson (1992), "Computing Simply Stable Equilibria," Econometrica, 60, 1039-1070.
27. R. Aumann (1987), "Game Theory," in The New Palgrave, Vol. II (J. Eatwell, M. Milgate, and P. Newman, Eds.), London: Macmillan, pp. 460-482. See specifically Subsection ii of the section entitled 1970-1986, on page 477, near the bottom of the left column.
28. W. Güth, R. Schmittberger, and B. Schwarze (1982), "An Experimental Analysis of Ultimatum Bargaining," Journal of Economic Behavior and Organization 3, 367-388. In this experiment, two players were asked to divide a considerable sum (varying as high as DM 100). The procedure was that P1 made an offer, which could be either accepted or rejected by P2; if it was rejected, nobody got anything. The players did not know each other and never saw each other; communication was a one-time affair via computer. The only subgame perfect equilibria of this game lead to a split of 99-1 or 100-0. But there are many Nash equilibria, of the form "P1 offers x, P2 rejects anything below x."
29. "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study," American Economic Review 81 (1991), 1068-1095. Roughly speaking, it was found in this experiment that in each of the four different venues, the accepted offers clustered around some specific x, which differed in the different venues.
30. The Selfish Gene, Oxford: Oxford University Press, 1976.
31. Cambridge, MA: Belknap Press, 1982.
32. See, e.g., J. Ferejohn and J. Kuklinski (Eds.) (1990), Information and Democratic Processes, Urbana, IL: University of Illinois Press.
33. Of course, as we mentioned, voting also has a cooperative side.
34. Op. cit. (Footnotes 8 and 9).
35. A Course in Game Theory, Cambridge, MA: MIT Press, 1995.
36. A. Rubinstein (1982), "Perfect Equilibrium in a Bargaining Model," Econometrica 50, 97-109.
37. "Nash Bargaining Theory II," in The Economics of Bargaining (K. G. Binmore and P. Dasgupta, Eds.), Oxford: Basil Blackwell, 1987, pp. 61-76.
38. "Values of Markets with Satiation or Fixed Prices," Econometrica 54 (1986), 1271-1318.
39. That is, the equivalence between competitive equilibrium in markets and game theoretic concepts like core and value.
40. "Games '95," Jerusalem.
41. Op. cit. (Footnote 18).
42. "On the Strategic Stability of Equilibrium," Econometrica 54 (1986), 1003-1034.
43. "The Bargaining Problem," Econometrica 18 (1950), 155-162.
44. "Persistent Equilibria in Strategic Games," International Journal of Game Theory 13 (1984), 129-144.
45. Op. cit. (Footnote 33).
46. D. Kreps and R. Wilson (1982), "Sequential Equilibrium," Econometrica 50, 863-894.
47. Op. cit. (Footnote 35).
48. "Signaling Games and Stable Equilibria," Quarterly Journal of Economics 102 (1987), 179-221.
49. A. Spence (1974), Market Signaling, Cambridge, MA: Harvard University Press.
50. Op. cit. (Footnote 33).
51. Op. cit. (Footnote 14).
52. Op. cit. (Footnote 16).
53. "Subjectivity and Correlation in Randomized Strategies," Journal of Mathematical Economics 1 (1974), 67-96.
54. Games and Economic Behavior 7 (1995), 6-19.
55. Op. cit. (Footnote 18).
56. H. Norde, J. Potters, H. Reynierse, and D. Vermeulen (1996), "Equilibrium Selection and Consistency," Games and Economic Behavior 12, 219-225.
57. J. Harsanyi and R. Selten (1988), A General Theory of Equilibrium Selection in Games, Cambridge, MA: MIT Press.
58. "Epistemic Conditions for Nash Equilibrium," Econometrica 63 (1995), 1161-1180.
59. "On the Non-Transferable Utility Value: A Comment on the Roth-Shafer Examples," Econometrica 53 (1985), 667-677; see specifically Section 8, 674-675.
60. They might answer that I'm making too much of a degenerate, nongeneric example. But that misses the point. Suppose we perturb the payoffs very slightly, so that the Harsanyi-Selten selection is pure. I would still select (L,L) in England and (R,R) in the Netherlands. They, of course, would select the same in both countries. That's almost as crazy.
61. W. Güth and H. Kliemt, "On the Justification of Strategic Equilibrium - Rationality Requirements versus Conceivable Adaptive Processes," DP 46, Economics Series, Humboldt University, Berlin, 1995.
62. Unpublished. See also S. H. Schanuel, L. K. Simon, and W. R. Zame (1991), "The Algebraic Geometry of Games and the Tracing Procedure," in Game Equilibrium Models II (R. Selten, Ed.), Berlin: Springer-Verlag.
63. See the Selfish Gene, op. cit. (Footnote 21).
64. Economic Analysis of Markets and Games, Essays in Honor of Frank Hahn (P. Dasgupta, D. Gale, O. Hart, and E. Maskin, Eds.), Cambridge, MA: MIT Press, 1992, pp. 214-227.
65. Op. cit. (Footnote 45).
66. "A Note on Evolutionarily Stable Strategies in Asymmetric Animal Conflicts," Journal of Theoretical Biology 84 (1980), 93-101; and "Evolutionary Stability in Extensive Two-Person Games," Mathematical Social Sciences 5 (1983), 269-363 (see also "Correction and Further Development," Mathematical Social Sciences 16 (1988), 223-266).
67. "A Note on Evolutionarily Stable Strategies in Asymmetric Animal Conflicts," Journal of Theoretical Biology 84 (1980), 93-101; and "Evolutionary Stability in Extensive Two-Person Games," Mathematical Social Sciences 5 (1983), 269-363 (see also "Correction and Further Development," Mathematical Social Sciences 16 (1988), 223-266).
68. "A Note on Evolutionarily Stable Strategies in Asymmetric Animal Conflicts," Journal of Theoretical Biology 84 (1980), 93-101; and "Evolutionary Stability in Extensive Two-Person Games," Mathematical Social Sciences 5 (1983), 269-363 (see also "Correction and Further Development," Mathematical Social Sciences 16 (1988), 223-266).
69. J. Maynard Smith (1982), Evolution and the Theory of Games, Cambridge: Cambridge University Press.
70. R. Selten (1964), "Valuation of n-Person Games," in Advances in Game Theory, Annals of Mathematics Study 52 (R. D. Luce, L. S. Shapley, and A. W. Tucker, Eds.), Princeton: Princeton University Press, pp. 577-627.
71. J. Harsanyi (1963), "A Simplified Bargaining Model for the n-Person Cooperative Game," International Economic Review 4, 194-220.