The present and future of game theory
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 1, pp. 93-116.

Voir la notice de l'article provenant de la source Math-Net.Ru

A broad nontechnical coverage of many of the developments in game theory since the 1950s is given together with some comments on important open problems and where some of the developments may take place. The nearly 90 references given serve only as a minimal guide to the many thousands of books and articles that have been written. The purpose here is to present a broad brush picture of the many areas of study and application that have come into being. The use of deep techniques flourishes best when it stays in touch with application. There is a vital symbiotic relationship between good theory and practice. The breakneck speed of development of game theory calls for an appreciation of both the many realities of conflict, coordination and cooperation and the abstract investigation of all of them.
Keywords: game theory, application and theory, law, experimental gaming, conflict, coordination and cooperation.
Mots-clés : social sciences
@article{MGTA_2012_4_1_a5,
     author = {Martin Shubik},
     title = {The present and future of game theory},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {93--116},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2012_4_1_a5/}
}
TY  - JOUR
AU  - Martin Shubik
TI  - The present and future of game theory
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2012
SP  - 93
EP  - 116
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2012_4_1_a5/
LA  - ru
ID  - MGTA_2012_4_1_a5
ER  - 
%0 Journal Article
%A Martin Shubik
%T The present and future of game theory
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2012
%P 93-116
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2012_4_1_a5/
%G ru
%F MGTA_2012_4_1_a5
Martin Shubik. The present and future of game theory. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 1, pp. 93-116. http://geodesic.mathdoc.fr/item/MGTA_2012_4_1_a5/

[1] Aghion P., Holder R., “Incomplete Contracts and the Theory of the Firm: What Have We Learned over the Past 25 Years?”, Journal of Economic Perspectives, 25:2 (2001), 181–197 | DOI

[2] Akerlof G. A., “The Market for “Lemons”: Quality Uncertainty and the Market Mechanism”, Quarterly Journal of Economics, 84:3 (1970), 488–500 | DOI

[3] Allen F., Morris S., “Game Theory and Finance Applications”, Advances in Business Applications of Game Theory, eds. K. Chatterjee, W. F. Samuelson, Kluwer Academic Press, 2001

[4] Arrow K. J., Social Choice and Individual Values, 2nd ed. (first published, 1951), John Wiley, New York, 1963 | MR

[5] Aumann R. J., “Agreeing to Disagree”, Annals of Statistics, 4:6 (1976), 1236–1239 | DOI | MR | Zbl

[6] Baird D., Gertner R., Picker R., Game Theory and the Law, Harvard University Press, Cambridge, 1994

[7] Balinski M., Lahiri R., Majority Judgment, MIT Press, Cambridge, 2011

[8] Banzhaf J. F., “Weighted Voting Doesn't Work: A Mathematical Analysis”, Rutgers Law Review, 19:2 (1965), 317–343

[9] Barth F., “Segmentary Opposition and the Theory of Games: A Study of Pathan Organization”, Journal of the Royal Anthropological Institute of Great Britain and Ireland, 89 (1959), 5–21 | DOI

[10] Bebchuk L. A., Asymmetric Information and the Choice of Corporate Governance Arrangements, Harvard Law and Economics Discussion Paper No. 398, 2002

[11] Blaquiere A. (ed.), Topics in Differential Games, North Holland, Amsterdam, 1973 | MR | Zbl

[12] Blume L. E., “The Statistical Mechanics of Strategic Interaction”, Games and Economic Behavior, 5 (1993), 387–424 | DOI | MR | Zbl

[13] Bracken J., Shubik M., “Worldwide Nuclear Coalition Games: A Valuation of Strategic Offensive and Defensive Forces”, Operations Research, 41:4 (1993), 655–668 | DOI | Zbl

[14] Brams S. J., Superior Beings: If They Exist, How Would We Know?, Game-theoretic Implications of Omniscience, Omnipotence, Immortality, and Incomprehensibility, Springer-Verlag, New York, 1983. | MR

[15] Cooper R., Coordination Games: Complementarities and economics, Cambridge University Press, Cambridge, 1999

[16] Cournot A. A., Researches into the Mathematical Principles of the Theory of Wealth, Bacon Translation of original 1838 French, Macmillan, New York, 1897 | Zbl

[17] Debreu G., “The Coefficient of Resource Utilization”, Econometrica, 19:3 (1951), 273–329 | DOI

[18] Debreu G., Scarf H., “A Limit Theorem on the Core of an Economy”, International Economic Review, 4 (1963), 235–246 | DOI | Zbl

[19] Dubey P., “Price-quantity Strategic Market Games”, Econometrica, 50:1 (1982), 111–126 | DOI | MR | Zbl

[20] Dubey P., Rogawski J. D., “Inefficiency of Smooth Market Mechanisms”, Journal of Mathematical Economics, 19 (1990), 285–304 | DOI | MR | Zbl

[21] Edgeworth F. Y., Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, (reprinted Augustus M. Kelley, New York, 1967), Kegan Paul, London, 1881

[22] Epstein J. L., Axtell R., Growing Artificial Societies: Social Science from the Bottom Up, MIT Press, Cambridge, 1996

[23] Farquharson R., Theory of Voting, Blackwell, Yale University Press, 1969 | MR

[24] Fishburn P. C., Utility Theory for Decision-making, Wiley, New York, 1970 | MR | Zbl

[25] Foley D., Smith E., Classical Thermodynamics and Economic General Equilibrium Theory, Research Paper December 15, 2005, Santa Fe Institute, 2005

[26] Friedman J., Oligopoly Theory, Cambridge University Press, New York, 1983

[27] Friedman D., Rust J. (eds.), The Double Auction Market: Institutions, Theories, and Evidence, Addison-Wesley, Reading, 1993

[28] Gale D., Shapley L. S., “College Admissions and the Stability of Marriage”, American Mathematics Monthly, 69 (1962), 9–15 | DOI | MR | Zbl

[29] Gardner M., “Mathematical Games: The Fantastic Combinations of John Conway's New Solitaire Game ‘Life’ ”, Scientific American, 223 (1970), 120–123 | DOI

[30] Gilboa I., Zemel E., “Nash and Correlated Equilibria: Some Complexity Considerations”, Games and Economic Behavior, 1 (1989), 80–93 | DOI | MR | Zbl

[31] Halpern J. Y., “A Computer Scientist Looks at Game Theory”, Games and Economic Behavior, 45 (2003), 114–131 | DOI | Zbl

[32] Halpern J. Y., “Computer Science and Game Theory: A Brief Survey”, Palgrave Dictionary of Economics, 2008

[33] Harsanyi J. C., “A Bargaining Model for the Cooperative Game”, Contributions to the Theory of Games, v. 4, eds. A. W. Tucker, R. D. Luce, Princeton University Press, Princeton, 1959, 324–356 | MR

[34] Harsanyi J. C., “Games with Incomplete Information Played by “Bayesian” Players, Parts I. The Basic Model”, Management Science, 14:3 (1967), 159–182 ; “Parts II. Bayesian Equilibrium Points”, Management Science, 14:5 (1968), 320–334 ; “Parts III. The Basic Probability Distribution of the Game”, Management Science, 14:7 (1968), 486–502 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[35] Hart O., Moore J., “Incomplete Contracts and Renegotiation”, Econometrica, 56:4 (1988), 755–785 | DOI | MR | Zbl

[36] Huber J., Shubik M., Sunder S., Everyone-a-banker or the Ideal Credit Acceptance Game: Theory and Evidence, Cowles Foundation Discussion Paper 1622, Yale University, 2007

[37] Hurwicz L., “But Who Will Guard the Guardians?”, American Economic Review, 98:3 (2008), 577–585 | DOI

[38] Isaacs R., Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, Dover Publications, New York, 1999 | Zbl

[39] Karatzas I., Shubik M., Sudderth W., “Construction of Stationary Markov Equilibria in a Strategic Market Game”, Journal of Mathematical Operations Research, 19:4 (1994), 975–1006 | DOI | MR | Zbl

[40] Leonard R., Von Neumann, Morgenstern, and the Creation of Game Theory, Cambridge University Press, Cambridge, 2010 | MR

[41] Lewontin R. C., “Evolution and the Theory of Games”, Journal of Theoretical Biology, 1 (1961), 382–403 | DOI

[42] Littlechild S. C., Thompson G. F., “Aircraft Landing Fees: A Game Theory Approach”, Bell Journal of Economics, 8 (1977), 186–204 | DOI

[43] Lucas W. F., “A Game with No Solution”, Bulletin of the American Mathematical Society, 74 (1968), 237–239 | DOI | MR | Zbl

[44] Luce R. D., Krantz D. M., Suppes P., Tversky A., Foundations of Measurement, v. 1, 1971; v. 2, 1989; v. 3, 1990

[45] Maskin E. S., “Mechanism Design: How to Implement Social Goals”, American Economic Review, 98:3 (2008), 567–576 | DOI

[46] Maynard Smith J., Evolution and the Theory of Games, Cambridge University Press, Cambridge, 1982 | Zbl

[47] Milgrom P., Putting Auction Theory to Work, Cambridge University Press, Cambridge, UK, 2004 | MR

[48] Myerson R. B., “Mechanism Design”, The New Palgrave Dictionary of Economics, Second Edition, eds. S. N. Durlauf, L. E. Blume, 2008

[49] Nash J. F., “Non-Cooperative Games”, Annals of Mathematics, 54 (1951), 286–295 | DOI | MR | Zbl

[50] Nash J. F., “The Bargaining Problem”, Econometrica, 18 (1950), 155–162 | DOI | MR | Zbl

[51] O'Neill B., Honor, Symbols and War, University of Michigan Press, Ann Arbor, 1999

[52] Papadimitriou C. H., Algorithms, Games, and the Internet, Presented at STOC/ICALP 2001. A survey of algorithmic problems related to Game Theory and the Internet, 2001 | MR

[53] Plott C. R., Public Economics, Political Processes and Policy Applications, Collected Papers on the Experimental Foundations of Economics and Political Science, v. I, Edward Elgar Publishing, Cheltenham, UK, 2001

[54] Rapoport A., Guyer M. J., Gordon D. G., The $2\times2$ Game, University of Michigan Press, Ann Arbor, 1976

[55] Rasmusen E., “Law and Game Theory”, The series Economic Approaches to Law, eds. R. A. Posner, F. Paris, Edward Elgar, 2007

[56] Roth A. E., Sotomayor M., Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, Cambridge University Press, Cambridge, 1990 | MR | Zbl

[57] Rothblum U. G., “Bounding the Inefficiency of Nash Equilibria in Games with Finitely Many Players”, Operations Research Letters, 35 (2007), 700–706 | DOI | MR | Zbl

[58] Roughgarden T., “The Price of Anarchy Is Independent of the Network Topology”, Journal of Computer System Science, 67 (2002), 341–364 | DOI | MR

[59] Rubinstein A., Economics and Language, Cambridge University Press, Cambridge, 2000

[60] Rubinstein A., “Finite Automata Play the Repeated Prisoner's Dilemma”, Journal of Economic Theory, 39 (1986), 83–96 | DOI | MR | Zbl

[61] Rubinstein A., Modeling Bounded Rationality, MIT Press, Cambridge, 1996

[62] Salanié B., The Economics of Contracts, MIT Press, Cambridge–London, 1997

[63] Schelling T. C., The Strategy of Conflict, Harvard University Press, Cambridge, 1960

[64] Shapley L. S., “A Value for $n$-Person Games”, Contributions to the Theory of Games, v. 2, eds. H. W. Kuhn, A. W. Tucker, Princeton University Press, Princeton, 1953, 307–317 | MR

[65] Shapley L. S., Rand Corporation research memorandum, Notes on the $N$-Person Game III: Some Variants of the von-Neumann-Morgenstern Definition of Solution, RM-817, 1952

[66] Shapley L. S., $n$-Person Games – Stable-Set Solutions Including an Arbitrary Closed Component, Rand Corporation, Santa Monica, 1952

[67] Shapley L. S., Shubik M., “A Method for Evaluating the Distribution of Power in a Committee System”, American Political Science Review, 48:3 (1954), 787–792 | DOI

[68] Shapley L. S., Shubik M., “The Assignment Game. I: The Core”, International Journal of Game Theory, 1 (1971), 111–130 | DOI | MR | Zbl

[69] Shapley L. S., Shubik M., “Trade Using One Commodity as a Means of Payment”, Journal of Political Economy, 85:5 (1977), 937–968 | DOI

[70] Shubik M., “A Game Theorist Looks at the Antitrust Laws and the Automobile Industry”, Stanford Law Review, 8:4 (1956), 594–630 | DOI

[71] Shubik M., Budgets in a Decentralized Organization with Incomplete Information, P1252, Rand Corporation, Santa Monica, 1970

[72] Shubik M., “Commodity Money, Oligopoly, Credit and Bankruptcy in a General Equilibrium Model”, Western Economic Journal, 11:1 (1973), 24–38

[73] Shubik M., “Edgeworth Market Games”, Contributions to the Theory of Games, v. 4, Annals of Mathematics Studies, 40, eds. A. W. Tucker, R. D. Luce, Princeton University Press, Princeton, 1959, 267–278 | MR

[74] Shubik M., “Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing”, Management Science, 8 (1962), 325–343 | DOI | MR | Zbl

[75] Shubik M. (ed.), Readings in Game Theory and Political Behavior, Doubleday, New York, 1954

[76] Shubik M., “Some Experimental Non Zero Sum Games with Lack of Information about the Rules”, Management Science, 8:2 (1962), 215–234 | DOI | MR | Zbl

[77] Shubik M., Strategy and Market Structure, Wiley, New York, 1959 | MR | Zbl

[78] Shubik M., “The Games within the Game: Modeling Politico-Economic Structures”, Guidance, Control, and Evaluation in the Public Sector, Part 5, eds. F.-X. Kaufmann, G. Majone, V. Ostrom, Walter de Gruyter, Berlin–New York, 1986

[79] Shubik M., The Theory of Money and Financial Institutions, v. 3, MIT Press, Cambridge, 2011

[80] Siegal S., Fouraker L. S., Bargaining and Group Decision Making. Experiments in Bilateral Monopoly, McGraw-Hill, New York, 1960

[81] Smith V., Research in Experimental Economics, v. I, JAI Press, Greenwich, CT, 1979

[82] Tirole J., The Theory of Industrial Organization, MIT Press, Cambridge, 1988

[83] von Neumann J., Morgenstern O., Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944 | MR | Zbl

[84] von Neumann J., Morgenstern O., Theory of Games and Economic Behavior, Second edition, Princeton University Press, Princeton, 1947 | MR | Zbl

[85] Weibull J. W., Evolutionary Game Theory, MIT Press, Cambridge, 1995 | MR | Zbl

[86] Zeuthern F., Problems of Monopoly and Economic Warfare, G. Routledge Sons, London, 1930