Abraham Neyman

Last updated
Abraham Neyman
Born (1949-06-14) June 14, 1949 (age 74)
Israel
Alma mater Hebrew University of Jerusalem
Scientific career
Fields Mathematics
Game theory
InstitutionsHebrew University of Jerusalem
Doctoral advisor Robert Aumann

Abraham Neyman (born June 14, 1949, Israel) is an Israeli mathematician and game theorist, Professor of Mathematics at the Federmann Center for the Study of Rationality [1] and the Einstein Institute of Mathematics [2] at the Hebrew University of Jerusalem in Israel. He served as president of the Israeli Chapter of the Game Theory Society (2014–2018). [3]

Contents

Biography

Neyman received his BSc in mathematics in 1970 and his MSc in mathematics in 1972 from the Hebrew University. His MSc thesis was on the subject of “The Range of a Vector Measure” and was supervised by Joram Lindenstrauss. His PhD thesis, "Values of Games with a Continuum of Players," was completed under Robert Aumann in 1977. [4]

Neyman has been professor of mathematics at the Hebrew University since 1982, including serving as the chairman of the institute of mathematics 1992–1994, as well as holding a professorship in economics, 1982–1990. He has been a member of the Center for the Study of Rationality at the Hebrew University since its inception in 1991. He held various positions at Stony Brook University of New York, 1985–2001. He has also held positions and has been visiting scholar at Cornell University, University of California at Berkeley, Stanford University, the Graduate School of Business Administration at Harvard University, and Ohio State University. [5] [6] [7]

Neyman has had 12 graduate students complete Ph.D. theses under his supervision, five at Stony Brook University and seven at the Hebrew University. [8] Neyman has also served as the Game Theory Area Editor for the journal Mathematics of Operations Research (1987–1993) and on the editorial board for Games and Economic Behavior (1993–2001) and the International Journal of Game Theory (2001–2007).

Awards and honors

Neyman has been a fellow of the Econometric Society since 1989. [9]

The Game Theory Society released, in March 2016, a special issue of the International Journal of Game Theory in honour of Neyman, "in recognition of his important contributions to game theory". [10] A Festschrift conference in Neyman's honour was held at Hebrew University in June 2015, on the occasion of Neyman's 66th birthday. [11] He gave the inaugural von-Neumann lecture [12] at the 2008 Congress of the Game Theory Society [13] as well as delivering it at the 2012 World Congress on behalf of the recently deceased Jean-Francois Mertens. [14]

His Ph.D. thesis won two prizes from the Hebrew University: the 1977 Abraham Urbach prize for distinguished thesis in mathematics and the 1979 Aharon Katzir prize (for the best Ph. D. thesis in the Faculties of Exact Science, Mathematics, Agriculture and Medicine). In addition, Neyman won the Israeli under 20 chess championship in 1966.

Research contributions

Neyman has made numerous contributions to game theory, including to stochastic games, the Shapley value, and repeated games.

Stochastic games

Together with Jean-Francois Mertens, he proved the existence of the uniform value of zero-sum undiscounted stochastic games. [15] This work is considered one of the most important works in the theory of stochastic games, solving a problem that had been open for over 20 years. [16] Together with Elon Kohlberg, he applied operator techniques to study convergence properties of the discounted and finite stage values. [17] Recently, he has pioneered a model of stochastic games in continuous time and derived uniform equilibrium existence results. [18] He also co-edited, together with Sylvain Sorin, a comprehensive collection of works in the field of stochastic games. [19]

Repeated games

Neyman has made many contributions to the theory of repeated games. One idea that appears, in different contexts, in some of his papers, is that the model of an infinitely repeated game serves also as a powerful paradigm for a long finitely repeated game. A related insight appears in a 1999 paper, where he showed that in a long finitely repeated game, an exponentially small deviation from common knowledge of the number of repetitions is enough to dramatically alter the equilibrium analysis, producing a folk-theorem-like result. [20]

Neyman is one of the pioneers and a most notable leader of the study of repeated games under complexity constraints. In his seminal paper [21] he showed that bounded memory can justify cooperation in a finitely repeated prisoner's dilemma game. His paper was followed by many others who started working on bounded memory games. Most notable was Neyman's M.Sc. student Elchanan Ben-Porath who was the first to shed light on the strategic value of bounded complexity. [22]

The two main models of bounded complexity, automaton size and recall capacity, continued to pose intriguing open problems in the following decades. A major breakthrough was achieved when Neyman and his Ph.D. student Daijiro Okada proposed a new approach to these problems, based on information theoretic techniques, introducing the notion of strategic entropy. [23] [24] His students continued to employ Neyman's entropy technique to achieve a better understanding of repeated games under complexity constraints. Neyman's information theoretic approach opened new research areas beyond bounded complexity. A classic example is the communication game he introduced jointly with Olivier Gossner and Penelope Hernandez. [25]

The Shapley value

Neyman has made numerous fundamental contributions to the theory of the value. In a "remarkable tour-de-force of combinatorial reasoning", [26] he proved the existence of an asymptotic value for weighted majority games. [27] The proof was facilitated by his fundamental contribution to renewal theory. [28] In subsequent work Neyman proved that many of the assumptions made in these works can be relaxed, while showing that others are essential.

Neyman proved the diagonality of continuous values, [29] which had many implications on further developments of the theory. Together with Pradeep Dubey and Robert James Weber he studied the theory of semivalues, and separately demonstrated its importance in political economy. [30] [31] Together with Pradeep Dubey [32] [33] he characterized the well-known phenomenon of value correspondence, a fundamental notion in economics, originating already in Edgeworth's work and Adam Smith before him. In loose terms, it essentially states that in a large economy consisting of many economically insignificant agents, the core of the economy coincides with the perfectly competitive outcomes, which in the case of differentiable preferences is a unique element that is the Aumann–Shapley value. Another major contribution of Neyman was the introduction of the Neyman value, [34] a far-reaching generalization of the Aumann–Shapley value to the case of non-differentiable vector measure games.

Other

Neyman has made contributions to other fields of mathematics, usually motivated by problems in game theory. Among these contributions are a renewal theorem for sampling without replacement (mentioned above as applied to the theory of the value), contributions to embeddings of Lp spaces, [35] contributions to the theory of vector measures, [36] and to the theory of non-expansive mappings. [37]

Business involvements

Neyman previously served (2005–8) as director at Tradus (previously named QXL). [38] He also held a directorship (2004–5) at Gilat Satellite Networks. [39] In 1999, Neyman co-founded Bidorbuy, the first online auction company to operate in India and in South Africa, and serves as the chairman of the board. [40] Since 2013, he has held a directorship at the Israeli bank Bank Mizrahi-Tefahot. [41]

Related Research Articles

<span class="mw-page-title-main">Shapley value</span> Concept in game theory

The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. To each cooperative game it assigns a unique distribution of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties. Hart (1989) provides a survey of the subject.

In game theory, a cooperative game is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior. Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing.

<span class="mw-page-title-main">Lloyd Shapley</span> American mathematician (1923–2016)

Lloyd Stowell Shapley was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design."

In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition. One can think of the core corresponding to situations where it is possible to sustain cooperation among all agents. A coalition is said to improve upon or block a feasible allocation if the members of that coalition can generate more value among themselves than they are allocated in the original allocation. As such, that coalition is not incentivized to stay with the grand coalition.

<span class="mw-page-title-main">Robert Aumann</span> Israeli-American mathematician

Robert John Aumann is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory.

Hobart Peyton Young is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learning in games. He is currently centennial professor at the London School of Economics, James Meade Professor of Economics Emeritus at the University of Oxford, professorial fellow at Nuffield College Oxford, and research principal at the Office of Financial Research at the U.S. Department of the Treasury.

In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization of the concept of finite measure, which takes nonnegative real values only.

In game theory, an epsilon-equilibrium, or near-Nash equilibrium, is a strategy profile that approximately satisfies the condition of Nash equilibrium. In a Nash equilibrium, no player has an incentive to change his behavior. In an approximate Nash equilibrium, this requirement is weakened to allow the possibility that a player may have a small incentive to do something different. This may still be considered an adequate solution concept, assuming for example status quo bias. This solution concept may be preferred to Nash equilibrium due to being easier to compute, or alternatively due to the possibility that in games of more than 2 players, the probabilities involved in an exact Nash equilibrium need not be rational numbers.

In game theory, a stochastic game, introduced by Lloyd Shapley in the early 1950s, is a repeated game with probabilistic transitions played by one or more players. The game is played in a sequence of stages. At the beginning of each stage the game is in some state. The players select actions and each player receives a payoff that depends on the current state and the chosen actions. The game then moves to a new random state whose distribution depends on the previous state and the actions chosen by the players. The procedure is repeated at the new state and play continues for a finite or infinite number of stages. The total payoff to a player is often taken to be the discounted sum of the stage payoffs or the limit inferior of the averages of the stage payoffs.

<span class="mw-page-title-main">Pradeep Dubey</span> Indian academic (born 1951)

Pradeep Dubey is an Indian game theorist. He is a Professor of Economics at the State University of New York, Stony Brook, and a member of the Stony Brook Center for Game Theory. He also holds a visiting position at Cowles Foundation, Yale University. He did his schooling at the St. Columba's School, Delhi. He received his Ph.D. in applied mathematics from Cornell University and B.Sc. from the University of Delhi. His research areas of interest are game theory and mathematical economics. He has published, among others, in Econometrica, Games and Economic Behavior, Journal of Economic Theory, and Quarterly Journal of Economics. He is a Fellow of The Econometric Society, ACM Fellow and a member of the council of the Game Theory Society.

<span class="mw-page-title-main">Yair Tauman</span> American economist

Yair Tauman is a Professor of Economics at State University of New York, Stony Brook and the Director of the Stony Brook Center for Game Theory. He studied at the Hebrew University of Jerusalem where he obtained his B.Sc. in Mathematics and Statistics and M.Sc. and Ph.D. in Mathematics, the latter two under the supervision of Robert Aumann. His areas of research interests are game theory and industrial organization. He has published, among others, in Econometrica, Games and Economic Behavior, Journal of Economic Theory, Quarterly Journal of Economics and RAND Journal of Economics.

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References

  1. ↑ Center for the Study of Rationality Members
  2. ↑ Einstein Institute of Mathematics Faculty
  3. ↑ Game Theory Society, announced April 9, 2014
  4. ↑ Mathematics Genealogy Project
  5. ↑ The Division for Development and Public Relations, Hebrew University of Jerusalem
  6. ↑ Bloomberg Business Week Executive Profile
  7. ↑ Personal CV Archived July 12, 2014, at the Wayback Machine
  8. ↑ Mathematics Genealogy Project
  9. ↑ Econometric Society Fellows Archived 2008-12-10 at the Wayback Machine
  10. ↑ Special issue in honor of Abraham Neyman, Gossner, O., Haimanko, O. & Solan, E. Int J Game Theory (2016) 45: 3
  11. ↑ Festschrift conferences in honor of Abraham Neyman and Sergiu Hart on the occasion of their 66th birthday
  12. ↑ The John von Neumann Lecture, given at each World Congress of the Game Theory Society, presents important developments in game theory that are of significant mathematical interest. Archived 2013-12-30 at the Wayback Machine
  13. ↑ "2008 World Games Conference Program". Archived from the original on 2022-01-05. Retrieved 2014-07-17.
  14. ↑ 2012 World Games Conference Program
  15. ↑ Mertens, J.F., and Neyman, A. (1981). "Stochastic Games," International Journal of Game Theory, 10: 53–66.
  16. ↑ Review by Tijs, H.S., MathSciNet
  17. ↑ Kohlberg, E. and Neyman, A (1981)., "Asymptotic Behavior of Nonexpansive Mappings in Normed Linear Spaces," Israel Journal of Mathematics, 38, pp. 269–275.
  18. ↑ Neyman, A. (2017), "Continuous-Time Stochastic Games," Games and Economic Behaviour, 104, pp. 92-130.
  19. ↑ Nato Science Series: Mathematical and Physical Sciences, Volume 570, Proceedings of the NATO Advanced Study Institute on Stochastic Games and Applications (Neyman, A. and Sorin, S. (eds)), held in Stony Brook, NY during July 7–17, 1999.
  20. ↑ Neyman, A. (1999), "Cooperation in Repeated Games when the Number of Stages is not Commonly Known," Econometrica, 67: 45–64.
  21. ↑ Neyman, A. (1985) "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma." Economics Letters, 19(3), 227–229.
  22. ↑ Ben-Porath, E. (1993) "Repeated games with finite automata." Journal of Economic Theory, 59(1), 17–32.
  23. ↑ Neyman, A. and Okada, D. (1999). "Strategic entropy and complexity in repeated games." Games and Economic Behavior, 29(1), 191–223.
  24. ↑ Neyman, A., & Okada, D. (2000). "Repeated games with bounded entropy." Games and Economic Behavior, 30(2), 228–247.
  25. ↑ Gossner, O., Hernandez, P., and Neyman, A. (2006). "Optimal use of communication resources." Econometrica, 74(6), 1603–1636.
  26. ↑ Aumann, R.J. (1980), "Recent Developments in the Theory of the Shapley Value", Proceedings of the International Congress of Mathematicians, Helsinki, 1978, pp. 995–1003, Academia Scientiarum Fennica
  27. ↑ Neyman, A., 1981, "Singular games have asymptotic values," Mathematics of Operations Research, 6, pp 205–212.
  28. ↑ Neyman, A., 1982, "Renewal theory for sampling without replacement," Annals of Probability, 10, pp 464–481.
  29. ↑ Neyman, A., 1977, "Continuous values are diagonal," Mathematics of Operations Research, 2, pp 338–342
  30. ↑ Dubey, P., Neyman, A., and Weber, R.J., 1981, "Value theory without efficiency," Mathematics of Operations Research, 6, pp 122–128
  31. ↑ Neyman, A., 1985, "Semi-values of political economic games," Mathematics of Operations Research, 10, pp 390–402
  32. ↑ Dubey. P. and Neyman, A., 1984, "Payoffs in nonatomic economies: An axiomatic approach," Econometrica, 52, pp 1129–1150
  33. ↑ Dubey, P. and Neyman, A., 1997, "An equivalence principle for perfectly competitive economies," Journal of Economic Theory, 75, pp 314–344
  34. ↑ Neyman, A., 2001, "Values of non-atomic vector measure games," Israel Journal of Mathematics, 124, pp 1–27
  35. ↑ Neyman, A. (1984), “Representation of Lp-Norms and Isometric Embedding in Lp–Spaces,” Israel Journal of Mathematics, 48, pp. 129–138.
  36. ↑ Neyman, A. (1981) “Decomposition of Ranges of Vector Measures,” Israel Journal of Mathematics, 40, pp. 54–64
  37. ↑ Kohlberg, E. and Neyman, A. (1999), “A Strong Law of Large Numbers for Nonexpansive Vector-Valued Stochastic Processes,” Israel Journal of Mathematics, 111, pp. 93–108
  38. ↑ Profile at Opencorporates Archived July 27, 2014, at the Wayback Machine
  39. ↑ "Wikinvest". Archived from the original on 2017-12-01. Retrieved 2014-07-11.
  40. ↑ FE Investigate
  41. ↑ Mizrahi Tefahot Bank Ltd, Officers and Directors
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