Tag Archives: Game theory

A Historical Picture Taken by Nimrod Megiddo

Last week I took a bus from Tel Aviv to Jerusalem and I saw (from behind) a person that I immediately recognized. It was Nimrod Megiddo, from IBM Almaden, one of the very first  to relate game theory with complexity theory, one of the pioneers of computational geometry, and one of the leaders in optimization and linear programming, the guy who (with Ehud Kalai) was the first to  invited me to an international conference, and a fresh Laureate of the John von Neumann theory Prize.  I did not see Nimrod more than a year after our last coincidental  meeting at the Berkeley Simons Institute, I called over to him and he was happy to see me as I was happy to see him, and we found a place together at the back of the bus and caught up on things.

Nimrod showed me on the bus a picture he found in his house, taken by him at the  1974  game theory workshop in Bad Salzuflen, Germany. With Nimrod’s kind permission I present the picture here: (The copyright © belongs to Nimrod Megiddo who took the picture).


Here are some of the people left to right, (on some I already told you in other posts):

David Schmeidler (only beard visible)
Guillermo Owen
Lloyd Shapley
Sergiu Hart
Yair Tauman (only back shown)
Robert Aumann
Werner Güth (behind Aumann)
Reinhard Selten
Ehud Kalai (just to the right of Selten looking at the camera)
Gerhard Schwedihauer
Elon Kohlberg (only back shown, looking to the left)
William Lucas (in the back, looking at the wall)
Robert Weber (only hair and jacket visible)
Bezalel Peleg (looking to the right)
Joel Moulen (looking to the left)
Thomas Marschak (sunglasses and beard)
Michael Maschler
Joachim Rosenmüller (with glasses behind Maschler)
Kenjiro Nakamura

Happy new 2015!

Do Politicians Act Rationally?

Well, I wrote an article (in Hebrew) about it in the Newspaper Haaretz. An English translation appeared in the English edition. Here is an appetizer:

During World War II, many fighter planes returned from bombing missions in Japan full of bullet holes. The decision was made to reinforce the planes, and their natural tendency was to bolster the hardest-hit sections in the body of the plane. However, the mathematician George Dantzig suggested that it was precisely the parts that were hit less that needed to be armored. Was he right?

Months after all the commentators described Hillary Clinton’s chances as so slim she was bound to lose her campaign for the Democratic presidential nomination, she continued to fight for her candidacy, saying she believed she would win and keeping up her attack on her rival. Did she act rationally? And did Benjamin Netanyahu and Tzipi Livni act rationally when each declared victory on election night? Did Meretz supporters who voted for Kadima act rationally? Is there an election method in which it would be rational for all voters to vote in accordance with their genuine preferences?

My conclusion is:

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Nati’s Influence

When do we say that one event causes another? Causality is a topic of great interest in statistics, physics, philosophy, law, economics, and many other places. Now, if causality is not complicated enough, we can ask what is the influence one event has on another one.  Michael Ben-Or and Nati Linial wrote a paper in 1985 where they studied the notion of influence in the context of collective coin flipping. The title of the post refers also to Nati’s influence on my work since he got me and Jeff Kahn interested in a conjecture from this paper.


The word “influence” (dating back, according to Merriam-Webster dictionary, to the 14th century) is close to the word “fluid”.  The original definition of influence is: “an ethereal fluid held to flow from the stars and to affect the actions of humans.” The modern meaning (according to Wictionary) is: “The power to affect, control or manipulate something or someone.”

Ben-Or and Linial’s definition of influence

Collective coin flipping refers to a situation where n processors or agents wish to agree on a common random bit. Ben-Or and Linial considered very general protocols to reach a single random bit, and also studied the simple case where the collective random bit is described by a Boolean function f(x_1,x_2,\dots,x_n) of n bits, one contributed by every agent. If all agents act appropriately the collective bit will be ‘1’ with probability 1/2. The purpose of collective coin flipping is to create a random bit R which is immune as much as possible against attempts of one or more agents to bias it towards ‘1’ or ‘0’. Continue reading

Rationality, Economics and Games

1. The “Center for Rationality”

“Founded in 1991, the Hebrew University’s Center for the Study of Rationality  [at first it was simply called “Center for Rationality”] is a unique venture in which faculty, students, and guests join forces to explore the rational basis of decision-making. Coming from a broad sweep of departments — mathematics, economics, psychology, biology, education, computer science, philosophy, business, statistics, and law — its members apply game- theoretic tools to examine the processes by which individuals seeking the path of maximum benefit respond to real-world situations where individuals with different goals interact.” 

Game theory was always strong at the Hebrew University of Jerusalem, and a nice aspect of it is the combination of mathematics and debating. As an undergraduate I was quite interested in game theory along with combinatorics and convexity, and my first published paper was on game theory, with Michael Maschler and Guillermo Owen. Later I moved in other directions, but more recently, in part because of my membership in the Center for the last ten years and in part because of my collaboration with economists Ariel Rubinstein (who was my classmate in my undergraduate years) and Rani Spiegler, I am trying to do research and write papers in theoretical economics. Not having the basic instincts of an economist, and lacking some basic background, makes it especially difficult.

Let me also mention that there are very interesting connections between computer science and economics and a very large emerging research community.  

2. Many many controversies

Among the many issues discussed and debated in seminars at the Center (the regular ones are the “Game Theory Seminar” on Sundays and the “Rationality on Friday” seminars on… Fridays,)  roundtables, the annual retreat, Sunday’s sandwich gatherings, and ample debates over e-mail were:

The controversy over expected utility theory (we will come back to it below); (Little updates: May, 21)

The role of psychology in economics;

The relevance of “neuroeconomy”;

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