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Publications | The Federmann Center for the Study of Rationality

Publications

2005
Yaniv, Ilan . Receiving Other People's Advice: Influence And Benefit. Discussion Papers 2005. Web. Publisher's VersionAbstract
Seeking advice is a basic practice in making real life decisions. Until recently, however, little attention has been given to it in either empirical studies or theories of decision making. The studies reported here investigate the influence of advice on judgment and the consequences of advice use for judgment accuracy. Respondents were asked to provide final judgments on the basis of their initial opinions and advice presented to them. The respondents' weighting policies were inferred. Analysis of the these policies show that (a) the respondents tended to place a higher weight on their own opinion than on the advisor's opinion (the self/other effect); (b) more knowledgeable individuals discounted the advice more; (c) the weight of advice decreased as its distance from the initial opinion increased; and (d) the use of advice improved accuracy significantly, though not optimally. A theoretical framework is introduced which draws in part on insights from the study of attitude change to explain the influence of advice. Finally the usefulness of advice for improving judgment accuracy is considered.
Toxvaerd, Flavio . Record Breaking And Temporal Clustering. Discussion Papers 2005. Web. Publisher's VersionAbstract
Casual observation suggests that athletics records tend to cluster over time. After prolonged periods without new records, a record breaking performance spurs other athletes to increase effort and thereby repeatedly set new standards. Subsequently, record breaking subsides and the pattern repeats itself. The clustering hypothesis is tested for the mile run, the marathon, the world hour record and long jump. For all four disciplines, the hypothesis of non-clustering is rejected at the 4 level or below. A theoretical rationale for this phenomenon is provided through a model of social learning under limited awareness. The agents are assumed to be unaware of the true limits to performance and to take the current record as the upper bound. The observation of a record breaking achievement spurs the agents to try harder and thus temporarily increase the probability of new records. Subsequently, record breaking trails off and the process is repeated.
Abba M. Krieger, Moshe Pollak, and Ester Samuel-Cahn. Select Sets: Rank And File. Discussion Papers 2005. Web. Publisher's VersionAbstract
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider situations where the available information is the rank of a present observation relative to its predecessors. Certain "natural" selection rules are investigated. Theoretical and Monte Carlo results are presented pertaining to the evolution of the number of items selected, measures of their quality and the time it would take to amass a group of a given size. A comparison between rules is made, and guidelines to the choice of good procedures are offered.
Gorodeisky, Ziv . Stability Of Mixed Equilibria. Discussion Papers 2005. Web. Publisher's VersionAbstract
We consider stability properties of equilibria in stochastic evolutionary dynamics. In particular, we study the stability of mixed equilibria in strategic form games. In these games, when the populations are small, all strategies may be stable. We prove that when the populations are large, the unique stable outcome of best-reply dynamics in 2 x 2 games with a unique Nash equilibrium that is completely mixed is the mixed equilibrium. The proof of this result is based on estimating transition times in Markov chains.
Kalai, Gil . Thoughts On Noise And Quantum Computation. Discussion Papers 2005. Web. Publisher's VersionAbstract
'We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on n qubits subject to noise operators that are obtained as products of tiny noise operators acting on a small number of qubits. We conjecture that for realistic random noise operators of this kind there will be substantial dependencies between the noise on individual qubits and, in addition, the dependence structure of the noise acting on individual qubits will necessarily depend (systematically) on the dependence structure of the qubits themselves. The main hypothesis of this paper is that these properties of noise are sufficient to reduce quantum computation to probabilistic classical computation. Some potentially relevant mathematical issues and problems will be described. Our line of thought appears to be related to that of physicists Alicki, Horodecki, Horodecki and Horodecki [AHHH].'
Safra, Gil Kalai, and Shmuel. Threshold Phenomena And Influence, With Some Perspectives From Mathematics, Computer Science, And Economics. Discussion Papers 2005. Web. Publisher's Version
Nitzan, Noa . Tight Correlated Equilibrium. Discussion Papers 2005. Web. Publisher's VersionAbstract
A correlated equilibrium of a strategic form n-person game is called tight if all the incentive constraints are satisfied as equalities. The game is called tight if all of its correlated equilibria are tight. This work shows that the set of tight games has positive measure.
Shahar Dobzinski, Noam Nisan, and Michael Schapira. Truthful Randomized Mechanisms For Combinatorial Auctions. Discussion Papers 2005. Web. Publisher's VersionAbstract
We design two computationally-efficient incentive-compatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentive-compatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion of incentive compatibility in expectation. The first mechanism obtains an O('ˆ\v sm)-approximation of the optimal social welfare for arbitrary bidder valuations – this is the best approximation possible in polynomial time. The second one obtains an O(log2 m)-approximation for a subclass of bidder valuations that includes all submodular bidders. This improves over the best previously obtained incentive-compatible mechanism for this class which only provides an O('ˆ\v sm)-approximation.
Ein-Ya, Gura . Using Game Theory To Increase Students' Motivation To Learn Mathematics. Discussion Papers 2005. Web. Publisher's VersionAbstract
This paper reports an attempt to teach game theory in order to increase students' motivation to learn mathematics. A course in game theory was created in order to introduce students to new mathematical content presented in a different way.
Dreze, R. J. Aumann, and J. H. When All Is Said And Done, How Should You Play And What Should You Expect?. Discussion Papers 2005. Web. Publisher's VersionAbstract
Modern game theory was born in 1928, when John von Neumann published his Minimax Theorem. This theorem ascribes to all two-person zero-sum games a value-what rational players may expect-and optimal strategies-how they should play to achieve that expectation. Seventy-seven years later, strategic game theory has not gotten beyond that initial point, insofar as the basic questions of value and optimal strategies are concerned. Equilibrium theories do not tell players how to play and what to expect; even when there is a unique Nash equilibrium, it it is not at all clear that the players "should" play this equilibrium, nor that they should expect its payoff. Here, we return to square one: abandon all ideas of equilibrium and simply ask, how should rational players play, and what should they expect. We provide answers to both questions, for all n-person games in strategic form.
Samuel-Cahn, Ester . When Should You Stop And What Do You Get? Some Secretary Problems. Discussion Papers 2005. Web. Publisher's VersionAbstract
{A version of a secretary problem is considered: Let Xj
Flekser, Judith Avrahami, and Oren. With The Eye Being A Ball, What Happens To Fixational Eye Movements In The Periphery?. Discussion Papers 2005. Web. Publisher's VersionAbstract
Although the fact that the eye is moving constantly has been known for a long time, the role of fixational eye movements (FEM) is still in dispute. Whatever their role, it is structurally clear that, since the eye is a ball, the size of these movements diminishes for locations closer to the poles. Here we propose a new perspective on the role of FEM from which we derive a prediction for a three-way interaction of a stimulus' orientation, location, and spatial frequency. Measuring time-to-disappearance for gratings located in the periphery we find that, as predicted, gratings located to the left and right of fixation fade faster when horizontal than when vertical in low spatial frequencies and faster when vertical than when horizontal in high spatial frequencies. The opposite is true for gratings located above and below fixation.
The Elements of Computing Systems
Nisan, Noam, and Shimon Schocken. The Elements Of Computing Systems. The MIT Press, 2005. Print.

In the early days of computer science, the interactions of hardware, software, compilers, and operating system were simple enough to allow students to see an overall picture of how computers worked. With the increasing complexity of computer technology and the resulting specialization of knowledge, such clarity is often lost. Unlike other texts that cover only one aspect of the field, The Elements of Computing Systems gives students an integrated and rigorous picture of applied computer science, as its comes to play in the construction of a simple yet powerful computer system.Indeed, the best way to understand how computers work is to build one from scratch, and this textbook leads students through twelve chapters and projects that gradually build a basic hardware platform and a modern software hierarchy from the ground up. In the process, the students gain hands-on knowledge of hardware architecture, operating systems, programming languages, compilers, data structures, algorithms, and software engineering. Using this constructive approach, the book exposes a significant body of computer science knowledge and demonstrates how theoretical and applied techniques taught in other courses fit into the overall picture.Designed to support one- or two-semester courses, the book is based on an abstraction-implementation paradigm; each chapter presents a key hardware or software abstraction, a proposed implementation that makes it concrete, and an actual project. The emerging computer system can be built by following the chapters, although this is only one option, since the projects are self-contained and can be done or skipped in any order. All the computer science knowledge necessary for completing the projects is embedded in the book, the only pre-requisite being a programming experience.The book's web site provides all tools and materials necessary to build all the hardware and software systems described in the text, including two hundred test programs for the twelve projects. The projects and systems can be modified to meet various teaching needs, and all the supplied software is open-source.

צמחי ישראל
מפה, . צמחי ישראל. 2005. Print.

צמחי ישראל הוא מדריך שימושי המאפשר את זיהוים של צמחי הבר הנפוצים בישראל בדרך חזותית פשוטה. זהו כלי עזר רב-ערך וחיוני לכל מי שמתעניין בצמחי ישראל ומבקש להעמיק את ידיעותיו בתחום. לקסיקון מפה: צמחי ישראל מביא את תיאורם של החשובים והנפוצים בצמחי הארץ שהים מקובצים בקבוצות לפי צבע פרחיהם. כל ערך בלקסיקון מביא תצלום ותיאור מלא של הצמח בנדון בו, מפת תפוצה ו"סגרל פריחה" של הצמח. ומידע בסיסי על מינים קרובים לצמח. בסך הכל מובאים בספר תיאורים של יותר מ-800 מיני צמחים, ושל עוד כ-1,000 מיני צמחים קרובים להם. בנוסף לכך הספר מביא מידע מרתק על עוד נושאים רבים אחרים. מאסטרטגיות רביית והגנה של צמחים, דרך פרסום ורמייה בצמחים, ועד השימוש שניתן לעשות ברבים מהצמחים המתוארים בספר במטבח וברפואה.

2004
Olle Haggstrom, Gil Kalai, and Elchanan Mossel. A Law Of Large Numbers For Weighted Majority. Discussion Papers 2004. Web. Publisher's VersionAbstract
Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is p > 1/2. Condorcet's Jury Theorem which he derived from the weak law of large numbers asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. The notion of influence of a voter or its voting power is relevant for extensions of the weak law of large numbers for voting rules which are more general than simple majority. In this paper we point out two different ways to extend the classical notions of voting power and influences to arbitrary probability distributions. The extension relevant to us is the "effect" of a voter, which is a weighted version of the correlation between the voter's vote and the election's outcomes. We prove an extension of the weak law of large numbers to weighted majority games when all individual effects are small and show that this result does not apply to any voting rule which is not based on weighted majority.
Toxvaerd, Flavio . A Theory Of Optimal Deadlines. Discussion Papers 2004. Web. Publisher's VersionAbstract
This paper sets forth a model of contracting for delivery in an environment with time to build and adverse selection. The optimal contract is derived and characterized and it takes the form of a deadline contract. Such a contract stipulates a deadline for delivery for each possible type of agent efficiency. The optimal contract induces inefficient delay by using delivery time as a screening device. Furthermore, rents are decreasing in the agent's efficiency. In meeting the deadline, the agent's effort is strictly increasing over time, due to discounting. It is shown that increasing the project's gross value decreases delivery time, while the scale or difficulty of the project decreases it. Last, it is shown that the agent's rents are increasing in both project difficulty and gross project value.
Hart, Sergiu . Adaptive Heuristics. Discussion Papers 2004. Web. Publisher's VersionAbstract
We exhibit a large class of simple rules of behavior, which we call adaptive heuristics, and show that they generate rational behavior in the long run. These adaptive heuristics are based on natural regret measures, and may be viewed as a bridge between rational and behavioral viewpoints. The results presented here, taken together, establish a solid connection between the dynamic approach of adaptive heuristics and the static approach of correlated equilibria.
Ilan Guttman, Ohad Kadan, and Eugene Kandel. Adding The Noise: A Theory Of Compensation-Driven Earnings Management. Discussion Papers 2004. Web. Publisher's VersionAbstract
Empirical evidence suggests that the distribution of earnings reports is discontinuous. This is puzzling since the distribution of true earnings is likely to be continuous. We present a model that rationalizes this phenomenon. In our model, managers report their earnings to rational investors, who price the stock accordingly. We assume that misreporting is costly, but since managers' compensation is based on the stock price, they may want to manipulate the reported earnings. The model fits into the general framework of signaling games with a continuum of types. The conventional equilibrium in this game is fully revealing (e.g. Stein 1989), and does not explain the observed discontinuity of earnings reports. We show that a partially pooling equilibrium exists in such games as well, and it generates an endogenous discontinuity in reports. By pooling reports of different types, the informed manager introduces "home-made" noise into his report. The resulting vagueness enables the manager to reduce the manipulation costs. While a priori pooling looks manipulative, it is actually a way to reduce earnings management. The empirical implications of our model relate earnings management and price reaction to price- and earnings-based compensation, growth opportunities of the firm, underlying volatility, and the stringency of accounting rules. We show that this equilibrium arises due to stock-based compensation of the managers, and does not arise when they are paid based on their earnings directly. Finally, we present a general version of this model describing the behavior of biased experts in many real-life situations.
Aumann, R. J. et al. Analyses Of The Gans Committee Report. Discussion Papers 2004. Web. Publisher's VersionAbstract
This document contains four separate analyses, each with a different author, of the "Gans" committee report on the Bible codes (DP 364 of the Center for the Study of Rationality, June 2004). The analyses appear in alphabetical order of the authors' names. Three of the authors were members of the committee; one, Doron Witztum, is active in Bible codes research. Two of the analyses-by Aumann and by Furstenberg-support the report of the committee; the other two-by Lapides and by Witztum-do not. This document contains material that was generated after the results of the committee's experiments became known; other than reporting the numerical results themselves,dp 364 contains only material generated before they became known.
Dreze, R. J. Aumann, and J. H. Assessing Strategic Risk. Discussion Papers 2004. Web. Publisher's VersionAbstract
In recent decades, the concept of subjective probability has been increasingly applied to an adversary s choices in strategic games. A careful examination reveals that the standard construction of subjective probabilities does not apply in this context. We show how the difficulty may be overcome by means of a different construction.