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Publications | The Federmann Center for the Study of Rationality

Publications

2007
Clelia Di Serio, Yosef Rinott, and Marco Scarsini. Simpson S Paradox For The Cox Model. Discussion Papers 2007. Web. Publisher's VersionAbstract
{In the context of survival analysis, we define a covariate X as protective (detrimental) for the failure time T if the conditional distribution of [T | X = x] is stochastically increasing (decreasing) as a function of x. In the presence of another covariate Y, there exist situations where [T | X = x
Peretz, Ron . Strategic Value Of Recall, The. Discussion Papers 2007. Web. Publisher's VersionAbstract
This work studies the value of two-person zero-sum repeated games in which at least one of the players is restricted to (mixtures of) bounded recall strategies. A (pure) k-recall strategy is a strategy that relies only on the last k periods of history. This work improves previous results [Lehrer, Neyman and Okada] on repeated games with bounded recall. We provide an explicit formula for the asymptotic value of the repeated game as a function of the stage game, the duration of the repeated game, and the recall of the agents.
Ben-Porath, Elchanan . Trade With Heterogeneous Beliefs. Discussion Papers 2007. Web. Publisher's VersionAbstract
The paper analyzes an economy with asymmetric information in which agents trade in contingent assets. The new feature in the model is that each agent may have any prior belief on the states of nature and thus the posterior belief of an agent maybe any probability distribution that is consistent with his private information. We study two solution concepts: Equilibrium, which assumes rationality and market clearing, and common knowledge equilibrium (CKE) which makes the stronger assumption that rationality, market clearing, and the parameters which de'łdots}ne the economy are common knowledge. The two main results characterize the set of equilibrium prices and the set of CKE prices in terms of parameters which specify for each state s and event E the amount of money in the hands of agents who know the event E at the state s. The characterizations that are obtained apply to a broad classof preferences which include all preferences that can be represented by the expectation of a state dependent monotone utility function. One implication of these results is a characterization of the information that is revealed in a CKE.
Babichenko, Yakov . Uncoupled Automata And Pure Nash Equilibria. Discussion Papers 2007. Web. Publisher's VersionAbstract
We study the problem of reaching Nash equilibria in multi-person games that are repeatedly played, under the assumption of uncoupledness: every player knows only his own payoff function. We consider strategies that can be implemented by 'łdots}finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash equilibrium is reached in every game where such an equilibrium exists.
Tamar Keasar, Adi Sadeh, and Avi Shmida. Variability In Nectar Production And Yield, And Their Relation To Pollinator Visits, In A Mediterranean Shrub. Discussion Papers 2007. Web. Publisher's VersionAbstract
Nectar yields (standing crops) in flowers within an individual plant are often highly variable. This variability may be a by-product of the foraging activity of insect pollinators. Alternatively, plants may be selected to produce highly variable rewards to reduce consecutive visitation by risk-averse pollinators, thus diminishing within-plant pollen transfer. This study evaluated the roles of pollinator control vs. plant control over nectar variability in the bee-pollinated shrub Rosmarinus officinalis L. We sampled nectar production, yield and pollinator visits in three shrubs of one population over 17 days during one blooming season. Nectar production rates were highly variable (CV=1.48), and increased after rainy days. Nectar yields were even more variable (CV=2.16), and decreased with increasing temperatures. Pollinator visit rates decreased with variability in nectar yields, increased with flower number per shrub, and were unaffected by variability in nectar production rates. Repeated sampling of marked flowers revealed no correlation between their nectar yields and production rates. These findings support the role of reward variance in reducing pollinator visits, but suggest that plants are not in complete control of this variability. Rather, plant-generated variability can be modified by intensive foraging activity of pollinators. Such pollinator control over nectar variability is likely to reduce the selective advantage of plant-generated reward variation. Plant-controlled variability may provide evolutionary advantage when pollinator activity is insufficient to generate reward variation.
The Economic Theory of Annuities
Sheshinski, Eytan . The Economic Theory Of Annuities. Princeton University Press, 2007. Print.

Annuities are financial products that guarantee the holder a fixed return so long as the holder remains alive, thereby providing insurance against lifetime uncertainty. The terms of these contracts depend on the information available to insurance firms. Unlike age and gender, information about individual survival probabilities cannot be readily ascertained. This asymmetric information causes market inefficiencies, such as adverse selection. Groundbreaking in its scope, The Economic Theory of Annuities offers readers a theoretical analysis of the functioning of private annuity markets. Starting with a general analysis of survival functions, stochastic dominance, and characterization of changes in longevity, Eytan Sheshinski derives the demand for annuities using a model of individuals who jointly choose their lifetime consumption and retirement age. The relation between life insurance and annuities that have a bequest option is examined and "annuity options" are proposed as a response to the lack of secondary markets. This book also investigates the macroeconomic policy implications of annuities and changes in longevity on aggregate savings. Sheshinski utilizes statistical population theory to shed light on the debate of whether the surge in savings and growth in Asia and other countries can be attributed to higher longevity of the population and whether this surge is durable. This book shows how understanding annuities becomes essential as governments that grapple with insolvency of public social security systems place greater emphasis on individual savings accounts.

Introduction to the Theory of Cooperative Games
Peleg, Bezalel, and Peter Sudhölter. Introduction To The Theory Of Cooperative Games. 2007. Print.

This book systematically presents the main solutions of cooperative games: the core, bargaining set, kernel, nucleolus, and the Shapley value of TU games as well as the core, the Shapley value, and the ordinal bargaining set of NTU games. The authors devote a separate chapter to each solution, wherein they study its properties in full detail. In addition, important variants are defined or even intensively analyzed.

הספר האדום : צמחים בסכנת הכחדה בישראל
שמידע, אבי, גדי פולק, and אורי פרגמן-ספיר. הספר האדום : צמחים בסכנת הכחדה בישראל. הוצאת רשות הטבע והגנים, 2007. Print.

בישראל 414 מיני צמחים בסכנת הכחדה ומתוכם 36 כבר נכחדו. רבים מצמחים אלה נדירים מאוד, חלקם אנדמיים. לכל מין צמח "אדום" נכתבו תיאור מפורט, תפוצתו בארץ ובעולם, היבטים ביוגיאוגרפיים וסיסטמטיים, מצב שמירת הטבע והמלצות לממשק, לשימור ולהגנה. לתיאור נלווים מפת אתרי התפוצה בארץ ותמונת הצמח. המידע בספר זה מהווה בסיס מדעי למדיניות ממשק ולקביעת עדיפות בשמירת הטבע ובהגנה על פי חוק.

Cold Intimacies
Eva, Illouz . Cold Intimacies. Cambridge University Press, 2007. Print.

It is commonly assumed that capitalism has created an a-emotional world dominated by bureaucratic rationality; that economic behavior conflicts with intimate, authentic relationships; that the public and private spheres are irremediably opposed to each other; and that true love is opposed to calculation and self-interest. Eva Illouz rejects these conventional ideas and argues that the culture of capitalism has fostered an intensely emotional culture in the workplace, in the family, and in our own relationship to ourselves. She argues that economic relations have become deeply emotional, while close, intimate relationships have become increasingly defined by economic and political models of bargaining, exchange, and equity. This dual process by which emotional and economic relationships come to define and shape each other is called emotional capitalism. Illouz finds evidence of this process of emotional capitalism in various social sites: self-help literature, women's magazines, talk shows, support groups, and the Internet dating sites. How did this happen? What are the social consequences of the current preoccupation with emotions? How did the public sphere become saturated with the exposure of private life? Why does suffering occupy a central place in contemporary identity? How has emotional capitalism transformed our romantic choices and experiences? Building on and revising the intellectual legacy of critical theory, this book addresses these questions and offers a new interpretation of the reasons why the public and the private, the economic and the emotional spheres have become inextricably intertwined.

2006
Zamir, Todd R. Kaplan, and Shmuel. Asymmetric Auctions: Analytic Solutions To The General Uniform Case. Discussion Papers 2006. Web. Publisher's VersionAbstract
While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions.
Zapechelnyuk, Yair Tauman, and Andriy. Bargaining With A Bureaucrat. Discussion Papers 2006. Web. Publisher's VersionAbstract
We consider a bargaining problem where one of the players, the bureaucrat, has the power to dictate any outcome in a given set. The other players, the agents, negotiate with him which outcome to be dictated. In return, the agents transfer some part of their payoffs to the bureaucrat. We state five axioms and characterize the solutions which satisfy these axioms on a class of problems which includes as a subset all submodular bargaining problems. Every solution is characterized by a number $\pm$ in the unit interval. Each agent in every bargaining problem obtains a weighted average of his individually rational level and his marginal contribution to the set of all players, where the weights are $\pm$ and 1 - $\pm$, respectively. The bureaucrat obtains the remaing surplus. The solution when $\pm$ = 1/2 is the nucleolus of a naturally related game in characteristic form.
Yaniv, Ilan . Benefit Of Additional Opinions, The. Discussion Papers 2006. Web. Publisher's VersionAbstract
In daily decision making, people often solicit one another's opinions in the hope of improving their own judgment. According to both theory and empirical results, integrating even a few opinions is beneficial, with the accuracy gains diminishing as the bias of the judges or the correlation between their opinions increases. Decision makers using intuitive policies for integrating others' opinions rely on a variety of accuracy cues in weighting the opinions they receive. They tend to discount dissenters and to give greater weight to their own opinion than to other people's opinions.
Avrahami, Yaakov Kareev, and Judith. Choosing Between Adaptive Agents: Some Unexpected Implications Of Level Of Scrutiny. Discussion Papers 2006. Web. Publisher's VersionAbstract
Even with ample time and data at their disposal, people often make do with small samples, which increases their risk of making the wrong decision. A theoretical analysis indicates, however, that when the decision involves selecting among competing, adaptive agents who are eager to be selected, an error-prone evaluation may be beneficial to the decision maker. In this case, the chance of an error can motivate competitors to exert greater effort, improving their level of performance which is the prime concern of the decision maker. This theoretical argument was tested empirically by comparing the effects of two levels of scrutiny of performance. Results show that minimal scrutiny can indeed lead to better performance than full scrutiny, and that the effect is conditional on a bridgeable difference between the competitors. We conclude by pointing out that error-prone decisions based on small samples may also maintain competition and diversity in the environment.
Hart, Sergiu, and Yishay Mansour. Communication Complexity Of Uncoupled Nash Equilibrium Procedures, The. Discussion Papers 2006. Web. Publisher's VersionAbstract
We study the question of how long it takes players to reach a Nash equilibrium in "uncoupled" setups, where each player initially knows only his own payoff function. We derive lower bounds on the number of bits that need to be transmitted in order to reach a Nash equilibrium, and thus also on the required number of steps. Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian setting; and (3) reaching a mixed Nash equilibrium. Finally, we show that some very simple and naive procedures lead to similar exponential upper bounds.
Spencer, Abraham Neyman, and Joel. Complexity And Effective Prediction. Discussion Papers 2006. Web. Publisher's VersionAbstract
Let G = (I,J,g) be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which player 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per stage payoff when the two automata face off. We are interested in the cases in which player 1 is "smart" in the sense that k is large but player 2 is "much smarter" in the sense that m>>k. Let S(g) be the value of G were the second player is clairvoyant, i.e., would know the player 1's move in advance. The threshold for clairvoyance is shown to occur for m near min(|I|, |J|)^k. For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).
Ifat Maoz, Ilan Yaniv, and Naama Ivri. Decision Framing And Support For Concessions In The Israeli-Palestinian Conflict. Discussion Papers 2006. Web. Publisher's VersionAbstract
The purpose of the study is to explore, in the context of the Israeli-Palestinian conflict, the influence of framing a decision task as inclusion or exclusion on Israeli-Jewish respondents' support for the concession of Jewish settlements in the West Bank and Gaza. Respondents received a list of 40 Jewish settlements. Details such as the number of residents and geographical location were provided for each settlement. The respondents were randomly assigned to one of two conditions. In the inclusion condition 55 respondents were asked to mark the settlements for which they recommended that Israeli sovereignty be conceded. In the exclusion condition 53 respondents were asked to mark the settlements for which they recommended that Israeli sovereignty not be conceded. The findings confirm the predictions tested and indicate that: (1) Framing the task in terms of inclusion or exclusion affects respondents' support for territorial compromise, so that respondents in the exclusion condition support the concession of more settlements than respondents in the inclusion condition. (2) Framing the task in terms of inclusion or exclusion has a greater effect on support for conceding options (settlements) that are perceived as ambiguous (less consensual in the climate of opinion) in comparison to options (settlements) that are perceived as more clear-cut (more consensual). The theoretical and practical implications of these findings are discussed.
Gorodeisky, Ziv . Deterministic Approximation Of Best-Response Dynamics For The Matching Pennies Game [Revised]. Discussion Papers 2006. Web. Publisher's VersionAbstract
We consider stochastic dynamics for the Matching Pennies game, hich behave, in expectation, like the best-response dynamics (i.e., the ontinuous fictitious play). Since the corresponding vector field is not ontinuous, we cannot apply the deterministic approximation results of Bena¯m and Weibull [2003]. Nevertheless, we prove such results for our dynamics by developing the notion of a "leading coordinate."
Sheshinski, Eytan . Differentiated Annuities In A Pooling Equilibrium. Discussion Papers 2006. Web. Publisher's VersionAbstract
Regular annuities provide payment for the duration of an owner's lifetime. Period-Certain annuities provide additional payment after death to a beneficiary provided the insured dies within a certain period after annuitization. It has been argued that the bequest option offered by the latter is dominated by life insurance which provides non-random bequests. This is correct if competitive annuity and life insurance markets have full information about individual longevities. In contrast, this paper shows that when individual longevities are private information, a competitive pooling equilibrium which offers annuities at common prices to all individuals may have positive amounts of both types of annuities in addition to life insurance. In this equilibrium, individuals self-select the types of annuities that they purchase according to their longevity prospects. The break-even price of each type of annuity reflects the average longevity of its buyers. The broad conclusion that emerges from this paper is that adverse-selection due to asymmetric information is reflected not only in the amounts of insurance purchased but, importantly, also in the choice of insurance products suitable for different individual characteristics. This conclusion is supported by recent empirical work about the UK annuity market (Finkelstein and Poterba (2004)).
Hart, Sergiu . Discrete Colonel Blotto And General Lotto Games. Discussion Papers 2006. Web. Publisher's VersionAbstract
A class of integer-valued allocation games – "General Lotto games" – is introduced and solved. The results are then applied to analyze the classical discrete "Colonel Blotto games"; in particular, optimal strategies are obtained for all symmetric Colonel Blotto games.
Weiss, Donald Ornstein, and Benjamin, Nathans. Entropy Is The Only Finitely Observable Invariant. Discussion Papers 2006. Web. Publisher's VersionAbstract
Our main purpose is to present a very surprising new characterization of the Shannon entropy of stationary ergodic processes. We will use two basic concepts: isomorphism of stationary processes and a notion of finite observability, and we will see how one is led, inevitably, to Shannon's entropy. A function J with values in some metric space, defined on all finite-valued, stationary, ergodic processes is said to be finitely observable (FO) if there is a sequence of functions Sn(x1,x2,...,xn) that for all processes \S converges to J(\S) for almost every realization x1ˆ\v z of \S. It is called an invariant if it returns the same value for isomorphic processes. We show that any finitely observable invariant is necessarily a continuous function of the entropy. Several extensions of this result will also be given.