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Publications | The Federmann Center for the Study of Rationality

Publications

2006
Ullmann-Margalit, Edna . Family Fairness. Discussion Papers 2006. Web. Publisher's VersionAbstract
This paper is the last part of a three-part project. The larger picture is important for the proper framing of the present paper. Here then is an abstract of the three-part paper, which is about considerateness. Focusing on two extreme poles of the spectrum of human relationships, the paper argues that considerateness is the foundation upon which relationships are to be organized in both the thin anonymous context of the public space and the thick intimate context of the family. The first part of the paper introduces the notion of considerateness among strangers and explores the idea that considerateness is the minimum that we owe to one another in the public space. By acting considerately toward strangers for example, by holding a door open so it does not slam in the face of the next person who enters we show respect to that which we all share as people, namely, our common humanity. The second part explores the idea that considerateness is the foundation underlying the constitution of the exemplary family. I hypothesize that each family adopts its own particular distribution of domestic burdens and benefits and I refer to it as the family deal.  The argument is that the considerate family deal embodies a notion of fairness that is a distinct, family-oriented notion of fairness. The third part of the larger paper which is the part I present here takes up the notion of family fairness and contrasts it with justice. In particular, I take issue with Susan Okin s notion of the just family and develop, instead, the notion of the not-unjust fair family. Driving a wedge between justice and fairness, I propose that family fairness is partial and sympathetic rather than impartial and empathic, and that it is particular and internal rather than universalizable. Furthermore, I claim that family fairness is based on ongoing comparisons of preferences among family members. I finally characterize the good family as a not-unjust family that is considerate and fair.
Irit Nowik, Idan Segev, and Shmuel Zamir. Games In The Nervous System: The Game Motoneurons Play. Discussion Papers 2006. Web. Publisher's VersionAbstract
Game theory is usually applied to biology through evolutionary games. However, many competitive processes in biology may be better understood by analyzing them on a shorter time-scale than the time-course considered in evolutionary dynamics. Instead of the change in the "fitness" of a player, which is the traditional payoff in evolutionary games, we define the payoff function, tailored to the specific questions addressed. In this work we analyze the developmental competition that arises between motoneurons innervating the same muscle. The "size principle" - a fundamental principle in the organization of the motor system, stating that motoneurons with successively higher activation-threshold innervate successively larger portions of the muscle - emerges as a result of this competition. We define a game, in which motoneurons compete to innervate a maximal number of muscle-fibers. The strategies of the motoneurons are their activation-thresholds. By using a game theoretical approach we succeed to explain the emergence of the size principle and to reconcile seemingly contradictory experimental data on this issue. The evolutionary advantage of properties as the size principle, emerging as a consequence of competition rather than being genetically hardwired, is that it endows the system with adaptation capabilities, such that the outcome may be fine-tuned to fit the environment. In accordance with this idea the present study provides several experimentally-testable predictions regarding the magnitude of the size principle in different muscles.
Tamar Keasar, Gad Pollak, Rachel Arnon Dan Cohen, and Avi Shmida. Honesty Of Signaling And Pollinator Attraction: The Case Of Flag-Like Bracts. Discussion Papers 2006. Web. Publisher's VersionAbstract
Bracts are nonfloral showy structures associated with inflorescences. They are generally hypothesized to enhance plant reproductive success by attracting pollinating insects. We investigated whether flag-like bracts at the top of inflorescences reliably signal of floral food reward for pollinators in Salvia viridis L. Field and greenhouse data indicate incomplete synchrony between the development of flowers and bracts. Various measures of bract size, however, positively correlate with the number of open flowers on the inflorescence, and with their nectar rewards. Experimental removal of bracts from inflorescences significantly reduced honeybee visitation in the field. We compared these findings with field data on Lavandula stoechas L., another labiate species with flag-like displays. The number of open flowers in L. stoechas cannot be reliably predicted from the presence or size of the bracts. Bract clipping does not significantly reduce honeybee visits in this species. We conjecture that bees learn to orient to those bracts that reliably signal food rewards, and disregard bracts if they provide unreliable signals. Asynchronous development of bracts and floral rewards can reduce the reliability of the signals, and may explain the rarity of flag-like displays in pollination systems. We discuss additional selective forces that may favor bract displays.
Peleg, Barry O'Neill, and Bezalel. Lexicographic Composition Of Simple Games. Discussion Papers 2006. Web. Publisher's VersionAbstract
A two-house legislature can often be modelled as a proper simple game whose outcome depends on whether a coalition wins, blocks or loses in two smaller proper simple games. It is shown that there are exactly five ways to combine the smaller games into a larger one. This paper focuses on one of the rules, lexicographic composition, where a coalition wins in G1''‡’G2 when it either wins in G1, or blocks in G1 and wins in G2. It is the most decisive of the five. A lexicographically decomposable game is one that can be represented in this way using components whose player sets partition the whole set. Games with veto players are not decomposable, and anonymous games are decomposable if and only if they are decisive and have two or more players. If a player's benefit is assessed by any semi-value, then for two isomorphic games a player is better off from having a role in the first game than having the same role in the second. Lexicographic decomposability is sometimes compatible with equality of roles. A relaxation of it is suggested for its practical benefits.
Zapechelnyuk, Alexander Matros, and Andriy. Optimal Mechanisms For An Auction Mediator. Discussion Papers 2006. Web. Publisher's VersionAbstract
We consider a multi-period auction with a seller who has a single object for sale, a large population of potential buyers, and a mediator of the trade. The seller and every buyer have independent private values of the object. The mediator designs an auction mechanism which maximizes her revenue subject to certain constraints for the traders. In each period the seller auctions the object to a set of buyers drawn at random from the population. The seller can re-auction the object (infinitely many times) if it is not sold in previous interactions. We characterize the class of mediator-optimal auction mechanisms. One of such mechanisms is a Vickrey auction with a reserve price where the seller pays to the mediator a fixed percentage from the closing price.
Eden, Maya . Optimal Ties In Contests. Discussion Papers 2006. Web. Publisher's VersionAbstract
I analyze a mechanism design of a tournament in which the principal can strategically enhance the probability of a tie. The principal decides on a "tie distance" and announces a rule according to which a tie is declared if the difference between the two contestants' performances is within the tie distance. I show that the contestants' equilibrium efforts do not depend on the prizes awarded in case of a tie. I find that there are cases in which the optimal mechanism has a positive tie distance.
Sheshinski, Eytan . Optimum Commodity Taxation In Pooling Equilibria. Discussion Papers 2006. Web. Publisher's VersionAbstract
This paper extends the standard model of optimum commodity taxation (Ramsey (1927) and Diamond-Mirrlees (1971)) to a competitive economy in which some markets are inefficient due to asymmetric information. As in most insurance markets, consumers impose varying costs on suppliers but firms cannot associate costs to customers and consequently all are charged equal prices. In a competitive pooling equilibrium, the price of each good is equal to average marginal costs weighted by equilibrium quantities. We derive modified Ramsey-Boiteux Conditions for optimum taxes in such an economy and show that they include general-equilibrium effects which reflect the initial deviations of producer prices from marginal costs, and the response of equilibrium prices to the taxes levied. It is shown that condition on the monotonicity of demand elasticities enables to sign the deviations from the standard formula. The general analysis is applied to the optimum taxation of annuities and life insurance.
Shapira, Jerker Denrell, and Zur. Performance Sampling And Bimodal Duration Dependence. Discussion Papers 2006. Web. Publisher's VersionAbstract
Performance sampling models of duration dependence in employee turnover and firm exit predict that hazard rates will initially be low, gradually rise to a maximum, and then fall. As we note in this paper, however, several empirical duration distributions have bimodal hazard rates. This paper shows that such bimodal hazard rates can be derived from existing models of performance sampling by small changes in the assumptions. In particular, bimodal hazard rates emerge if the mean or the variance of performances changes over time, which would occur if employees or firms face more challenging tasks over time. Using data on turnover in law firms, we show that the hazard rate predicted by these models fit data better than existing models.
Shapira, Elizabeth Boyle, and Zur. Perils Of Betting To Win: Aspiration And Survival In Jeopardy! Tournament Of The Champions (Revision Of Discussion Paper #331), The. Discussion Papers 2006. Web. Publisher's VersionAbstract
Behavior in competitive situations requires decision makers to evaluate their own as well as their competitors' positions. Using data from a realistic competitive risk-taking setting, Jeopardy's Tournament of Champions (TOC), we test whether players choose the strategic best response when making their betting decisions. Analyses show that the percentage of players choosing the strategic best response is very low, a surprising finding because the TOC is contested by the best and most experienced players of the game. We conjecture that performance aspiration and survival targets that guide risk-taking behavior in competitive situations may lead players to select inferior competitive strategies.
Russo, Abraham Neyman, and Tim. Public Goods And Budget Deficit. Discussion Papers 2006. Web. Publisher's VersionAbstract
We examine incentive-compatible mechanisms for fair financing and efficient selection of a public budget (or public good). A mechanism selects the level of the public budget and imposes taxes on individuals. Individuals' preferences are quasilinear. Fairness is expressed as weak monotonicity (called scale monotonicity) of the tax imposed on an individual as a function of his benefit from an increased level of the public budget. Efficiency is expressed as selection of a Pareto-optimal level of the public budget. The budget deficit is the difference between the public budget and the total amount of taxes collected from the individuals. We show that any efficient scale-monotonic and incentive-compatible mechanism may generate a budget deficit. Moreover, it is impossible to collect taxes that always cover a fixed small fraction of the total cost.
Hart, Sergiu . Robert Aumann'S Game And Economic Theory. Discussion Papers 2006. Web. Publisher's VersionAbstract
An overview of the landmark contributions of Robert J. Aumann, winner of the 2005 Nobel Memorial Prize in Economic Sciences.
Kalai, Gil . Science, Beliefs And Knowledge: A Personal Reflection On Robert J. Aumann S Approach. Discussion Papers 2006. Web. Publisher's VersionAbstract
On the occasion of Robert J. Aumann's being awarded the 2005 Nobel Prize in Economics, this paper gives a personal view on some of Aumann's contributions, and primarily on his approach to foundational issues in game theory, economics, and science as a whole. It is based on numerous discussions and e-mail exchanges we had in the 1990's, dealing with various scientific and political matters, including our long debate on the ``Bible Code' controversy.
Hart, Sergiu . Shapley Value. Discussion Papers 2006. Web. Publisher's VersionAbstract
The Shapley value is an a priori evaluation of the prospects of a player in a multi-person game. Introduced by Lloyd S. Shapley in 1953, it has become a central solution concept in cooperative game theory. The Shapley value has been applied to economic, political, and other models.
Perry, Alex Gershkov, and Motty. Tournaments With Midterm Reviews. Discussion Papers 2006. Web. Publisher's VersionAbstract
In many tournaments investments are made over time and conducting a review only once at the end, or also at points midway through, is a strategic decision of the tournament designer. If the latter is chosen, then a rule according to which the results of the different reviews are aggregated into a ranking must also be determined. This paper takes a first step in the direction of answering how such rules should be optimally designed. A characterization of the optimal aggregation rule is provided for a two-agent two-stage tournament. In particular, we show that treating the two reviews symmetrically may result in an equilibrium effort level that is inferior to the one in which only a final review is conducted. However, treating the two reviews lexicographically by first looking at the final review, and then using the midterm review only as a tie-breaking rule, strictly dominates the option of conducting a final review only. The optimal mechanism falls somewhere in between these two extreme mechanisms. It is shown that the more effective the first-stage effort is in determining the final review's outcome, the smaller is the weight that should be assigned to the midterm review in determining the agents' ranking.
Rachel Arnon, Tamar Keasar, Dan Cohen, and Avi Shmida. Vertical Orientation And Color Contrast And Choices By Bumblebees (Bombus Terrestris L.). Discussion Papers 2006. Web. Publisher's VersionAbstract
The vertical inflorescences of several plant species are terminated by colorful bracts, which attract insect pollinators. The bracts contrast in color with the leaves below them, and are oriented perpendicular to the flowers on the inflorescence. We conducted laboratory experiments to determine the effects of color contrast and perpendicular orientation on the feeding choices of bumblebees. We first trained bees to feeders with color-contrasting perpendicular displays, composed of a horizontal and a vertical display component. We subsequently recorded the bees' choices among feeders that displayed only one of these cues. The bees preferred perpendicular displays that resembled the training model in the color of the horizontal component. None of them chose a color-contrasting display that was not perpendicular. We then evaluated the effects of the horizontal vs. vertical components of perpendicular displays on the bees' choices. After training bees to color-contrasting perpendicular displays, we allowed them to choose between displays that had either the same horizontal or the same vertical component as the training model. Foragers mostly oriented to the horizontal displays to which they had been trained. Our results suggest that (a) bumblebees can learn to associate three-dimensional perpendicular color-contrasting displays with food rewards; (b) these displays are processed hierarchically, with orientation dominating color contrast; (c) The horizontal component of perpendicular displays dominates the vertical component. We discuss possible implications of our findings for the evolution of flower signals based on extra-floral bracts.
Aumann, Robert J. . War And Peace. Discussion Papers 2006. Web. Publisher's VersionAbstract
Nobel Lecture.
The New Unconscious
Ran, Hassin, James S. Uleman, and John A. Bargh. The New Unconscious. ‎Oxford University Press, 2006. Print.

Over the past two decades, a new picture of the cognitive unconscious has emerged from a variety of disciplines that are broadly part of cognitive science. According to this picture, unconscious processes seem to be capable of doing many things that were thought to require intention, deliberation, and conscious awareness. Moreover, they accomplish these things without the conflict and drama of the psychoanalytic unconscious. These processes range from complex information processing, through goal pursuit and emotions, to cognitive control and self-regulation. This collection of 20 original chapters by leading researchers examines the cognitive unconscious from social, cognitive, and neuroscientific viewpoints, presenting some of the most important developments at the heart of this new picture of the unconscious. The volume, the first book in the new Social Cognition and Social Neuroscience series, will be an important resource on the cognitive unconscious for researchers in cognitive psychology and neuroscience.

2005
Hart, Sergiu . An Interview With Robert Aumann. Discussion Papers 2005. Web. Publisher's VersionAbstract
Who is Robert Aumann? Is he an economist or a mathematician? A rational scientist or a deeply religious man? A deep thinker or an easygoing person? These seemingly disparate qualities can all be found in Aumann; all are essential facets of his personality. A pure mathematician who is a renowned economist, he has been a central figure in developing game theory and establishing its key role in modern economics. He has shaped the field through his fundamental and pioneering work, work that is conceptually profound, and much of it mathematically deep. He has greatly influenced and inspired many people: his students, collaborators, colleagues, and anyone who has been excited by reading his papers or listening to his talks. Aumann promotes a unified view of rational behavior, in many different disciplines: chiefly economics, but also political science, biology, computer science, and more. To mention just a few of the areas of Aumann's groundbreaking work: perfect competition, repeated games, correlated equilibrium, interactive knowledge and rationality, and coalitions and cooperation. But Aumann is not just a theoretical scholar, closed in his ivory tower. He is interested in real-life phenomena and issues, to which he applies insights from his research. He is a devoutly religious man; and he is one of the founding fathers-and a central and most active member-of the multidisciplinary Center for the Study of Rationality at the Hebrew University in Jerusalem. Aumann enjoys skiing, mountain climbing, and cooking-no less than working out a complex economic question or proving a deep theorem. He is a family man, a very warm and gracious person-of an extremely subtle and sharp mind. This interview catches a few glimpses of Robert Aumann's fascinating world. It was held in Jerusalem on three consecutive days in September of 2004. I hope the reader will learn from it and enjoy it as much as we two did.
Ron Holzman, Bezalel Peleg, and Peter Sudholter. Bargaining Sets Of Majority Voting Games (Revision Of Discussion Paper #376). Discussion Papers 2005. Web. Publisher's VersionAbstract
Let A be a finite set of m alternatives, let N be a finite set of n players and let RN be a profile of linear preference orderings on A of the players. Let uN be a profile of utility functions for RN. We define the NTU game VuN that corresponds to simple majority voting, and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m 3 and it may be empty for m ¥ 4. However, in a simple probabilistic model, for fixed m, the probability that the Aumann-Davis-Maschler bargaining set is nonempty tends to one if n tends to infinity. The Mas-Colell bargaining set is nonempty for m 5 and it may be empty for m ¥ 6. Furthermore, it may be empty even if we insist that n be odd, provided that m is sufficiently large. Nevertheless, we show that the Mas-Colell bargaining set of any simple majority voting game derived from the k-th replication of RN is nonempty, provided that k ¥ n + 2.
Ullmann-Margalit, Edna . Big Decisions: Opting, Converting, Drifting. Discussion Papers 2005. Web. Publisher's Version