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Publications | The Federmann Center for the Study of Rationality

Publications

2010
Jay Bartroff, Larry Goldstein, Yosef Rinott, and Ester Samuel-Cahn. On Optimal Allocation Of A Continuous Resource Using An Iterative Approach And Total Positivity. Discussion Papers 2010. Web. Publisher's VersionAbstract
We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount x of ammunition is intercepted by enemy airplanes arriving according to a homogenous Poisson process over a fixed time duration t. Upon encountering an enemy, the aircraft has the choice of spending any amount 0
Halbersberg, Yoed . On The Deduction Of National Insurance Payments From Tort Victims' Claims. Discussion Papers 2010. Web. Publisher's VersionAbstract
In CA 1093/07 Bachar v. Fokmann [2009] (request for additional hearing denied, 2010) , the Israeli Supreme Court has formed a formula for calculating the deduction of NII payments from a tort victim's claim, when only some of the victim's impairment is causally linked to the tortious act in question. Overall, six Supreme Court Justices have reviewed and affirmed this simple formula. However, this formula is incorrect, as it contradicts some of the most basic tort premises, ignores the way impairment is calculated, and necessarily leads to the under-compensation of the victim, and to an unjust enrichment of either the tortfeasor, the National Insurance Institute, or both. This Article, therefore, calls for the adoption of a different formula that is both legally and arithmetically correct.
Bezalel Peleg, Peter Sudh¶lter, Jos\copyright M. Zarzuelo . On The Impact Of Independence Of Irrelevant Alternatives. Discussion Papers 2010. Web. Publisher's VersionAbstract
On several classes of n-person NTU games that have at least one Shapley NTU value, Aumann characterized this solution by six axioms: Non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives (IIA). Each of the first five axioms is logically independent of the remaining axioms, and the logical independence of IIA is an open problem. We show that for n = 2 the first five axioms already characterize the Shapley NTU value, provided that the class of games is not further restricted. Moreover, we present an example of a solution that satisffies the first 5 axioms and violates IIA for 2-person NTU games (N;V) with uniformly p-smooth V(N).
Marco Francesconi, Christian Ghiglino, and Motty Perry. On The Origin Of The Family. Discussion Papers 2010. Web. Publisher's VersionAbstract
This paper presents an overlapping generations model to explain why humans live in families rather than in other pair groupings. Since most non-human species are not familial, something special must be behind the family. It is shown that the two necessary features that explain the origin of the family are given by uncertain paternity and overlapping cohorts of dependent children. With such two features built into our model, and under the assumption that individuals care only for the propagation of their own genes, our analysis indicates that fidelity families dominate promiscuous pair bonding, in the sense that they can achieve greater survivorship and enhanced genetic fitness. The explanation lies in the free riding behavior that characterizes the interactions between competing fathers in the same promiscuous pair grouping. Kin ties could also be related to the emergence of the family. When we consider a kinship system in which an adult male transfers resources not just to his offspring but also to his younger siblings, we find that kin ties never emerge as an equilibrium outcome in a promiscuous environment. In a fidelity family environment, instead, kinship can occur in equilibrium and, when it does, it is efficiency enhancing in terms of greater survivorship and fitness. The model can also be used to shed light on the issue as to why virtually all major world religions are centered around the importance of the family.
Moldovanu, Alex Gershkov, and Benny. Optimal Search, Learning And Implementation. Discussion Papers 2010. Web. Publisher's VersionAbstract
We characterize the incentive compatible, constrained efficient policy ("second-best") in a dynamic matching environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents' values. We also derive conditions on the learning process ensuring that the complete-information, dynamically efficient allocation of resources ("first-best") is incentive compatible. Our analysis reveals and exploits close, formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem, posed by Rothschild [19], of finding optimal stopping policies for search that are characterized by a reservation price property .
Deniz Dizdar, Alex Gershkov, and Benny Moldovanu. Revenue Maximization In The Dynamic Knapsack Problem. Discussion Papers 2010. Web. Publisher's VersionAbstract
We analyze maximization of revenue in the dynamic and stochastic knapsack problem where a given capacity needs to be allocated by a given deadline to sequentially arriving agents. Each agent is described by a two-dimensional type that reflects his capacity requirement and his willingness to pay per unit of capacity. Types are private information. We first characterize implementable policies. Then we solve the revenue maximization problem for the special case where there is private information about per-unit values, but capacity needs are observable. After that we derive two sets of additional conditions on the joint distribution of values and weights under which the revenue maximizing policy for the case with observable weights is implementable, and thus optimal also for the case with two-dimensional private information. In particular, we investigate the role of concave continuation revenues for implementation. We also construct a simple policy for which per-unit prices vary with requested weight but not with time, and prove that it is asymptotically revenue maximizing when available capacity/ time to the deadline both go to infinity. This highlights the importance of nonlinear as opposed to dynamic pricing.
Kareev, Judith Avrahami, and Yaakov. Role Of Impulses In Shaping Decisions, The. Discussion Papers 2010. Web. Publisher's VersionAbstract
This article explores the extent to which decision behavior is shaped by short-lived reactions to the outcome of the most recent decision. We inspected repeated decision-making behavior in two versions of each of two decision-making tasks, an individual task and a strategic one. By regressing behavior onto the outcomes of recent decisions, we found that the upcoming decision was well predicted by the most recent outcome alone, with the tendency to repeat a previous action being affected both by its actual outcome and by the outcomes of actions not taken. Because the goodness of predictions based on the most recent outcome did not diminish as participants gained experience with the task, we conclude that repeated decisions are continuously affected by impulsive reactions.
Aumann, Robert J. . Role Of Incentives In The World Financial Crisis, The. Discussion Papers 2010. Web. Publisher's VersionAbstract
A lecture explaining the causes of the 2008 9 world financial crisis in terms of ordinary economic processes. The lecture was delivered at the 39th St. Gallen Symposium, University of St. Gallen, Switzerland, 8 May 2009.
Larry Goldstein, Yosef Rinott, and Marco Scarsini. Stochastic Comparisons Of Stratifed Sampling Techniques For Some Monte Carlo Estimators. Discussion Papers 2010. Web. Publisher's VersionAbstract
We compare estimators of the (essential) supremum and the integral of a function f defined on a measurable space when f may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that more refined stratification is better with respect to different criteria. The emphasis is on criteria related to stochastic orders. For example, rather than compare estimators of the integral of f by their variances (for unbiased estimators), or mean square error, we attempt the stronger comparison of convex order when possible. For the supremum the criterion is based on the stochastic order of estimators.For some of the results no regularity assumptions for f are needed, whilefor others we assume that f is monotone on an appropriate domain.
Noga Alon, Michal Feldman, Ariel D. Procaccia, and Moshe Tennenholtz. Strategyproof Approximation Mechanisms For Location On Networks. Discussion Papers 2010. Web. Publisher's VersionAbstract
We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost.We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a tight approximation ratio of 3/2 for the maximum cost when the network is a circle; and weshow that no randomized SP mechanism can provide an approximation ratio better than 2-o(1) to the maximum cost even when the network is a tree, thereby matching a trivial upper bound of two.
David Azriel, Micha Mandel, and Yosef Rinott. Treatment Versus Experimentation Dilemma In Dose-Finding Studies, The. Discussion Papers 2010. Web. Publisher's VersionAbstract
Phase I clinical trials are conducted in order to find the maximum tolerated dose (MTD) of a given drug from a finite set of doses. For ethical reasons, these studies are usually sequential, treating patients or group of patients with the best available dose according to the current knowledge. However, it is proved here that such designs, and, more generally, designs that concentrate on one dose from some time on, cannot provide consistent estimators for the MTD unless very strong parametric assumptions hold. We describe a family of sequential designs that treat individuals with one of the two closest doses to the estimated MTD, and prove that such designs, under general conditions, concentrate eventually on the two closest doses to the MTD and estimate the MTD consistently. It is shown that this family contains randomized designs that assign the MTD with probability that approaches 1 as the size of the experiment goes to infinity. We compare several designs by simulations, studying their performances in terms of correct estimation of the MTD and the proportion of individuals treated with the MTD.
Edith Cohen, Michal Feldman, Amos Fiat Haim Kaplan, and Svetlana Olonetsky. Truth And Envy In Capacitated Allocation Games. Discussion Papers 2010. Web. Publisher's VersionAbstract
We study auctions with additive valuations where agents have a limit on the number of items they may receive. We refer to this setting as capacitated allocation games. We seek truthful and envy free mechanisms that maximize the social welfare. I.e., where agents have no incentive to lie and no agent seeks to exchange outcomes with another.In 1983, Leonard showed that VCG with Clarke Pivot payments (which is known to be truthful, individually rational, and have no positive transfers), is also an envy free mechanism for the special case of n items and n unit capacity agents. We elaborate upon this problem and show that VCG with Clarke Pivot payments is envy free if agent capacities are all equal. When agent capacities are not identical, we show that there is no truthful and envy free mechanism that maximizes social welfare if one disallows positive transfers.For the case of two agents (and arbitrary capacities) we show a VCG mechanism that is truthful, envy free, and individually rational, but has positive transfers. We conclude with a host of open problems that arise from our work.
Noam Bar-Shai, Tamar Keasar, and Avi Shmida. Use Of Numerical Information By Bees In Foraging Tasks, The. Discussion Papers 2010. Web. Publisher's VersionAbstract
The ability of invertebrates to perform complex cognitive tasks is widely debated. Bees utilize the number of landmarks en-route to their destination as cues for navigation, but their use of numerical information in other contexts has not been studied. Numerical regularity in the spatial distribution of food occurs naturally in some flowers, which contain a fixed number of nectaries. Bees that collect nectar from such flowers are expected to increase their foraging efficiency by avoiding return visits to empty nectaries. This can be achieved if bees base their flowerdeparture decisions on the number of nectaries they had already visited, or on other sources of information that co-vary with this number.We tested, through field observations and laboratory experiments, whether bees adapt their departure behavior to the number of available food resources. Videorecorded observations of bumblebees that visited Alcea setosa flowers with five nectaries revealed that the conditional probability of flower departure after five probings was 93%. Visit duration, the spatial attributes of the flowers and scent marks could be excluded as flower-leaving cues, while the volume of nectar collected may have guided part of the departure decisions. In the laboratory the bees foraged on two patches, each with three computer-controlled feeders, but could receive only up to two sucrose-solution rewards in each patch visit. The foragers gradually increased their tendency to leave the patches after the second reward, while the frequency of patch departure after the first reward remained constant. Patch-visit duration, nectar volume, scent marks and recurring visit sequences in a patch were ruled out as possible sources of patch-leaving information.We conclude that bumblebees distinguish among otherwise identical stimuli by their serial position in a sequence, and use this capability to increase foraging efficiency. Our findings support an adaptive role for a complicated cognitive skill in a seemingly small and simple invertebrate.
Ro'i Zultan, 5a Bar-Hillel, Nitsan Guy . When Being Wasteful Is Better Than Feeling Wasteful. Discussion Papers 2010. Web. Publisher's VersionAbstract
"Waste not want not" expresses our culture's aversion to waste. "I could have gotten the same thing for less" is a sentiment that can diminish pleasure in a transaction. We study people's willingness to "pay" to avoid this spoiler. In one scenario, participants imagined they were looking for a rental apartment, and had bought a subscription to an apartment listing. If a cheaper subscription had been declined, respondents preferred not to discover post hoc that it would have sufficed. Specifically, they preferred ending their quest for the ideal apartment after seeing more, rather than fewer, apartments. Other scenarios produced similar results. We conclude that people may sometimes prefer to be wasteful in order to avoid feeling wasteful.
Self Control in Society, Mind, and Brain
Ran, Hassin, Kevin Ochsner, and Yaacov Trope. Self Control In Society, Mind, And Brain. Oxford Series in Social Cognition and Social Neuroscience, 2010. Print.
Strategic Social Choice: Stable Representations of Constitutions
Peleg, Bezalel, and Hans Peters. Strategic Social Choice: Stable Representations Of Constitutions. Springer, 2010. Print.

This monograph studies representations of effectivity functions by game forms that are at least Nash consistent, which means that they have a Nash equilibrium for any profile of preferences. In the second part the focus is on social choice functions that admit a strong Nash equilibrium resulting in the sincere outcome. A central interpretation of an effectivity function is that it models a constitution.

2009
Hart, Sergiu . A Simple Riskiness Order Leading To The Aumann &Ldquo;Serrano Index Of Riskiness. Discussion Papers 2009. Web. Publisher's VersionAbstract
We introduce a simple "riskier than" order between gambles, from which the index of riskiness developed by Aumann and Serrano (2008) is directly obtained.
Hellman, Ziv . Bargaining Set Solution Concepts In Repeated Cooperative Games. Discussion Papers 2009. Web. Publisher's VersionAbstract
This paper is concerned with the question of extending the definition of the bargaining set, a cooperative game solution, when cooperation takes place in a repeated setting. The focus is on situations in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative games in each time period. Two alternative definitions of what a `sequence of coalitions' means in such a context are considered, in respect to which the concept of a repeated game bargaining set may be defined, and existence and non-existence results are studied. A solution concept we term subgame-perfect bargaining set sequences is also defined, and sufficient conditions are given for the nonemptiness of subgame-perfect solutions in the case of a finite number of time periods.
Schuster, Amir Perelberg, and Richard. Bottlenose Dolphins (Tursiops Truncatus) Prefer To Cooperate When Petted: Integrating Proximate And Ultimate Explanations Ii. Discussion Papers 2009. Web. Publisher's VersionAbstract
' Cooperation poses theoretical problems because the behaviors of individuals can benefit others. Evolutionary and game-theory explanations that focus on maximizing one's own material outcomes are usually supported by experimental models with isolated and anonymous subjects. Cooperation in the natural world, however, is often a social act whereby familiar individuals coordinate behaviors for shared outcomes. Social cooperation is also associated with a cooperation bias expressed as a preference for cooperation even when noncooperation is immediately more beneficial. The authors report on evidence for such a bias in a captive group of bottlenose dolphins that voluntarily preferred to receive petting from human guides by using a pairwise coordinated approach, even though this was more difficult, and total petting amount was thereby reduced. To explain why this bias occurs, the authors propose an integrated behavioral-evolutionary approach whereby performance is determined by two kinds of immediate outcomes: material gains and intrinsic affective states associated with cooperating. The latter can provide reinforcement when immediate material gains are reduced, delayed, or absent. Over a lifetime, this proximate mechanism can lead to cooperative relationships whose long-term ultimate consequences can be adaptive.
Perry, Alex Gershkov, and Motty. Contracts For Providers Of Medical Treatments. Discussion Papers 2009. Web. Publisher's VersionAbstract
We analyze the nature of optimal contracts in a dynamic model of repeated (and persistent) adverse selection and moral hazard. In particular we consider the case of surgeons who diagnose patients and then decide whether to perform an operation, and if so, whether to exert a costly but unobservable effort. The probability of a successful operation is a function of the surgeon's effort, his quality, and the severity of the patient's problem, all of which are the surgeon's private information.The principal observes only the history of successes and failures and is allowed to promise financial rewards as a function of the observed history. His goal is to provide incentives at minimum cost so that if the patient needs minor surgery he will be treated by any type of surgeon (low- or high-quality) but if he needs major surgery, only a high-quality surgeon will perform the operation.The optimal contract-pair is characterized and is shown to reflect the practice often observed in the medical industry. Performing an operation is a gamble whose probability of success is higher, the higher the quality of the surgeon. A sequence of operations is exponentially less likely to be successful if the surgeon is not high-quality. An optimal contract for a high-quality surgeon exploits this fact by stipulating a high reward conditional on a long history of successes, while such a stipulation makes the contract much less attractive to a low-quality surgeon.