2011
Loewenstein, Tal Neiman, and Yonatan.
“Reinforcement Learning In Professional Basketball Players”.
Discussion Papers 2011. Web.
Publisher's VersionAbstractReinforcement learning in complex natural environments is a challenging task because the agent should generalize from the outcomes of actions taken in one state of the world to future actions in different states of the world. The extent to which human experts find the proper level of generalization is unclear. Here we show, using the sequences of field goal attempts made by professional basketball players, that the outcome of even a single field goal attempt has a considerable effect on the rate of subsequent 3 point shot attempts, in line with standard models of reinforcement learning. However, this change in behaviour is associated with negative correlations between the outcomes of successive field goal attempts. These results indicate that despite years of experience and high motivation, professional players overgeneralize from the outcomes of their most recent actions, which leads to decreased performance.
Cao, Zhigang .
“Remarks On Bargaining And Cooperation In Strategic Form Games”.
Discussion Papers 2011. Web.
Publisher's VersionAbstractAlthough possessing many beautiful features, the Hart and Mas-Colell bargaining model is not flawless: the concept of threat in this model may behave quite counter-intuitive, and its SP equilibrium expected payoff vector may not be the same as the min-max solution payoff vector in zero-sum games. If we postpone realizations of all threats to the end of the game, the two problems can be solved simultaneously. This is exactly the 2(a) model suggested by Hart and Mas-Colell in the last section of their paper. I show that the new model, unfortunately, can only guarantee the existence of an SP equilibrium in the two player case. For the original model, I reduce the computation of an SP equilibrium to a system of linear inequalities. Quantitative efficiency and symmetric SP equilibria are also discussed.
Hassin, Asael Y. Sklar, and Ran R. “Unseen But Not Unsolved: Doing Arithmetic Non-Consciously”.
Discussion Papers 2011. Web.
Publisher's VersionAbstractThe modal view in the cognitive sciences holds that consciousness is necessary for abstract, symbolic and rule-following computations. Hence, mathematical thinking in general, and doing arithmetic more specifically, are widely believed to require consciousness. In the current paper we use continuous flash suppression to expose participants to extremely long-duration (up to 2000 milliseconds) subliminal arithmetic equations. The results of three experiments show that the equations were solved without ever reaching consciousness. In other words, they show that arithmetic can be done unconsciously. These findings imply that the modal view of the unconscious needs to be significantly updated, to include symbolic processes that were heretofore considered to be uniquely conscious.
Maya Bar-Hillel, Ro`i Zultan .
“We Sing The Praise Of Good Displays: How Gamblers Bet In Casino Roulette”.
Discussion Papers 2011. Web.
Publisher's VersionAbstractGambling frequencies on single numbers in real casino roulette were displayed in a contour map. This resulted not only in a confirmation that gamblers are subject to middle bias, but also to accessibility effects. The figure allowed us to infer the location of the roulette wheel and croupier from the gambling data, as well as infer bounds on the dimensions of the roulette table.
Knafo, Ariel et al. Pathological Altruism. Oxford University Press, 2011. Print.
The benefits of altruism and empathy are obvious. These qualities are so highly regarded and embedded in both secular and religious societies that it seems almost heretical to suggest they can cause harm. Like most good things, however, altruism can be distorted or taken to an unhealthy extreme. Pathological Altruism presents a number of new, thought-provoking theses that explore a range of hurtful effects of altruism and empathy. Pathologies of empathy, for example, may trigger depression as well as the burnout seen in healthcare professionals. The selflessness of patients with eating abnormalities forms an important aspect of those disorders. Hyperempathy - an excess of concern for what others think and how they feel - helps explain popular but poorly defined concepts such as codependency. In fact, pathological altruism, in the form of an unhealthy focus on others to the detriment of one's own needs, may underpin some personality disorders. Pathologies of altruism and empathy not only underlie health issues, but also a disparate slew of humankind's most troubled features, including genocide, suicide bombing, self-righteous political partisanship, and ineffective philanthropic and social programs that ultimately worsen the situations they are meant to aid. Pathological Altruism is a groundbreaking new book - the first to explore the negative aspects of altruism and empathy, seemingly uniformly positive traits. The contributing authors provide a scientific, social, and cultural foundation for the subject of pathological altruism, creating a new field of inquiry. Each author's approach points to one disturbing truth: what we value so much, the altruistic "good" side of human nature, can also have a dark side that we ignore at our peril.
2010
Bar-Hillel, Maya .
“A Commentary On Mel Rutherford's 'On The Use And Misuse Of The "Two Children Brainteaser'”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractRutherford (2010) criticizes the way some people have analyzed the 2-children problem, claiming (correctly) that slight nuances in the problem's formulation can change the correct answer. However, his own data demonstrate that even when there is a unique correct answer, participants give intuitive answers that differ from it systematically – replicating the data reported by those he criticizes. Thus, his critique reduces to an admonition to use care in formulating and analyzing this brainteaser – which is always a good idea – but contributes little to what is known, analytically or empirically, about the 2-children problem.
Aumann, Robert J. .
“A Response Regarding The Matter Of The Man With Three Wives”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractA response to criticism of the paper "On the Matter of the Man with Three Wives," Moriah 22 (1999), 98- 107 (see also Rationality Centerdp 102, June 1996). The Moriah paper is a non-mathematical account, written in Hebrew for the Rabbinic public, of "Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud," by R. Aumann and M. Maschler, J. Econ. Th. 36 (1985), 195- 213. The current response appeared in Hama'yan 50 (2010), 1- 11.
Maya Bar-Hillel, Alon Maharshak, Avital Moshinsky Ruth Nofech .
“A Rose By Any Other Name: A Social-Cognitive Perspective On Poets And Poetry”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractEvidence, anecdotal and scientific, suggests that people treat (or are affected by) products of prestigious sources differently than those of less prestigious, or of anonymous, sources. The products which are the focus of the present study are poems, and the sources are the poets. We explore the manner in which the poet s name affects the experience of reading a poem. Study 1 establishes the effect we wish to address: a poet s reputation enhances the evaluation of a poem. Study 2 asks whether it is only the reported evaluation of the poem that is enhanced by the poet s name (as was the case for The Emperor s New Clothes) or the enhancement is genuine and unaware. Finding for the latter, Study 3 explores whether the poet s name changes the reader s experience of it, so that in a sense one is reading a different poem. We conclude that it is not so much that the attributed poem really differs from the unattributed poem, as that it is just ineffably better. The name of a highly regarded poet seems to prime quality, and the poem becomes somehow better. This is a more subtle bias than the deliberate one rejected in Study 2, but it is a bias nonetheless. Ethical implications of this kind of effect are discussed.
Lev, Omer .
“A Two-Dimensional Problem Of Revenue Maximization”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractWe consider the problem of finding the mechanism that maximizes the revenue of a seller of multiple objects. This problem turns out to be significantly more complex than the case where there is only a single object (which was solved by Myerson [5]). The analysis is difficult even in the simplest case studied here, where there are two exclusive objects and a single buyer, with valuations uniformly distributed on triangular domains. We show that the optimal mechanisms are piecewise linear with either 2 or 3 pieces, and obtain explicit formulas for most cases of interest
Hellman, Ziv .
“Almost Common Priors”.
Discussion Papers 2010. Web.
Publisher's VersionAbstract{What happens when priors are not common? We show that for each type pro¬le „ over a knowledge space (\copyright, ), where the state space \copyright is connected with respect to the partition pro¬le , we can associate a value 0 / 1 that we term the prior distance of „
Arieli, Itai .
“Backward Induction And Common Strong Belief Of Rationality”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractIn 1995, Aumann showed that in games of perfect information, common knowledge of rationality is consistent and entails the back- ward induction (BI) outcome. That work has been criticized because it uses "counterfactual" reasoning|what a player "would" do if he reached a node that he knows he will not reach, indeed that he him- self has excluded by one of his own previous moves. This paper derives an epistemological characterization of BI that is outwardly reminiscent of Aumann's, but avoids counterfactual reason- ing. Specifically, we say that a player strongly believes a proposition at a node of the game tree if he believes the proposition unless it is logically inconsistent with that node having been reached. We then show that common strong belief of rationality is consistent and entails the BI outcome, where - as with knowledge - the word "common" signifies strong belief, strong belief of strong belief, and so on ad infinitum. Our result is related to - though not easily derivable from - one obtained by Battigalli and Sinischalchi [7]. Their proof is, however, much deeper; it uses a full-blown semantic model of probabilities, and belief is defined as attribution of probability 1. However, we work with a syntactic model, defining belief directly by a sound and complete set of axioms, and the proof is relatively direct.
Noga Alon, Yuval Emek, Michal Feldman, and Moshe Tennenholtz.
“Bayesian Ignorance”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractWe quantify the effect of Bayesian ignorance by comparing the social cost obtained in a Bayesian game by agents with local views to the expected social cost of agents having global views. Both benevolent agents, whose goal is to minimize the social cost, and selfish agents, aiming at minimizing their own individual costs, are considered. When dealing with selfish agents, we consider both best and worst equilibria outcomes. While our model is general, most of our results concern the setting of network cost sharing (NCS) games. We provide tight asymptotic results on the effect of Bayesian ignorance in directed and undirected NCS games with benevolent and selfish agents. Among our findings we expose the counter-intuitive phenomenon that "ignorance is bliss": Bayesian ignorance may substantially improve the social cost of selfish agents. We also prove that public random bits can replace the knowledge of the common prior in attempt to bound the effect of Bayesian ignorance in settings with benevolent agents. Together, our work initiates the study of the effects of local vs. global views on the social cost of agents in Bayesian contexts.
Rinott, Yaakov Malinovsky, and Yosef.
“Best Invariant And Minimax Estimation Of Quantiles In Finite Populations”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractWe study estimation of finite population quantiles, with emphasis on estimators that are invariant under monotone transformations of the data, and suitable invariant loss functions. We discuss non-randomized and randomized estimators, best invariant and minimax estimators and sampling strategies relative to different classes. The combination of natural invariance of the kind discussed here, and finite population sampling appears to be novel, and leads to interesting statistical and combinatorial aspects.
Hart, Sergiu .
“Comparing Risks By Acceptance And Rejection”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractStochastic dominance is a partial order on risky assets ("gambles") that is based on the uniform preference, of all decision-makers (in an appropriate class), for one gamble over another. We modify this, first, by taking into account the status quo (given by the current wealth) and the possibility of rejecting gambles, and second, by comparing rejections that are substantive (that is, uniform over wealth levels or over utilities). This yields two new stochastic orders: wealth-uniform dominance and utility-uniform dominance. Unlike stochastic dominance, these two orders are complete: any two gambles can be compared. Moreover, they are equivalent to the orders induced by, respectively, the Aumann-Serrano (2008) index of riskiness and the Foster-Hart (2009a) measure of riskiness.
Babichenko, Yakov .
“Completely Uncoupled Dynamics And Nash Equilibria”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractA completely uncoupled dynamic is a repeated play of a game, where each period every player knows only his action set and the history of his own past actions and payoffs. One main result is that there exist no completely uncoupled dynamics with finite memory that lead to pure Nash equilibria (PNE) in almost all games possessing pure Nash equilibria. By "leading to PNE" we mean that the frequency of time periods at which some PNE is played converges to 1 almost surely. Another main result is that this is not the case when PNE is replaced by "Nash epsilon-equilibria": we exhibit a completely uncoupled dynamic with finite memory such that from some time on a Nash epsion-equilibrium is played almost surely.
Kareev, Judith Avrahami, and Yaakov.
“Detecting Change In Partner's Preferences”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractStudies of the detection of change have commonly been concerned with individuals inspecting a system or a process, whose characteristics were fully determined by the researcher. We, instead, study the detection of change in the preferences - and hence the behavior - of others with whom an individual interacts. More specifically, we study situations in which one's benefits are the result of the joint actions of one and one's partner when at times the preferred combination is the same for both and at times it is not. In other words, what we change is the payoffs associated with the different combinations of interactive choices and then look at choice behavior following such a change. We find that players are extremely quick to respond to a change in the preferences of their counterparts. This responsiveness can be explained by the players' impulsive reaction to regret - if one was due - at their most recent decision.
Linial1, Amir Ban, and Nati.
“Dynamics Of Reputation Systems, The”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractOnline reputation systems collect, maintain and disseminate reputations as a summary numerical score of past interactions of an establishmentwith its users. As reputation systems, including web search engines, gain inpopularity and become a common method for people to select sought services, adynamical system unfolds: Experts' reputation attracts the potential customers.The experts' expertise affects the probability of satisfying the customers. Thisrate of success in turn influences the experts' reputation. We consider hereseveral models where each expert has innate, constant, but unknown level ofexpertise and a publicly known, dynamically varying, reputation.The specific
Edith Cohen, Michal Feldman, Amos Fiat Haim Kaplan, and Svetlana Olonetsky.
“Envy-Free Makespan Approximation”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractWe study envy-free mechanisms for scheduling tasks on unrelated machines (agents) that approximately minimize the makespan. For indivisible tasks, we put forward an envy-free poly-time mechanism that approximates the minimal makespan to within a factor of O(logm), where m is the number of machines. We also show a lower bound of Omega(log m/log logm). This improves the recent result of Mu'alem [22] who give an upper bound of (m + 1)/2, and a lower bound of 2 - 1/m. For divisible tasks, we show that there always exists an envy-free poly-time mechanism with optimal makespan. Finally, we demonstrate how our mechanism for envy free makespan minimization can be interpreted as a market clearing problem.
Samuel-Cahn, Jay Bartroff, and Ester.
“Fighter Problem: Optimal Allocation Of A Discrete Commodity, The”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractThe Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with n anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If j of the n missiles are spent at an encounter they destroy an enemy plane with probability a(j), where a(0)=0 and a(j) is a known, strictly increasing concave sequence, e.g., a(j)=1 - qj, 0 < 1. If the enemy is not destroyed, the enemy shoots the fighter down with known probability 1 - u, where 0 u 1. The goal of the fighter is to shoot down as many enemy airplanes as possible during a given time period [0,T ]. Let K(n, t) be an optimal number of missiles to be used at a present encounter, when the fighter has flying time t remaining and n missiles remaining. Three seemingly obvious properties of K(n, t) have been conjectured: [A] The closer to the destination, the more of the n missiles one should use, [B] the more missiles one has, the more one should use, and [C] the more missiles one has, the more one should save for possible future encounters. We show that [C] holds for all 0 u 1, that [A] and [B] hold for the "Invincible Fighter" (u = 1), and that [A] holds but [B] fails for the "Frail Fighter" (u = 0).
Samet, Ziv Hellman, and Dov.
“How Common Are Common Priors?”.
Discussion Papers 2010. Web.
Publisher's VersionAbstractTo answer the question in the title we vary agents' beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the set of consistent type profiles, those that are derived from a common prior (or a common improper prior in the case of an infinite state space). The answer depends on what we term the tightness of the partition profile. A partition profile is tight if in some state it is common knowledge that any increase of any single agent's knowledge results in an increase in common knowledge. We show that for partition profiles which are tight the set of consistent type profiles is topologically large, while for partition profiles which are not tight this set is topologically small.