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Publications | The Federmann Center for the Study of Rationality

Publications

2008
Robert J. Aumann, Ein-Ya Gura, Sergiu Hart Bezalel Peleg Hana Shemesh, and Shmuel Zamir. Michael Maschler: In Memoriam. Discussion Papers 2008. Web. Publisher's Version
Hart, Sergiu . Nash Equilibrium And Dynamics. Discussion Papers 2008. Web. Publisher's VersionAbstract
John F. Nash, Jr., submitted his Ph.D. dissertation entitled Non-Cooperative Games to Princeton University in 1950. Read it 58 years later, and you will find the germs of various later developments in game theory. Some of these are presented below, followed by a discussion concerning dynamic aspects of equilibrium.
Tom de Jong, Avi Shmida, and Frank Thuijsman. Optimal Sex Allocation In Plants And The Evolution Of Monoecy. Discussion Papers 2008. Web. Publisher's VersionAbstract
Question: Which ecological factors favor the transition from plants with hermaphrodite flowers to monoecious plants with separate male and female flowers on the same individual?Mathematical methods: ESS computation in sex allocation models Key assumptions: Within a flower, costs of attraction, pollen production, style/ovary and fruit with seeds are assumed fixed. Often costs of fruit with seeds outweigh other costs. Female flowers produce more seeds than hermaphrodite flowers, due to less pollen-stigma interference.Conclusions: When sex allocation is female-biased at the flower level, plants respond by producing either male flowers or flowers without fruit. Hermaphroditism evolves to andromonoecy (male and hermaphrodite flowers on the same plant) and then to monoecy. In species with large fruits, sex allocation is female-biased at the flower level and the production of male flowers is favored. This facilitates the production of female flowers. The alternative route via gynomonoecy (female and hermaphrodite flowers on the same plant) is improbable since it requires unrealistically high levels of seed production in female flowers. Monoecious species are likely to have: (i) small, inexpensive flowers, (ii) large, costly fruits and seeds, and (iii) high fertilization rates.
Tamar Keasar, Avi Shmida, and Asaph Zylbertal. Pollination Ecology Of The Red Anemone Coronaria (Ranunculaceae): Honeybees May Select For Early Flowering. Discussion Papers 2008. Web. Publisher's VersionAbstract
Large red bowl-shaped flowers characterize the Mediterranean poppy guild  plants, andwere suggested to reflect convergence for beetle pollination. However, the earliest-bloomingspecies in this guild, Anemone coronaria (L.), starts flowering about a month before beetleemergence. Early flowering can be adaptive if the plant receives sufficient pollination by othermeans during this period. We investigated A. coronaria s pollination prospects throughout itsflowering season by monitoring its flowering phenology, the composition of the surroundinginsect community, and insect visitors. Clear protogyny precluded self pollination, and anthesisoccurred gradually over several days. Released pollen was quickly collected by insects,suggesting no major role for wind pollination. Beetles, flies and bees were trapped at the studysite throughout the flowering period. Honeybees were the main anemone visitors during the firstseven weeks of flowering, and were joined by Glaphyrid beetles in the remaining three weeks.Early- and late-blooming flowers had similar female reproductive success. We propose thateffective pollination by honeybees may allow anemones to bloom in early spring and therebyreduce competition for pollinators with later-blooming species. Our results support previousevidence for pollination of red flowers by bees, and for the importance of generalization inpollination interactions in heterogeneous environments.
Arieli, Itai . Rationalizability In Continuous Games. Discussion Papers 2008. Web. Publisher's VersionAbstract
Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff
Aumann, Robert J. . Rule-Rationality Versus Act-Rationality. Discussion Papers 2008. Web. Publisher's VersionAbstract
People's actions often deviate from rationality, i.e., self-interested behavior. We propose a paradigm called rule-rationality, according to which people do not maximize utility in each of their acts, but rather follow rules or modes of behavior that usually-but not always-maximize utility. Specifically, rather than choosing an act that maximizes utility among all possible acts in a given situation, people adopt rules that maximize average utility among all applicable rules, when the same rule is applied to many apparently similar situations. The distinction is analogous to that between Bentham's "act-utilitarianism" and the "rule-utilitarianism" of Mill, Harsanyi, and others. The genesis of such behavior is examined, and examples are given. The paradigm may provide a synthesis between rationalistic neo-classical economic theory and behavioral economics.
Lehmann, Daniel . Similarity-Projection Structures: The Logical Geometry Of Quantum Physics. Discussion Papers 2008. Web. Publisher's VersionAbstract
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical meaning. They provide a formal framework that subsumes both classical boolean logic concerned with sets and subsets and quantum logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel notion that is free of linear algebra.
Ilan Yaniv, Shoham Choshen-Hillel, and Maxim Milyavsky. Spurious Consensus And Opinion Revision: Why Might People Be More Confident In Their Less Accurate Judgments?. Discussion Papers 2008. Web. Publisher's VersionAbstract
In the interest of improving their decision-making, individuals revise their opinions on the basis of samples of opinions obtained from others. However, such a revision process may lead decision-makers to experience greater confidence in their less accurate judgments. We theorize that people tend to underestimate the informative value of independently drawn opinions, if these appear to conflict with one another, yet place some confidence even in the "spurious consensus" which may arise when opinions are sampled interdependently. The experimental task involved people s revision of their opinions (caloric estimates of foods) on the basis of advice. The method of sampling the advisory opinions (independent or interdependent) was the main factor. The results reveal a dissociation between confidence and accuracy. A theoretical underlying mechanism is suggested whereby people attend to consensus (consistency) cues at the expense of information on interdependence. Implications for belief-updating and for individual and group decisions are discussed.
Gorodeisky, Ziv . Stochastic Approximation Of Discontinuous Dynamics. Discussion Papers 2008. Web. Publisher's VersionAbstract
We consider stochastic dynamics whose expected (average) vector field is not necessarily continuous. We generalize the ordinary differential equation method for analyzing stochastic processes to this case, by introducing leading functions that 'lead  the stochastic process across the discontinuities, which yields approximation results for the asymptotic behavior of the stochastic dynamic. We then apply the approximation results to the classical best-response dynamics used in game theory.
Arieli, Itai . Towards A Characterization Of Rational Expectations. Discussion Papers 2008. Web. Publisher's VersionAbstract
R. J. Aumann and J. H. Dr¨ze (2008) define a rational expectation of a player i in a game G as the expected payo of some type of i in some belief system for G in which common knowledge of rationalityand common priors obtain. Our goal is to characterize the set of rational expectations in terms of the game's payoff matrix. We provide such a characterization for a specific class of strategic games, calledsemi-elementary, which includes Myerson's "elementary" games.
Game Theoretic Analysis of Voting in Committees
Peleg, Bezalel . Game Theoretic Analysis Of Voting In Committees. Cambridge University Press, 2008. Print.

This book is a theoretical and completely rigorous analysis of voting in committees that provides mathematical proof of the existence of democratic voting systems, which are immune to the manipulation of preferences of coalitions of voters. The author begins by determining the power distribution among voters that is induced by a voting rule, giving particular consideration to choice by plurality voting and Borda's rule. He then constructs, for all possible committees, well-behaved representative voting procedures which are not distorted by strategic voting, giving complete solutions for certain important classes of committees. The solution to the problem of mass elections is fully characterised.

תורת המשחקים
זמיר, שמואל, מיכאל משלר, and אילון סולן. תורת המשחקים. מגנס, 2008. Print.

ספר קורס. תורת המשחקים היא ענף במתמטיקה העוסק במידול מצבי החלטה אינטראקטיביים ובניתוחם. במצבים אלה מעורבים כמה מקבלי החלטות שמטרותיהם שונות, וההחלטה של כל אחד מהם עשויה להשפיע על כל האחרים. ראשיתה של תורה המשחקים בשנות הארבעים של המאה העשרים, ומאז שנות החמישים היא מיושמת בכלכלה, בביולוגיה, במדעי המחשב ובמדעי המדינה. הספר תורת המשחקים מיועד לתלמידי התואר הראשון והשני במתמטיקה, בכלכלה, במדעי המחשב, ולכל תלמיד בעל בסיס מתמטי מתאים. הספר עוסק בתורת המשחקים השיתופית והלא-שיתופית, ונכללים בו נושאים בסיסיים המתאימים הן לקורס ראשון בתורת המשחקים והן לקורסים מתקדמים. בספר דוגמאות רבות ומגוונות ותרגילים בדרגות קושי שונות, המאפשרים תרגול יעיל של החומר הנלמד והטמעתו.

2007
Guttel, Ehud . (Hidden) Risk Of Opportunistic Precautions, The. Discussion Papers 2007. Web. Publisher's VersionAbstract
Under the conventional tort law paradigm, a tortfeasor behaves unreasonably when two conditions are met: the tortfeasor could have averted the harm by investing in cost-effective precautions and failed to do so, and other, more cost-effective precautions were not available to the victim. Torts scholarship has long argued that making such a tortfeasor responsible for the ensuing harm induces optimal care. This Article shows that by applying the conventional analysis, courts create incentives for opportunistic investments in prevention. In order to shift liability to others, parties might deliberately invest in precautions even where such investments are inefficient. The Article presents two possible solutions to the problem. By instituting a combination of (1) broader restitution rules and (2) an extended risk-utility standard, legislators and judges can reform tort law to discourage opportunistic precautions and maximize social welfare.
Nir Halevy, Gary Bornstein, and Lilach Sagiv. Ingroup Love" And Outgroup Hate" As Motives For Individual Participation In Intergroup Conflict: A New Game Paradigm. Discussion Papers 2007. Web. Publisher's VersionAbstract
What motivates individual self-sacrificial behavior in intergroup conflicts? Is it the altruistic desire to help the ingroup or the aggressive drive to hurt the outgroup? This paper introduces a new game paradigm, the Intergroup Prisoner s Dilemma "Maximizing Difference (IPD-MD) game, designed specifically to distinguish between these two motives. The game involves two groups. Each group member is given a monetary endowment and can decide how much of it to contribute. Contribution can be made to either of two pools, one which benefits the ingroup at a personal cost, and another which, in addition, harms the outgroup. An experiment demonstrated that contributions in the IPD-MD game are made almost exclusively to the cooperative within-group pool. Moreover, pre-play intragroup communication increases intragroup cooperation but not intergroup competition. These results are compared with those observed in the Intergroup Prisoner's Dilemma (IPD) game, where group members' contributions are restricted to the competitive between-group pool.
Bornstein, Gary . A Classification Of Games By Player Type. Discussion Papers 2007. Web. Publisher's VersionAbstract
In this paper I classify situations of interdependent decision-making, or games based on the type of decision-makers, or players involved. The classification builds on a distinction between three basic types of decision-making agents: individuals, cooperative or unitary groups – groups whose members can reach a binding (and costless) agreement on a joint strategy – and non-cooperative groups – groups whose members act independently without being able to make a binding agreement. Pitting individuals, unitary groups, and non-cooperative groups against one another, and adding Nature as a potential opponent , generates a 3 (type of agent) X 4 (type of opponent) matrix of social situations. This framework is used to review the experimental decision-making literature and point out the gaps that still exist in it.
Lehmann, Daniel . A Presentation Of Quantum Logic Based On An And Then Connective. Discussion Papers 2007. Web. Publisher's VersionAbstract
When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the and then operation that combines old and new information. The and then connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claimed. Classical physical systems are exactly characterized by the commutativity, the associativity, or the monotonicity of the and then connective. Entailment is defined in this logic and can be proved to be a partial order. In orthomodular lattices, the operation proposed by Finch in [3] satisfies all the properties studied in this paper. All properties satisfied by Finch's operation in modular lattices are valid in Quantum Logic. It is not known whether all properties of Quantum Logic are satisfied by Finch's operation in modular lattices.
Jean-Francois Mertens, Abraham Neyman, and Dinah Rosenberg. Absorbing Games With Compact Action Spaces. Discussion Papers 2007. Web. Publisher's VersionAbstract
We prove that games with absorbing states with compact action sets have a value.
Serrano, Robert J. Aumann, and Roberto. An Economic Index Of Riskiness. Discussion Papers 2007. Web. Publisher's VersionAbstract
Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a "duality" axiom which, roughly speaking, asserts that less risk-averse individuals accept riskier gambles. The index is homogeneous of degree 1, monotonic with respect to first and second order stochastic dominance, and for gambles with normal distributions, is half of variance/mean. Examples are calculated, additional properties derived, and the index is compared with others in the literature.
Ariel D. Procaccia, Michal Feldmany, and Jeffrey S. Rosenschein. Approximability And Inapproximability Of Dodgson And Young Elections. Discussion Papers 2007. Web. Publisher's VersionAbstract
The voting rules proposed by Dodgson and Young are both designed to find the candidate closest to being a Condorcet winner, according to two different notions of proximity; the score of a given candidate is known to be hard to compute under both rules. In this paper, we put forward an LP-based randomized rounding algorithm which yields an O(log m) approximation ratio for the Dodgson score, where m is the number of candidates. Surprisingly, we show that the seemingly simpler Young score is NP-hard to approximate by any factor.
Hart, Dean P. Foster, and Sergiu. An Operational Measure Of Riskiness. Discussion Papers 2007. Web. Publisher's VersionAbstract
We define the riskiness of a gamble g as that unique number R(g) such that no-bankruptcy is guaranteed if and only if one never accepts gambles whose riskiness exceeds the current wealth.