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Publications | The Federmann Center for the Study of Rationality

Publications

2013
Itai Arieli, Robert J. Aumann . Logic Of Backward Induction, The. Discussion Papers 2013. Web. Publisher's VersionAbstract
The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility maximization if and only if it is the BI outcome. Both BS's formulation, and their proof, are complex and deep. We show that the result continues to hold when utility maximization is replaced by a rationality condition that is even more compelling; more important, the formulation and proof become far more transparent, accessible, and self-contained.
Gonczarowski, Yannai A. . Manipulation Of Stable Matchings Using Minimal Blacklists. Discussion Papers 2013. Web. Publisher's VersionAbstract
Gale and Sotomayor (1985) have shown that in the Gale-Shapley matching algorithm (1962), the proposed-to side W (referred to as women there) can strategically force the W-optimal stable matching as the M-optimal one by truncating their preference lists, each woman possibly blacklisting all but one man. As Gusfield and Irving have already noted in 1989, no results are known regarding achieving this feat by means other than such preference-list truncation, i.e. by also permuting preference lists.We answer Gusfield and Irving's open question by providing tight upper bounds on the amount of blacklists and their combined size, that are required by the women to force a given matching as the M-optimal stable matching, or, more generally, as the unique stable matching. Our results show that the coalition of all women can strategically force any matching as the unique stable matching, using preference lists in which at most half of the women have nonempty blacklists, and in which the average blacklist size is less than 1. This allows the women to manipulate the market in a manner that is far more inconspicuous, in a sense, than previously realized. When there are less women than men, we show that in the absence of blacklists for men, the women can force any matching as the unique stable matching without blacklisting anyone, while when there are more women than men, each to-be-unmatched woman may have to blacklist as many as all men. Together, these results shed light on the question of how much, if at all, do given preferences for one side a priori impose limitations on the set of stable matchings under various conditions. All of the results in this paper are constructive, providing efficient algorithms for calculating the desired strategies.
Sergiu Hart, Andreu Mas-Colell . Markets, Correlation, And Regret-Matching. Discussion Papers 2013. Web. Publisher's VersionAbstract
Inspired by the existing work on correlated equilibria and regret-based dynamics in games, we carry out a first exploration of the links between the leading equilibrium concept for (exchange) economies, Walrasian equilibrium, and the dynamics, specifically regret-matching dynamics, of trading games that fit the economic structure and have the property that their pure Nash equilibria implement the Walrasian outcomes. Interestingly, in the case of quasilinear utilities (or "transferable utility"), all the concepts essentially coincide, and we get simple deterministic dynamics converging to Walrasian outcomes. Connections to sunspot equilibria are also studied.
Sergiu Hart, Noam Nisan . Menu-Size Complexity Of Auctions, The. Discussion Papers 2013. Web. Publisher's VersionAbstract
We consider the menu size of auctions as a measure of auction complexity and study how it affects revenue. Our setting has a single revenue-maximizing seller selling two or more heterogenous items to a single buyer whose private values for the items are drawn from a (possibly correlated) known distribution, and whose valuation is additive over the items. We show that the revenue may increase arbitrarily with menu size and that a bounded menu size can not ensure any positive fraction of the optimal revenue. The menu size turns out to "nail down" the revenue properties of deterministic auctions: their menu size may be at most exponential in the number of items and indeed their revenue may be larger than that achievable by the simplest types of auctions by a factor that is exponential in the number of items but no larger. Our model is related to a previously studied "unit-demand" model and our results also answer an open problem in that model.
Yaari, Menahem . Newcomb`s Problem: Paradox Lost. Discussion Papers 2013. Web. Publisher's VersionAbstract
' An agent needs to decide which of two available actions, A or B, to take. The agent's payoffs are such that A dominates B, i.e., taking A yields a better payoff than taking B, in every contingency. On the other hand, the agent's expected payoffs, given the action taken, are in the reverse order, i.e., E(payoff | B) > E(payoff | A) , which can happen if the probabilities of the various contingencies are not independent of the action being taken. What should the agent do? This dilemma has come to be known as Newcomb's Paradox (Nozick, 1969). The present essay shows that the rule "keep away, as much as possible, from any dominated action" is perfectly consistent with actually taking the dominated action, when appropriate. No paradox.''
Rune Midjord, Tom s Rodr �guez-Barraquer, Justin Valasek . Over-Caution Of Large Committees Of Experts. Discussion Papers 2013. Web. Publisher's VersionAbstract
In this paper, we demonstrate that payoffs linked to a committee member's individual vote may explain over-cautious behavior in committees. A committee of experts must decide whether to approve or reject a proposed innovation on behalf of society. In addition to a payoff linked to the adequateness of the committee's decision, each expert receives a disesteem payoff if he/she voted in favor of an ill-fated innovation. An example is FDA committees, where committee members can be exposed to a disesteem (negative) payoff if they vote to pass a drug that proves to be fatal for some users. We show that no matter how small the disesteem payoffs are, information aggregation fails in large committees: under any majority rule, the committee rejects the innovation almost surely. We then show that this inefficiency can be mitigated by pre-vote information pooling, but only if the decision is take under unanimity: in the presence of disesteem payoffs, committee members will only vote efficiently if they are all responsible for the final decision.
Tamar Keasar, Miriam Kishinevsky, Avi Shmida Yoram Gerchman Nicka Chinkov Avi Koplovich Gadi Katzir . Plant-Derived Visual Signals May Protect Beetle Herbivores From Bird Predators. Discussion Papers 2013. Web. Publisher's VersionAbstract
Insect herbivores often use chemical signals obtained from their food plants to deter enemies and/or attract sexual partners. Do plant-based visual signals act similarly, i.e., repel consumers' enemies and appeal to potential mates? We explored this question using the pollen-feeding beetle Pygopleurus israelitus (Glaphyridae), a specialized pollinator of Anemone coronaria's chemically defended red-morph flowers. We presented dead beetles, which had fed either on anemones or on cat-food, to young domestic chicks on a red (anemone-like) or a green (leaf-like) background. We determined whether the beetles' background color and diet affected the chicks' feeding. Cuticle surface extracts from anemone-fed beetles, but not from cat-food-fed beetles, contained a secondary metabolite characteristic of anemones. Latencies to the first picking-up and consuming of beetles from green backgrounds were shorter than of beetles from red backgrounds. The picking-up order of beetles also indicated that prey from the green background was preferred. The chicks retained this preference when re-tested, three days later. Handling times of anemone-fed beetles were longer than of cat-food-fed beetles. A previous study showed that glaphyrids improve their mate-finding prospects by orienting to large red anemone flowers. Here, female beetles preferred cat-food-fed to anemone-fed males in mate-choice assays, thus anemone-derived chemicals did not increase mating success. Instead, the combined results indicate that A. coronaria's red flowers provide a visual signal that may both deter its herbivore's predators and attract its mates. To our knowledge, this is the first experimental evidence for a potential protective role of plant-derived visual signals for insect herbivores/pollinators. Keywords: Predation; secondary metabolite; tritrophic interactions; warning coloration; domestic chick; Glaphyridae; pollination.
Sergiu Hart, Noam Nisan . Query Complexity Of Correlated Equilibria, The. Discussion Papers 2013. Web. Publisher's VersionAbstract
We consider the complexity of finding a Correlated Equilibrium in an n-player game in a model that allows the algorithm to make queries for players' utilities at pure strategy profiles. Many randomized regret-matching dynamics are known to yield an approximate correlated equilibrium quickly: in time that is polynomial in the number of players, n, the number of strategies of each player, m, and the approximation error, 1/?. Here we show that both randomization and approximation are necessary: no efficient deterministic algorithm can reach even an approximate equilibrium and no efficient randomized algorithm can reach an exact equilibrium.
Bezalel Peleg, Shmuel Zamir . Representation Of Constitutions Under Incomplete Information. Discussion Papers 2013. Web. Publisher's VersionAbstract
We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizen are private information. We investigate whether there exist decision schemes (i. e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties. When applied to n-person games in strategic form, a decision scheme d is a mapping from profiles of (dichotomous) preferences on the set of pure strategy vectors to probability distributions over outcomes (or equivalently, over pure strategy vectors). We prove that for any feasible and individually rational payoff vector of a strategic game, there exists a decision scheme that yields that payoff vector as a (pure) Nash equilibrium payoff in the game induced by the strategic game and the decision scheme. This can be viewed as a kind of purification result.
Neyman, Abraham . Stochastic Games With Short-Stage Duration. Discussion Papers 2013. Web. Publisher's VersionAbstract
We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k'geq 0$, of a stochastic game $'Gamma_'delta$ with stage duration $'delta$ is interpreted as the play in time $k'delta'leq t0$ as the stage duration $'delta$ goes to $0$, and study the asymptotic behavior of the value, optimal strategies, and equilibrium. The asymptotic analogs of the discounted, limiting-average, and uniform equilibrium payoffs are defined. Convergence implies the existence of an asymptotic discounted equilibrium payoff, strong convergence implies the existence of an asymptotic limiting-average equilibrium payoff, and exact convergence implies the existence of an asymptotic uniform equilibrium payoff.
Aboodi, Ron . Why Good People Reevaluate Underived Moral Beliefs?. Discussion Papers 2013. Web. Publisher's VersionAbstract
Are good people motivated to behave in accordance the moral truth whatever it is? Michael Smith, who has named this motivation the de-dicto moral motivation, famously criticized it. According to Smith, good people are instead motivated directly by more concrete moral concerns, such as 'the well-being of their fellows, people getting what they deserve, justice, equality, and the like . Here I argue for the non-Smithian view that good people have (also) a de-dicto moral motivation. The argument runs roughly as follows: given that good people tend to behave appropriately, and that in some situations it is appropriate to reevaluate one s underived moral beliefs, good people tend to seriously reevaluate underived moral beliefs sometimes. Theories of motivation have to account for this fact (a point overlooked by Smith and his respondents). What motivates a good person to pay attention to evidence that is contrary to her underived moral beliefs? What does she aim for in reevaluating those beliefs? I argue that the view that good people are motivated to act morally de-dicto is in a better position to explain the relevant facts about good people s reevaluation of underived moral beliefs.
מדוע האהבה כואבת
אילוז, אווה. מדוע האהבה כואבת. כתר, 2013. Print.

מעטים האנשים שלא חוו את הייסורים הכרוכים במערכות יחסים אינטימיות. לייסורים אלה צורות רבות: אנחנו אוהבים גבר או אישה שלא מוכנים להתחייב לנו, לבנו נשבר כאשר אהובנו או אהובתנו עוזבים אותנו, אנחנו שקועים בחיפושים סיזיפיים באינטרנט, חוזרים גלמודים מברים, ממסיבות או מפגישות עיוורות, משתעממים במערכת יחסים הרחוקה כל כך מציפיותינו. בספרה החדש והנועז, מדוע האהבה כואבת, מנסה פרופסור אווה אילוז, מבכירי הסוציולוגים בעולם, לבחון את החוויות האלה, הפרטיות לכאורה, באמצעות התבוננות ביקורתית בדרכים שבהן מיוצרת, נכתבת, משווקת ונחווית האהבה בימינו. לטענת אילוז, הפסיכואנליזה והפסיכולוגיה הפופולרית הפליאו לשכנע אותנו שיחידים נושאים באחריות לאומללות חייהם הרומנטיים והארוטיים. ואילו מטרתו של הספר הזה היא לשנות את זווית הניתוח של הבעיה במערכות יחסים בימינו ולהסביר כי לא ילדות לקויה היא הבעיה אלא הכוחות המוסדיים שמעצבים את האופן שבו אנחנו אוהבים. אווה אילוז היא פרופסור לסוציולוגיה באוניברסיטה העברית בירושלים ונשיאת האקדמיה לאמנות ועיצוב בצלאל. עבודותיה בתחום הסוציולוגיה של הרגשות זכו להכרה רחבה. מדוע האהבה כואבת פורסם באנגלית, בצרפתית ובגרמנית, עורר הדים רבים, זכה לשבחים ואף היה לרב-מכר. בעברית ראו אור עד כה ארבעה מספריה הקודמים, ביניהם אינטימיות קרה – עלייתו של הקפיטליזם הרגשי וגאולת הנפש המודרנית – פסיכולוגיה, רגשות ועזרה עצמית. כמו כן מפרסמת אילוז מסות בענייני תרבות וחברה במוסף "הארץ".

2012
Levy, Yehuda (John) . A Cantor Set Of Games With No Shift-Homogeneous Equilibrium Selection. Discussion Papers 2012. Web. Publisher's VersionAbstract
We construct a continuum of games on a countable set of players that does not possess a measurable equilibrium selection that satisfies a natural homogeneity property. The explicit nature of the construction yields counterexamples to the existence of equilibria in models with overlapping generations and in games with a continuum of players.
Levy, Yehuda (John) . A Discounted Stochastic Game With No Stationary Equilibria: The Case Of Absolutely Continuous Transitions. Discussion Papers 2012. Web. Publisher's VersionAbstract
We present a discounted stochastic game with a continuum of states, finitely many players and actions, such that although all transitions are absolutely continuous w.r.t. a fixed measure, it possesses no stationary equilibria. This absolute continuity condition has been assumed in many equilibrium existence results, and the game presented here complements a recent example of ours of a game with no stationary equilibria but which possess deterministic transitions. We also show that if one allows for compact action spaces, even games with state-independent transitions need not possess stationary equilibria.
Levy, Yehuda (John) . A Discounted Stochastic Game With No Stationary Nash Equilibrium. Discussion Papers 2012. Web. Publisher's VersionAbstract
We present an example of a discounted stochastic game with a continuum of states, finitely many players and actions, and deterministic transitions, that possesses no measurable stationary equilibria, or even stationary approximate equilibria. The example is robust to perturbations of the payoffs, the transitions, and the discount factor, and hence gives a strong nonexistence result for stationary equilibria. The example is a game of perfect information, and hence it also does not possess stationary extensive-form correlated equilibrium. Markovian equilibria are also shown not to exist in appropriate perturbations of our example.
Hellman, Ziv . A Game With No Bayesian Approximate Equilibria. Discussion Papers 2012. Web. Publisher's VersionAbstract
Simon (2003) presented an example of a 3-player Bayesian games with no Bayesian equilibria but it has been an open question whether or not there are games with no approximate Bayesian equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states that possesses no approximate Bayesian equilibria, thus resolving the question. As a side benefit we also have for the first time an an example of a 2-player Bayesian game with no Bayesian equilibria and an example of a strategic-form game with no approximate Nash equilibria. The construction makes use of techniques developed in an example by Y. Levy of a discounted stochastic game with no stationary equilibria.
Kareev, Yaakov . Advantages Of Cognitive Limitations. Discussion Papers 2012. Web. Publisher's VersionAbstract
Being a product of evolutionary pressures, it would not be surprising to find that what seems to be a limitation of the cognitive system is actually a fine-tuned compromise between a set of competing needs. This thesis is demonstrated using the case of the limited capacity of short-term memory, which is often regarded as the prime example of a cognitive limitation.
Konigsberg, Amir . Aesthetic Autonomy. Discussion Papers 2012. Web. Publisher's VersionAbstract
The acquaintance principle (AP) and the view it expresses have recently been tied to a debatesurrounding the possibility of aesthetic testimony, which, plainly put, deals with the questionwhether aesthetic knowledge can be acquired through testimony-typically aesthetic and non-aesthetic descriptions communicated from person to person. In this context a number of suggestions have been put forward opting for a restricted acceptance of AP. This paper is an attempt to restrict AP even more
Schreiber, Amnon . An Economic Index Of Relative Riskiness. Discussion Papers 2012. Web. Publisher's VersionAbstract
In their seminal works, Arrow (1965) and Pratt (1964) defined two aspects of risk aversion: absolute risk aversion and relative risk aversion. Based on their definitions, we define two aspects of risk: absolute risk and relative risk. We consider situations in which, by making an investment, an agent exchanges a certain amount of wealth w by a random distributed level of wealth W. In such situations, we define absolute risk as the riskiness of a gamble that is distributed as W-w, and relative risk as the riskiness of a security that is distributed as W/w. We measure absolute risk by the Aumann and Serrano (2008) index of riskiness and relative risk by an equivalent index that we develop in this paper. The two concepts of risk do not necessarily agree on which one of two investments is riskier, and hence they capture two different aspects of risk.
Fabrizio Germano, Peio Zuazo-Garin . Approximate Knowledge Of Rationality And Correlated Equilibria. Discussion Papers 2012. Web. Publisher's VersionAbstract
We extend Aumann's theorem (Aumann, 1987) in deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weakernotion, p-belief of rationality, where agents believe the other agents are rational with probabilities p or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p sufficiently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's theorem (Aumann and Dreze, 2008) on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.