2006
Zamir, T. R. K., & Shmuel, . (2006).
Asymmetric Auctions: Analytic Solutions to the General Uniform Case.
Discussion Papers. presented at the 9. Retrieved from
/files/dp432.pdf Publisher's VersionAbstractWhile auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions.
Zapechelnyuk, Y. T., & Andriy, . (2006).
Bargaining with a Bureaucrat.
Discussion Papers. presented at the 6. Retrieved from
/files/dp425.pdf Publisher's VersionAbstractWe consider a bargaining problem where one of the players, the bureaucrat, has the power to dictate any outcome in a given set. The other players, the agents, negotiate with him which outcome to be dictated. In return, the agents transfer some part of their payoffs to the bureaucrat. We state five axioms and characterize the solutions which satisfy these axioms on a class of problems which includes as a subset all submodular bargaining problems. Every solution is characterized by a number $\pm$ in the unit interval. Each agent in every bargaining problem obtains a weighted average of his individually rational level and his marginal contribution to the set of all players, where the weights are $\pm$ and 1 - $\pm$, respectively. The bureaucrat obtains the remaing surplus. The solution when $\pm$ = 1/2 is the nucleolus of a naturally related game in characteristic form.
Yaniv, I. . (2006).
Benefit of Additional Opinions, The.
Discussion Papers. presented at the 5, Current Directions in Psychological Science 13 (2004), 75-78. Retrieved from
/files/dp422.pdf Publisher's VersionAbstractIn daily decision making, people often solicit one another's opinions in the hope of improving their own judgment. According to both theory and empirical results, integrating even a few opinions is beneficial, with the accuracy gains diminishing as the bias of the judges or the correlation between their opinions increases. Decision makers using intuitive policies for integrating others' opinions rely on a variety of accuracy cues in weighting the opinions they receive. They tend to discount dissenters and to give greater weight to their own opinion than to other people's opinions.
Avrahami, Y. K., & Judith, . (2006).
Choosing Between Adaptive Agents: Some Unexpected Implications of Level of Scrutiny.
Discussion Papers. presented at the 10. Retrieved from
/files/dp436.pdf Publisher's VersionAbstractEven with ample time and data at their disposal, people often make do with small samples, which increases their risk of making the wrong decision. A theoretical analysis indicates, however, that when the decision involves selecting among competing, adaptive agents who are eager to be selected, an error-prone evaluation may be beneficial to the decision maker. In this case, the chance of an error can motivate competitors to exert greater effort, improving their level of performance which is the prime concern of the decision maker. This theoretical argument was tested empirically by comparing the effects of two levels of scrutiny of performance. Results show that minimal scrutiny can indeed lead to better performance than full scrutiny, and that the effect is conditional on a bridgeable difference between the competitors. We conclude by pointing out that error-prone decisions based on small samples may also maintain competition and diversity in the environment.
Hart, S., & Mansour, Y. . (2006).
Communication Complexity of Uncoupled Nash Equilibrium Procedures, The.
Discussion Papers. presented at the 4. Retrieved from
Publisher's VersionAbstractWe study the question of how long it takes players to reach a Nash equilibrium in "uncoupled" setups, where each player initially knows only his own payoff function. We derive lower bounds on the number of bits that need to be transmitted in order to reach a Nash equilibrium, and thus also on the required number of steps. Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian setting; and (3) reaching a mixed Nash equilibrium. Finally, we show that some very simple and naive procedures lead to similar exponential upper bounds.
Spencer, A. N., & Joel, . (2006).
Complexity and Effective Prediction.
Discussion Papers. presented at the 10. Retrieved from
/files/dp435.pdf Publisher's VersionAbstractLet G = (I,J,g) be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which player 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per stage payoff when the two automata face off. We are interested in the cases in which player 1 is "smart" in the sense that k is large but player 2 is "much smarter" in the sense that m>>k. Let S(g) be the value of G were the second player is clairvoyant, i.e., would know the player 1's move in advance. The threshold for clairvoyance is shown to occur for m near min(|I|, |J|)^k. For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).
Ifat Maoz, I. Y., & Ivri, N. . (2006).
Decision Framing and Support for Concessions in the Israeli-Palestinian Conflict.
Discussion Papers. presented at the 5, Journal of Peace Research (forthcoming). Retrieved from
/files/dp423.pdf Publisher's VersionAbstractThe purpose of the study is to explore, in the context of the Israeli-Palestinian conflict, the influence of framing a decision task as inclusion or exclusion on Israeli-Jewish respondents' support for the concession of Jewish settlements in the West Bank and Gaza. Respondents received a list of 40 Jewish settlements. Details such as the number of residents and geographical location were provided for each settlement. The respondents were randomly assigned to one of two conditions. In the inclusion condition 55 respondents were asked to mark the settlements for which they recommended that Israeli sovereignty be conceded. In the exclusion condition 53 respondents were asked to mark the settlements for which they recommended that Israeli sovereignty not be conceded. The findings confirm the predictions tested and indicate that: (1) Framing the task in terms of inclusion or exclusion affects respondents' support for territorial compromise, so that respondents in the exclusion condition support the concession of more settlements than respondents in the inclusion condition. (2) Framing the task in terms of inclusion or exclusion has a greater effect on support for conceding options (settlements) that are perceived as ambiguous (less consensual in the climate of opinion) in comparison to options (settlements) that are perceived as more clear-cut (more consensual). The theoretical and practical implications of these findings are discussed.
Gorodeisky, Z. . (2006).
Deterministic Approximation of Best-Response Dynamics for the Matching Pennies Game [Revised].
Discussion Papers. presented at the 11. Retrieved from
/files/dp437.pdf Publisher's VersionAbstractWe consider stochastic dynamics for the Matching Pennies game, hich behave, in expectation, like the best-response dynamics (i.e., the ontinuous fictitious play). Since the corresponding vector field is not ontinuous, we cannot apply the deterministic approximation results of Bena¯m and Weibull [2003]. Nevertheless, we prove such results for our dynamics by developing the notion of a "leading coordinate."
Sheshinski, E. . (2006).
Differentiated Annuities in a Pooling Equilibrium.
Discussion Papers. presented at the 9. Retrieved from
/files/dp433.pdf Publisher's VersionAbstractRegular annuities provide payment for the duration of an owner's lifetime. Period-Certain annuities provide additional payment after death to a beneficiary provided the insured dies within a certain period after annuitization. It has been argued that the bequest option offered by the latter is dominated by life insurance which provides non-random bequests. This is correct if competitive annuity and life insurance markets have full information about individual longevities. In contrast, this paper shows that when individual longevities are private information, a competitive pooling equilibrium which offers annuities at common prices to all individuals may have positive amounts of both types of annuities in addition to life insurance. In this equilibrium, individuals self-select the types of annuities that they purchase according to their longevity prospects. The break-even price of each type of annuity reflects the average longevity of its buyers. The broad conclusion that emerges from this paper is that adverse-selection due to asymmetric information is reflected not only in the amounts of insurance purchased but, importantly, also in the choice of insurance products suitable for different individual characteristics. This conclusion is supported by recent empirical work about the UK annuity market (Finkelstein and Poterba (2004)).
Hart, S. . (2006).
Discrete Colonel Blotto and General Lotto Games.
Discussion Papers. presented at the 10, International Journal of Game Theory 36 (2008), 3-4, 441-460. Retrieved from
Publisher's VersionAbstractA class of integer-valued allocation games – "General Lotto games" – is introduced and solved. The results are then applied to analyze the classical discrete "Colonel Blotto games"; in particular, optimal strategies are obtained for all symmetric Colonel Blotto games.
Weiss, D. O., & Benjamin, Nathans, . (2006).
Entropy Is the Only Finitely Observable Invariant.
Discussion Papers. presented at the 5. Retrieved from
/files/dp420.pdf Publisher's VersionAbstractOur main purpose is to present a very surprising new characterization of the Shannon entropy of stationary ergodic processes. We will use two basic concepts: isomorphism of stationary processes and a notion of finite observability, and we will see how one is led, inevitably, to Shannon's entropy. A function J with values in some metric space, defined on all finite-valued, stationary, ergodic processes is said to be finitely observable (FO) if there is a sequence of functions Sn(x1,x2,...,xn) that for all processes \S converges to J(\S) for almost every realization x1ˆ\v z of \S. It is called an invariant if it returns the same value for isomorphic processes. We show that any finitely observable invariant is necessarily a continuous function of the entropy. Several extensions of this result will also be given.
Ullmann-Margalit, E. . (2006).
Family Fairness.
Discussion Papers. presented at the 8, Social Research 73 (2006), 575-596. Retrieved from
/files/dp427.pdf Publisher's VersionAbstractThis 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, I. S., & Zamir, S. . (2006).
Games in the Nervous System: The Game Motoneurons Play.
Discussion Papers. presented at the 12. Retrieved from
/files/dp440.pdf Publisher's VersionAbstractGame 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, R. A. D. C., & Shmida, A. . (2006).
Honesty of Signaling and Pollinator Attraction: The Case of Flag-Like Bracts.
Discussion Papers. presented at the 12, Israel Journal of Plant Sciences 54 (2006), 119-128. Retrieved from
/files/dp438.pdf Publisher's VersionAbstractBracts 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, B. O. 'N., & Bezalel, . (2006).
Lexicographic Composition of Simple Games.
Discussion Papers. presented at the 2, Games and Economic Behavior 62 (2008), 628-642. Retrieved from
/files/db415.pdf Publisher's VersionAbstractA 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.
