Publications

1997
Peleg, Peter Sudholter, and Bezalel. Nucleoli As Maximizers Of Collective Satisfaction Functions. Discussion Papers 1997. Web. Publisher's VersionAbstract
Two preimputations of a given TU game can be compared via the Lorenz order applied to the vectors of satisfactions. One preimputation is `socially more desirable' than the other, if its corresponding vector of satisfactions Lorenz dominates the satisfaction vector with respect to the second preimputation. It is shown that the prenucleolus, the anti-prenucleolus, and the modified nucleolus are maximal in this Lorenz order. Here the modified nucleolus is the unique preimputation which lexicographically minimizes the envies between the coalitions, i.e. the differences of excesses. Recently Sudh?lter developed this solution concept. Properties of the set of all undominated preimputations, the maximal satisfaction solution, are discussed. A function on the set of preimputations is called collective satisfaction function if it respects the Lorenz order. We prove that both classical nucleoli are unique minimizers of certain `weighted Gini inequality indices', which are derived from some collective satisfaction functions. For the (pre)nucleolus the function proposed by Kohlberg, who characterized the nucleolus as a solution of a single minimization problem, can be chosen. Finally, a collective satisfaction function is defined such that the modified nucleolus is its unique maximizer.
Reny, Motty Perry, and Philip J. On The Failure Of The Linkage Principle In Multi-Unit Auctions. Discussion Papers 1997. Web. Publisher's VersionAbstract
It is shown that the linkage principle (Milgrom and Weber(1982)) does not extend to the multi-unit auction setting. An analysis of the equilibium bidding strategies is carried out for the gneral two-agent/two-unit Vickrey auction in order to provide economic insight into the nature of the failure. In addition, an explicit counterexample is provided.
Samuel-Cahn, David Assaf, and Ester. Optimal Multivariate Stopping Rules. Discussion Papers 1997. Web. Publisher's VersionAbstract
For fixed i let X(i)=(X1(i),...,Xd(i) be a d-dimensional random vector with some known joint distribution. Here i should be considered a time variable. Let X(i)=1,...,n be a sequence of n independent vectors, where n is the total horizon. In many examples Xj(i) can be thought of as the return to partner j, when there are d2 partners, and one stops with the i-th observation. If the j-th partner alone could decide on a (random) stopping rule t, his goal would be to maximize EXj(t) over all possible stopping rules tn. In the present "multivariate" setup the d partners must however cooperate and stop at the same stopping time t, so as to maximize some agreed upon function h( ) of the individual expected returns. The goal is thus to find a stopping rule t* for which h(EX1(t),...,EXd(t)=h(EX(t) is maximized. For continuous and monotone h we describe the class of optimal stopping rules t*. With some additional symmetry assumptions we show that the optimal rule is one which (also) maximizes EZt where Zi= Xj(i), and hence has a particularly simple structure. Examples are included, and the results are extended both to the infinite horizon case and to the case when X(1),..., X(n) are dependent. Asymptotic comparisons between the present problem of finding sup h(E X(t)) and the "classical" problem of finding sup Eh( X(t)) are given. Comparisons between the optimal return to the statistician and to a "prophet" are also included. In the present context a "prophet" is someone who can base his (random)choice g on the full sequence X(1),..., X(n), with corresponding return sup h(E X(g)).
Samuel-Cahn, Harold Sackrowitz, and Ester. P-Values As Random Variables; Expected P-Values. Discussion Papers 1997. Web. Publisher's VersionAbstract
P-values for hypotheses are considered as random variables. Their expected value (EPV) is expressed in a simple form. In simple examples they are directly computable, also under the alternative hypothesis, and in more complicated examples they are easily simulated. Their major advantage is that they do not depend on any significant level. It is suggested that the use of EPV can replace the use of power, which is always significance level dependent EPV can also be used for comparison of tests when more than one test is available for a given hypothesis. Examples are given, as well as tables which relate significance level and power to EPV. A comparison of the two-sample one-sided Kolmogorov-Smirnov, Mann-Whitney and t tests is included, for a variety of underlying distributions.
Foster, Ilan Yaniv, and Dean. Precision And Accuracy Of Judgmental Estimation. Discussion Papers 1997. Web. Publisher's VersionAbstract
Whereas probabilistic calibration has been a central normative concept of accuracy in previous research on interval estimates, we suggest here that normative approaches for the evaluation of judgmental estimates should consider the communicative interaction between the individuals who produce the judgements and those who receive or use them for making decisions. We analyze precision and error in judgement and consider the role of accuracy-informativeness trade-off (Yaniv & Foster, 1995) in the communication of estimates. The results shed light on puzzling findings reported earlier in the literature concerning the calibration accuracy of subjective confidence intervals.
Solan, Eilon . Repeated Team Games With Absorbing States. Discussion Papers 1997. Web. Publisher's VersionAbstract
Two teams meet every day to play the same matrix game. Every entry in the matrix contains five numbers: a payoff that each player in the first team receives whenever this entry is chosen, a similar payoff for the players of the second team, a probability that once this entry is chosen the game becomes "static", a payoff that each player in the first team receives in each future day if the game becomes "static" by this entry, and a similar payoff for the players of the second team.We prove that every such game has an equilibrium payoff.
Simon, Robert S. . Separation Of Joint Plan Equilibrium Payoffs From The Min-Max Functions. Discussion Papers 1997. Web. Publisher's VersionAbstract
This article concerns infinitely repeated and un-discounted two-person non-zero-sum games of incomplete information on one side. Following the spirit of the Folk Theorem it establishes sufficient conditions for the existence of Nash equilibria with payoffs superior to what the players would receive from observable deviation. Examples are presented that show both the difficulty and the desirability for stronger results than those presented here.
Maschler, Daniel Granot, and Michael, Howlett. Spanning Network Games. Discussion Papers 1997. Web. Publisher's VersionAbstract
We study fundamental properties of monotone network enterprises which contain public vertices and have positive and negative costs on edges and vertices. Among the properties studied are the nonemptiness of the core, characterization of nonredundent core constraints, ease of computation of the core and the nucleolus, and cases of decomposition of the core and the nucleolus.
Solan, Eilon . Stochastic Games With 2 Non-Absorbing States. Discussion Papers 1997. Web. Publisher's VersionAbstract
In the present paper we consider recursive games that satisfy an absorbing property defined by Vieille. We give two sufficient conditions for existence of an equilibrium payoff in such a game, and prove that if the game has at most two non- absorbing states, then at least one of the conditions is satisfied. Using a reduction of Vieille, we conclude that every stochastic game which has at most two non-absorbing states has an equilibrium payoff.
Yaniv, Ilan . Weighting And Trimming: Heuristics For Aggregating Judgments Under Uncertainty. Discussion Papers 1997. Web. Publisher's VersionAbstract
In making major decisions (e.g., about medical treatment, acceptance of manuscripts for publication, or investment), decision makers frequently poll the opinions and subjective estimates of other judges. The aggregation of these opinions is often beset by difficulties. First, decision makers often encounter conflicting subjective estimates. Second, estimates are often expressed with a measure of uncertainty. The decision maker thus needs to reconcile inconsistencies among judgmental estimates and determine their influence on the overall aggregate judgement. In the empirical studies, I examine the idea that weighting and trimming are two important heuristics in the aggregation of opinions under uncertainty. The results from these studies are contrasted with the findings of a normative study using a computer simulation that was designed to assess the objective effects of weighting and trimming operations on the accuracy of estimation.
Peleg, Werner Guth, and Bezalel. When Will Payoff Maximization Survive?. Discussion Papers 1997. Web. Publisher's VersionAbstract
Survival of the fittest means that phenotypes behave as if they would maximize reproductive success. An indirect evolutionary analysis allows for stimuli which are not directly related to reproductive success although they affect behavior. One first determines the solution for all possible constelations of stimuli and then the evolutionarily stable stimuli. Our general analysis confirms the special results of former studies that survival of the fittest in case of commonly known stimuli requires either that own success does not depend on other's behavior or that other's behavbior is not influenced by own stimuli. When stimuli are private information one can derive similar necessary conditions for the survival of the fittest.
1996
Aumann, Robert J. . A Note On The Centipede Game. Discussion Papers 1996. Web. Publisher's VersionAbstract
In Rosenthal's Centipede Game, if it is commonly known that the players choose rationally at vertices that are actually reached, then the first player "goes out" at the first move.
Robert J. Aumann, Sergiu Hart, and Motty Perry. Absent-Minded Driver, The. Discussion Papers 1996. Web. Publisher's VersionAbstract
The example of the "absent-minded driver" was introduced by Piccione & Rubinstein [1995] in the context of games and decision problems with imperfect recall. They claim that a "paradox" or "inconsistency" arises when the decision reached at the "planning stage" – before the game is played – is compared with that at the "action stage" – when the game is played. Though the example is provocative and worth having, their analysis is unsound. A careful analysis reveals that while the considerations at the planing and action stages do differ, there is no paradox or inconsistency. 94R. Robert J. Aumann, Sergiu Hart & Motty Perry, "The Absent-Minded Driver" (Revised, December 1996). The example of the "absent-minded driver" was introduced by Piccione & Rubinstein [1995] in the context of games and decision problems with imperfect recall. They claim that a "paradox" or "inconsistency" arises when the decision reached at the "planning stage" is compared with that at the "action stage". Though the example is provocative and worth having, their analysis is questionable. A careful analysis reveals that while the considerations at the planing and action stages do differ, there is no paradox or inconsistency.
Wolinsky, Asher . A Theory Of The Firm With Non-Binding Employment Contracts. Discussion Papers 1996. Web. Publisher's VersionAbstract
This paper analyzes a dynamic model of a firm in which the wage of each employee is determined in separate bilateral negotiations with the firm. The contractsbetween the firm and its employees are non-binding in the sense that they can be repeatedly renegotiated to adjust to changing situations. The Bargaining power of an employee stems from the threat of quitting that will deprive the firm of this worker's marginal contribution and will put the firm in a weaker position against the remaining workers. This threat is offset to some extent by the replacement opportunities that the firm has, but these are only imperfect in the sense that replacement of quits requires time and effort. The paper characterizes a class of equilibria for this scenario and examines their features. These include a sharp decline of the wage at the firm's target employment level, a mark-up of the wage over the employees' reservation wage and over-employment.
Driessen, Theo S. H. . An Alternative Game-Theoretic Analysis Of A Bankruptcy Problem From The Talmud: The Case Of The Greedy Bankruptcy Game. Discussion Papers 1996. Web. Publisher's VersionAbstract
The bankruptcy problem from the Talmud is modelled as a game (in coalitional form with transferable utility) which differs from the "standard bankruptcy game". A non-game theoretic solution to the bankruptcy problem is recovered by two different game theoretic approaches applied to the alternative game. The major game theoretic approach enables to interpret pairwise greedy or modest claims of creditors as largest or smallest core-allocations to creditors in the alternative game. A theory of consistency is elucidated with elementary game theoretic tools and proofs. As a separate topic, the indirect function of the "standard bankruptcy game" is determined and interpreted in an economic manner. The indirect function may be helpful to describe the game itself as well as its core (due to the duality between games and indirect functions).
Aumann, Robert J. . Case Of The Three Widows, The. Discussion Papers 1996. Web. Publisher's VersionAbstract
Part I of a non-technical account, written in Hebrew for the Rabbinic Community, of "Game Theoretic Analysis of a Bankruptcy Problem from the Talmud", by R. Aumann and M. Maschler, Journal of Economic Theory 36 (1985), 195-213. The Talmudic passage in question is explained in more detail than in the JET paper, and additional Talmudic sources are adduced.
Amitai, Mor . Cheap-Talk With Incomplete Information On Both Sides. Discussion Papers 1996. Web. Publisher's VersionAbstract
We provide a characterization of the set of equilibria of two-person cheap-talk games with incomplete information on both sides. Each equilibrium generates a martingale with certain properties and one can obtain an equilibrium from each such martingale. Moreover, the characterization depends on the number of possible messages. It is shown that for every natural number n, there exist equilibrium payoffs that can be obtained only when the number of possible messages is at least n.
Amitai, Mor . Cheap-Talk With Random Stopping. Discussion Papers 1996. Web. Publisher's VersionAbstract
Cheap-Talk with Random Stopping is a Cheap-Talk game in which after each period of communication, with probability 1- %, the talk ends and the players play the original game (i.e., choose actions and receive payoffs). In this paper the relations between Cheap-Talk games and Cheap-Talk with Random Stopping are analyzed.
Gossner, Olivier . Comparison Of Information Structures. Discussion Papers 1996. Web. Publisher's VersionAbstract
We introduce two ways of comparing two information structures, say I and J. First, I is richer than J when for every compact game G, all correlated equilibrium distributions of G induced by J are also induced by I. Second, J is faithfully reproducible from I when all the players can compute from their information in the I "new information" that reproduces what they could have from J. We prove that I is richer than J if and only if J is faithfully reproducible from I.
El-Yaniv, Ran . Competitive Solutions For Online Financial Problems: A Survey. Discussion Papers 1996. Web. Publisher's VersionAbstract
This paper surveys results concerning online algorithms for solving problems related to the management of money and other assets. In particular, the survey focuses on search, replacement and portfolio selection problems.