A 4-person quota game is analyzed and discussed, in which players find it beneficial to pay others, in order to encourage favorable coalition structure.

This work follows "Evolutionary dynamics and backward induction" (Hart [2000]) in the study of dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large. Under the assumption that there is a single backward induction (or subgame perfect) equilibrium of a perfect information game, Hart [2000] proved that this point is the only stable state. In this work, we examine the case where there are multiple backward induction equilibria.

The existence of a value and optimal strategies is proved for the class of two-person repeated games where the state follows a Markov chain independently of players' actions and at the beginning of each stage only player one is informed about the state. The results apply to the case of standard signaling where players' stage actions are observable, as well as to the model with general signals provided that player one has a nonrevealing repeated game strategy. The proofs reduce the analysis of these repeated games to that of classical repeated games with incomplete information on one side.

One way to express bounded rationality of a player in a game theoretic models is by specifying a set of feasible strategies for that player. In dynamic game models with finite automata and bounded recall strategies, for example, feasibility of strategies is determined via certain complexity measures: the number of states of automata and the length of recall. Typically in these models, a fixed finite bound on the complexity is imposed resulting in finite sets of feasible strategies. As a consequence, the number of distinct feasible strategies in any subgame is finite. Also, the number of distinct strategies induced in the first T stages is bounded by a constant that is independent of T. In this paper, we initiate an investigation into a notion of feasibility that reflects varying degree of bounded rationality over time. Such concept must entail properties of a strategy, or a set of strategies, that depend on time. Specifically, we associate to each subset ¨i of the full (theoretically possible) strategy set a function yi from the set of positive integers to itself. The value ˆi(t) represents the number of strategies in ¨i that are distinguishable in the first t stages. The set ¨i may contain infinitely many strategies, but it can differ from the fully rational case in the way yi grows reflecting a broad implication of bounded rationality that may be alleviated, or intensified, over time. We examine how the growth rate of yi affects equilibrium outcomes of repeated games. In particular, we derive an upper bound on the individually rational payoff of repeated games where player 1, with a feasible strategy set ¨1, plays against a fully rational player 2. We will show that the derived bound is tight in that a specific, and simple, set ¨1 exists that achieves the upper bound. As a special case, we study repeated games with non-stationary bounded recall strategies where the length of recall is allowed to vary in the course of the game. We will show that a player with bounded recall can guarantee the minimax payoff of the stage game even against a player with full recall so long as he can remember, at stage t, at least K log(t) stages back for some constant K >0. Thus, in order to guarantee the minimax payoff, it suffices to remember only a vanishing fraction of the past. A version of the folk theorem is provided for this class of games.

While traditional mechanism design typically assumes isomorphism between the agents' type- and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in single-parameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the information-theoretically optimal social-choice rule can be implemented in dominant strategies, and prove that any multilinear social-choice rule is dominant-strategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of action-bounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear social-choice rule, the optimal mechanism with k actions incurs an expected loss of O(1/k2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, public-good models and routing in networks.

The paper starts from the fact that Israel is described as a 'Jewish and Democratic' state. It opens with a rejection of some preliminary charges that Israel cannot be both Jewish and democratic or that maintaining its Jewish particularity is in principle unjustified. The main part of the paper analyzes various issues, such as the right to participate in elections, immigration, and education, to show what arrangements may be required by a wish to maintain the Jewishness of the state while, at the same time, respecting the human rights of all its residents.

The paper analyses the development of the constitutional process in Israel since 1950, and especially since the 1992 basic laws. It argues that this process should be viewed within a frameworks distinguishing between three stages of constitution-making: the initial enactment of a constitution, amendments of the constitution, and application and interpretation of the constitution. The distinction between stages has institutional implications. Constitution-making should be primarily done by constituent assemblies. Regular legislatures are a second choice. The process should seek broad consensus, and involve big compromises between segments of the public. Amendments should also be undertaken by legislatures with broad consensus, but they can be more local, and their ratification procedures may be less demanding. Application and interpretation should be done in an ongoing way by all branches of government. Courts are authoritative interpreters but they do not necessarily have the final word on the constitution. When we study the Israeli process we see that does not conform to this model at all. It reflects judicial involvement in all stages, including the initial making of the constitution. There is thus a 'legitimacy deficit' in the constitutional process, which may perpetuate the current instability in the constitutional situation.

To explain why pre-play communication increases cooperation in games, one refers to a) strategic causes such as efficient communication or reputation effects, and b) changes in the utilities due to social processes. Hitherto experimental support for both explanations is mixed and confounded. Our experimental design eliminates all strategic factors and allows to focus on the effects of communication processes. We clearly find social effects, but none of revealed anonymity or salient communication. The social processes invoked are very heterogeneous but not irregular for different communicators.

For the last fifty years, countries in Asia and elsewhere witnessed a surge in aggregate savings per capita. Many empirical studies attribute this trend to the highly significant increases in life longevity of the populations of these countries. Some argue that the rise in savings is short-run, to be eventually dissipated by the dissaving of the elderly, whose proportion in the population rises along with longevity. This paper examines whether these conclusions are supported by economic theory. A model of life cycle decisions with uncertain survival is used to derive individuals'savings and chosen retirement age response to changes in longevity. Conditions on the age-profile of improvements in survival probabilities are shown to be necessary in order to predict the direction of this response (the uneven history of age specific improvements in longevity is recorded by Cutler (2004)). Population theory (e.g. Coale (1952)) is used to derive the dependence of the steady-state population age density on longevity. This, in turn, enables the explicit aggregation of individual response functions and a comparative steady-state analysis. Sufficient conditions for a sustainable positive effect of increased longevity on aggregate savings per capita are then derived. The importance of the availability of insurance markets is briefly discussed.

An invited contribution to a symposium on Information and Knowledge in Economics,  to appear in Econ Journal Watch. Topics discussed include the distinction between information and knowledge; awareness; logical omniscience; the cost of calculation; semantic and syntactic models of knowledge, and the equivalence between them; and common knowledge of the model. Finally, some aspects of the symposium contributions of Ken Binmore, Jim Friedman, and Eric Rasmusen are discussed.

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model - i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries - which has a Nash consistent representation. In other words, there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions, where lotteries are evaluated by their expected utility. No additional condition on the original effectivity function is needed.

These two papers (one in English and one in Hebrew) describe the unique educational experience of the Neve Shalom school, which is a fully integrated Jewish-Arab school within a system where Jews and Arabs regularly study in separate schools and languages. They are similar but have different emphases since the audiences are expected to be different in terms of background knowledge and familiarity with facts and situations. The paper studies the way the school handles issues of culture, language, religion and national identity. It then analyzes the school and makes suggestions concerning both the improvement of the effectiveness of the school itself and what can be learned from its experience to the educational system in Israel as a whole.

In this paper we study the social preferences obtained from monotone neutral social welfare functions for random individual preferences. It turns out that there are two extreme types of behavior. On one side, there are social welfare functions, such as the majority rule, that lead to stochastic stability of the outcome in terms of perturbations of individual preferences. We identify and study a class of social welfare functions that demonstrate an extremely different type of behavior which is a completely chaotic: they lead to a uniform probability distribution on all possible social preference relations and, for every''>0, if a small fraction'' of individuals change their preferences (randomly) the correlation between the resulting social preferences and the original ones tends to zero as the number of individuals in the society increases. This class includes natural multi-level majority rules.

Recent advancement in genetics testing for late-onset diseases raises fundamental decision dilemmas. The first study surveyed people's willingness to undergo predictive testing to find out about their own predisposition for certain incurable, late-onset diseases. The second study investigated the respondents' willingness to be tested as a function of the base rate of the disease, test diagnosticity, and the availability of treatment for the disease. In addition we surveyed (in the first study) people's willingness to disclose to others personal information about their genetic predisposition. The findings show that people often prefer not to know, as if they are choosing "protective ignorance". Respondents' verbal justifications of their choices were also analyzed. Respondents offered emotional, cognitive-instrumental, and strategic reasons for their preferences. The findings are compared with other issues in behavioral decision theory, including attitudes towards uncertainty and desire for control. The implications of the findings for policies and legislation on genetic tests are also considered.

We study the computational power and limitations of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their "demand under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natural types of queries; (2) that such auctions can solve linear programming relaxations of winner determination problems; (3) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries can not do so. We also initiate the study of how can the prices of bundles be represented when they are not linear, and show that the "default representation has severe limitations.

We embark on a systematic analysis of the power and limitations of iterative ascending-price combinatorial auctions. We prove a large number of results showing the boundaries of what can be achieved by different types of ascending auctions: item prices vs. bundle prices, anonymous prices vs. personalized prices, deterministic vs. non-deterministic, ascending vs. descending, preference elicitation vs. full elicitation, adaptive vs. non-adaptive, and single trajectory vs. multi trajectory. Two of our main results show that neither ascending item-price auctions nor ascending anonymous bundle-price auctions can determine the optimal allocation among general valuations. This justifies the use of personalized bundle prices in iterative combinatorial auctions like the FCC spectrum auctions.

Seeking advice is a basic practice in making real life decisions. Until recently, however, little attention has been given to it in either empirical studies or theories of decision making. The studies reported here investigate the influence of advice on judgment and the consequences of advice use for judgment accuracy. Respondents were asked to provide final judgments on the basis of their initial opinions and advice presented to them. The respondents' weighting policies were inferred. Analysis of the these policies show that (a) the respondents tended to place a higher weight on their own opinion than on the advisor's opinion (the self/other effect); (b) more knowledgeable individuals discounted the advice more; (c) the weight of advice decreased as its distance from the initial opinion increased; and (d) the use of advice improved accuracy significantly, though not optimally. A theoretical framework is introduced which draws in part on insights from the study of attitude change to explain the influence of advice. Finally the usefulness of advice for improving judgment accuracy is considered.

Casual observation suggests that athletics records tend to cluster over time. After prolonged periods without new records, a record breaking performance spurs other athletes to increase effort and thereby repeatedly set new standards. Subsequently, record breaking subsides and the pattern repeats itself. The clustering hypothesis is tested for the mile run, the marathon, the world hour record and long jump. For all four disciplines, the hypothesis of non-clustering is rejected at the 4 level or below. A theoretical rationale for this phenomenon is provided through a model of social learning under limited awareness. The agents are assumed to be unaware of the true limits to performance and to take the current record as the upper bound. The observation of a record breaking achievement spurs the agents to try harder and thus temporarily increase the probability of new records. Subsequently, record breaking trails off and the process is repeated.

In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider situations where the available information is the rank of a present observation relative to its predecessors. Certain "natural" selection rules are investigated. Theoretical and Monte Carlo results are presented pertaining to the evolution of the number of items selected, measures of their quality and the time it would take to amass a group of a given size. A comparison between rules is made, and guidelines to the choice of good procedures are offered.

We consider stability properties of equilibria in stochastic evolutionary dynamics. In particular, we study the stability of mixed equilibria in strategic form games. In these games, when the populations are small, all strategies may be stable. We prove that when the populations are large, the unique stable outcome of best-reply dynamics in 2 x 2 games with a unique Nash equilibrium that is completely mixed is the mixed equilibrium. The proof of this result is based on estimating transition times in Markov chains.