We present three axioms for a power index defined on the domain of simple (voting) games. Positivity requires that no voter has negative power, and at least one has positive power. Transfer requires that, when winning coalitions are enhanced in a game, the change in voting power depends only on the change in the game, i.e., on the set of new winning coalitions. The most crucial axiom is composition: the value of a player in a compound voting game is the product of his power in the relevant first-tier game and the power of his delegate in the second-tier game. We prove that these three axioms categorically determine the Banzhaf index.

Voting problems with a continuum of voters and finitely many alternatives are considered. The classical Arrow and Gibbard-Satterthwaite theorems are shown to persist in this model, not for single voters but for coalitions of positive size. The emphasis of the study is on strategic considerations, relaxing the nonmanipulability requirement: are there social choice functions such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the social choice function? Such social choice functions are called exactly and strongly consistent. The study offers an extension of the work of Peleg (1978a) and others. Specifically, a class of anonymous social choice functions with the required property is characterized through blocking coefficients of alternatives, and associated effectivity functions are studied. Finally, representation of effectivity functions by game forms having a strong Nash Equilibrium is studied.

A game form constitutionally implements a social choice correspondence if it implements it in Nash equilibrium and, moreover, the associated effectivity functions coincide. This paper presents necessary and sufficient conditions for a unanimous social choice correspondence to be constitutionally implementable, and sufficient and almost necessary conditions for an arbitrary (but surjective) social choice correspondence to be constitutionally implementable. It is shown that the results apply to interesting classes of scoring and veto rules.

We address the issue of the representation as well as the evolution of (possibly) mistaken beliefs. We develop a formal setup (a mutual belief space) in which agents might have a mistaken view of what the model is. We then model a communication process, by which agents communicate their beliefs to one another. We define a revision rule that can be applied even when agents have contradictory beliefs. We study its properties and, in particular, show that, when mistaken, agents do not necessarily eventually agree after communicating their beliefs. We finally address the dynamics of revision and show that when beliefs are mistaken, the order of communication may affect the resulting belief structure.

We prove a difference equation analogue for the decay-of-mass result for the nonlinear parabolic equation ut = ”u + ¼ |ˆ‡u| when ¼ 0.

We analyse a common value, alternating ascending bid, first price auction as a repeated game of incomplete information where the bidders hold equal property rights to the object auctioned off. Consequently they can accept (by quitting) or veto any proposed settlement. We characterise the essentially unique, sequentially rational dynamic Bayesian Nash equilibrium of this game under incomplete information on one side and discuss its properties.

A Nobel Prize in Economics was given to the psychologist Daniel Kahneman for his joint research with the late psychologist Amos Tversky on decision making under uncertainty and on subjective judgments of uncertainty. The two proposed Prospect Theory as a descriptive alternative to Utility Theory, the reigning normative theory of choice under uncertainty. Kahneman and Tversky argued that human psychology prevents people from being rational in the sense required by Utility Theory – consistency – for two main reasons. First, people are more sensitive to changes in position (economic or otherwise) than to final positions, a fact ignored by Utility Theory. Thus, they value a 50% discount on a 100NIS item more than a 5% discount on a 1000 NIS item. Moreover, they are more sensitive to changes for the worse than to changes for the better. Second, we are sensitive not just to outcomes, but to outcomes-under-a-description, which makes us inconsistent from a consequentialist veiwpoint (e.g., we don't feel the same about losing 100 NIS on our way to the theater boxoffice, vs. losing a 100 NIS ticket on our way to the theater). The article describes some of the empirical observations that led to the development of Prospect Theory, and some of its basic tenets.

Models have been put forward recently that seem to be successful in explaining apparently anomalous experimental results in the Ultimatum Game, where responders reject positive offers. While imparting fixed preference orders to fully rational agents, these models depart from traditional models by assuming preferences that take account not only of the material payoff to oneself, but also of that which is given to others. However, they leave open the question of how an agent's economic survival is helped by a preference order that advises him to leave money on the table. Our answer is that, indeed, doing so does not help. But that the same envious preference order that ill advises in some circumstances to reject an "insultingly" small offer, advises well in other circumstances, when it helps the same agent to overcome his risk- aversion and to offer a risky, tough offer that yields him a higher expected dollar gain. We show the existence of population distributions where the two effects exactly balance out across different preference types. These distributions are stable, stationary, and inefficient, in which different preferences asymptotically are represented, and where, as commonly observed in an Ultimatum Game, positive offers are made, of which some are rejected with positive probability. Our theory yields new testable hypotheses.

We propose two sequential mechanisms for efficient production of public goods. Our analysis differs from the existing literature in allowing for the presence of multiple public goods and in also being simple.  While both mechanisms ensure efficiency, the payoffs in the first mechanism are asymmetric, being sensitive to the order in which agents move. The second mechanism corrects for this through a two-stage game where the order of moves in the second stage are randomly determined. The payoffs from the second mechanism correspond to the Shapley value of a well-defined game which summarizes the production opportunities available to coalitions in the economy.

Animal conflicts are often characterized by time dependent strategy sets. This paper considers the following type of animal conflicts: a member of a group is at risk and needs the assistance of another member to be saved. As long as assistance is not provided, the individual which is at risk has a positive, time dependent rate of dying. Each of the other group members is a potential helper. Assisting this individual accrues a cost, but losing him decreases the inclusive fitness of each group member. A potential helper s interval between the moment an individual finds itself at risk and the moment it assists is a random variable, hence its strategy is to choose the probability distribution for this random variable. Assuming that each of the potential helpers knows the others strategies, we show that the ability to observe their realizations influences the Evolutionarily Stable Strategies (ESS) of the game. According to our results, where the realizations can be observed ESS always exist: immediate assistance, no assistance and delayed assistance. Where the realizations cannot be observed ESS do not always exist, immediate assistance and no assistance are possible ESS, while delayed assistance cannot be an ESS. We apply our model to the n brothers problem and to the parental investment conflict.

It has been shown (Hart [2]) that the backward induction (or subgame-perfect) equilibrium of a perfect information game is the unique stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large, under the assumption that the expected number of mutations per generation is bounded away from zero.Here it is shown that one can dispense with this last condition. In particular, it follows that the backward induction equilibrium is evolutionarily stable for large populations.

Foraging bees spend less time flying between flowers of the same species than when flying between individuals of different species. This time saving has been suggested as a possible advantage of flower-constant foraging. We hypothesized that the time required to switch flower type increases if (a) such switches are infrequent and (b) the bees need to decide whether to switch or not. Laboratory reared bumblebees were taught to forage on artificial feeders that were identical in morphology and reward schedule, but were marked by either a blue or a yellow landing surface. In the first two experiments bees foraged alternatively between two feeders. The landing surface was manipulated to coerce the bees to perform either a color-constant or a color-shift flight movement. In Experiment 1 we switched the landing surfaces every 2-3 visits, while in Experiment 2 the bees performed 6-7 color-constant flights before having to perform a color-shift flight. In the third experiment, the bees were presented with binary choices and had to decide to make a color-constant or a color-shift flight. When feeder colors were changed frequently (Experiment 1), we detected no difference between color-constant and color-shift inter-visit times. When bees were repeatedly exposed to one color (Experiment 2), color shifts required a significantly longer time than color-constant flights. When allowed to choose (Experiment 3), bees performed more color-constant flights than color-shift flights. Inter-visit times were similar for color-constant and color-shift flights in this experiment. Overall flight times were slightly but non-significantly longer than in experiments 1 and 2. The results suggest that bees indeed save flight time though flower-constant foraging. However, this time saving is small (  1 s / flower visit), and appears only when switches between flower types are infrequent. Additional selective advantages likely favor flower-constant foraging.

Optimal incentive mechanisms may require that agents are rewarded differentially even when they are completely identical and are induced to act the same. We demonstrate this point by means of a simple incentive model where agents decisions about effort exertion is mapped into a probability that the project will succeed. We give necessary and sufficient conditions for optimal incentive mechanisms to be discriminatory. We also show that full discrimination across all agents is required if and only if the technology has increasing return to scale. In the non-symmetric framework we show that negligible differences in agents attributes may result in major differences in rewards in the unique optimal mechanism.

A committee is a collection of members, where every member has a linear ordering on the alternatives of a finite ground set X. The committee chooses between pairs of alternatives drawn from X by a simple majority vote. The committee's choices induce a preference relation on X. In this paper, we study the possibility of learning preference relations of small committees from examples. We prove that it is impossible to precisely learn the preference relation of a committee before seeing all its choices, even if a teacher guides the learner through the learning process. We also prove that a learner can approximately learn the preference relation of a committee from a relatively few random examples.

We develop a dynamic model of an order-driven market populated by discretionary liquidity traders. These traders differ by their impatience and seek to minimize their trading costs by optimally choosing between market and limit orders. We characterize the equilibrium order placement strategies and the waiting times for limit orders. In equilibrium less patient traders are likely to demand liquidity, more patient traders are more likely to provide it. We find that the resiliency of the limit order book increases with the proportion of patient traders and decreases with the order arrival rate. Furthermore, the spread is negatively related to the proportion of patient traders and the order arrival rate. We show that these findings yield testable predictions on the relation between the trading intensity and the spread. Moreover, the model generates predictions for time-series and cross-sectional variation in the optimal order-submission strategies. Finally, we find that imposing a minimum price variation improves the resiliency of a limit order market. For this reason, reducing the minimum price variation does not necessarily reduce the average spread in limit order markets.

' A choice function is a rule that chooses a single alternative from every set of alternatives drawn from a finite ground set. A rationalizable choice function satisfies the consistency condition; i.e., if an alternative is chosen from a set A, then the same alternative is also chosen from every subset of A that contains it. In this paper we study computational aspects of choice, through choice functions. We explore two simple models that demonstrate two important aspects of choice procedures: the ability to remember the past and the capability to perform complex computations. We show that a choice function is optimal in terms of the amount of memory and the computational power required for its computation if and only if the function is rationalizable. We also show that the computation of most other choice functions, including some natural  ones, requires much more memory and computational power.''

We consider the consequences of competition between two types of experimental exchange mechanisms, a decentralized bargaining  market, and a centralized  market. The experiment demonstrates that decentralized bargaining is subject to a process of unraveling in which relatively weak traders (buyers with high willingness to pay and sellers with low costs) continuously find trading in the centralized market more attractive until almost no opportunities for mutually beneficial trade remain outside the centralized marketplace.

In a perfectly competitive market for annuities with full information, the price of annuities is equal to individuals' (discounted) survival probabilities. That is, prices are actuarially fair. In contrast, the pricing implicit in social security systems invariably allows for cross subsidization between different risk groups (males/females). We examine the utilitarian approach to the optimum pricing of annuities and show how the solution depends on the joint distribution of survival probabilities and incomes in the population.

It has been argued that in the presence of an Atmosphere Externality and competitive behavior by households, a uniform commodity tax on the externality - generating good attains the first best. It is demonstrated, however, that if income redistribution is desirable then personalized taxes are required for a second-best optimum. Each of these taxes is the sum of a uniform (across households) tax and a component, positive or negative, which depends on the household s income and demand elasticities. Second-best optimal indirect taxes and rules for investment in externality - reducing measures are also considered.

The information used in reaching a decision between alternatives is often gleaned through samples drawn from the distributions of their outcomes. Since in most cases it is the direction of the difference in value, rather than its magnitude, that is of primary interest, the decision maker may benefit from sampling data in a way that will accentuate, rather than accurately estimate, the magnitude of that difference, as it helps to reach a decision swiftly and confidently. A reanalysis of performance in a study by Fiedler, Brinkmann, Betsch, and Wild (Journal of Experimental Psychology: General, 2000, 129, 399-418), in which participants had the freedom to sample data any way they wished, demonstrates that their apparently poor performance as estimators of conditional probability may actually reflect sophisticated sampling, which resulted in accentuating the sample value of the degree of contingency in the data. Thus, participants might be characterized as "sensitive research designers", intent on increasing the chances of detecting an effect (if one existed).