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).

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society's choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that specified by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.

The minmax in repeated games with imperfect monitoring can differ from the minmax of those games with perfect monitoring. This can happen when two or more players are able to gain common information known only to themselves, and utilize this information at a later stage. Gossner and Tomala [1] showed that in a class of such games, the minmax is given by a weighted average of the payoffs of two main strategies: one in which the information is gained, and the other in which the information is utilized. While this result is implicit, all examples analyzed to date require a single main strategy in which information is created and utilized simultaneously. We show that two strategies are indeed needed by providing and solving a concrete example of a three-player game.

We studied asymmetric competition between two (three-person) groups. Each group member received an initial endowment and had to decide whether or not to contribute it. The group with more  contributions won the competition and each of its members received a reward. The members of the losing group received nothing. The asymmetry was created by randomly and publicly selecting one group beforehand to be the winning group in the case of a tie. A theoretical analysis of this  asymmetric game generates two qualitatively different solutions, one in which members of the group that wins in the case of a tie are somewhat more likely to contribute than members of the group that loses, and another in which members of the group that loses in the case of a tie are much more likely to contribute than members of the group that wins. The experimental results are clearly in line with the first solution.

In a repeated game with perfect monitoring, correlation among a group of players may evolve in the common course of play (online correlation). Such a correlation may be concealed from a boundedly rational player. The feasibility of such "online concealed correlation" is quantified by the individually rational payoff of the boundedly rational player.We show that "strong" players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate online correlation of the actions of "weak" players, in a manner that is concealed from an opponent of "intermediate" strength. The result is illustrated in two models, each captures another aspect of bounded rationality. In the first, players use bounded recall strategies. In the second, players use strategies that are implementable by finite automata.

We study a repeated game in which one player, the prophet, acquires more information than another player, the follower, about the play that is going to be played. We characterize the optimal amount of information that can be transmitted online by the prophet to the follower, and provide applications to repeated games played by finite automata, and by players with bounded recall.

When information on longevity (survival functions) is unknown early in life, individuals have an interest to insure themselves against future 'risk-class' classification. Accordingly, the First-Best typically involves transfers across states of nature. Competitive equilibrium cannot provide such transfers if insurance firms are unable to precommit their customers. On the other hand, public insurance plans that do not distinguish between 'risk-class' realizations are also inefficient. It is impossible, a-priori, to rank these alternatives from a welfare point of view.

A central question for pension design is how benefits should vary with the age of retirement beyond early eligibility age. It is often argued that in order to be neutral with respect to individual retirement decisions benefits should be actuarially fair, that is, the present value of additional contributions and benefits ('Delayed Retirement Credit' - DRC) due to postponed retirement should be equal. We show that in a self-selection, asymmetric information model, because individual decisions are suboptimal, the socially optimal benefit structure should be less than actuarially fair.

Bar-Hillel and Neter (1996) found that although people are willing to trade identical objects, they are reluctant to trade identical lottery tickets. Is this simply due to the fact that these are gambles? It was found that if the value of the tickets is guaranteed to be ex-post, not just ex ante, identical, people are more willing to exchange them. Indeed, just the possibility of ex-post difference between the lottery tickets induces as much reluctance to exchange them as when ex-post difference is guaranteed. In addition, this study examines how the vividness of lottery tickets influences the willingness to trade them. Specifically, it examines whether people are equally reluctant to exchange lottery tickets (when given a bonus for doing so) when they cannot even distinguish between them (e.g., when the tickets are concealed in envelopes). When one cannot see the ticket, it is less vivid and it is harder to imagine it winning. Indeed, it was found that people are more willing to exchange when they cannot distinguish between the tickets than when they can.In 2011, a revised version of this paper was published under the title To trade or not to trade:  The moderating role of vividness when exchanging gambles in Judgment and Decision Making, 6, 147-155.  In the link todp341, it follows the original manuscript. 

Regret-based dynamics have been introduced and studied in the context of discrete-time repeated play. Here we carry out the corresponding analysis in continuous time. We observe that, in contrast to (smooth) fictitious play or to evolutionary models, the appropriate state space for this analysis is the space of distributions on the product of the players' pure action spaces (rather than the product of their mixed action spaces). We obtain relatively simple proofs for some results known in the discrete case (related to "no-regret" and correlated equilibria), and also a new result on two-person potential games (for this result we also provide a discrete-time proof).

In this note we propose to use the mathematical formalism of Quantum Mechanics to capture the idea that agents preferences, in addition to being typically uncertain, can also be indeterminate. They are determined (realized, and not merely revealed) only when the action takes place. An agent is described by a state which is asuperposition of potential types (or preferences or behaviors). This superposed state is projected (or collapses ) onto one of the possible behaviors at the time of the interaction. In addition to the main goal of modelling uncertainty of preferences which is not due to lack of information, this formalism, seems to be adequate to describe widely observed phenomena like framing and instances of noncommutativityin patterns of behavior. We propose two experiments to test the theory.