check
Publications | The Federmann Center for the Study of Rationality

Publications

2003
Schweinzer, Paul . Dissolving A Common Value Partnership In A Repeated 'Queto' Game. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Bar-Hillel, Maya . E Psychologist Daniel Kahneman. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Bergman, Nitai Bergman, and Yaacov. Ecologies Of Preferences With Envy As An Antidote To Risk-Aversion In Bargaining. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Winter, Suresh Mutuswami, and Eyal. Efficient Mechanisms For Multiple Public Goods. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Motro, Osnat Yaniv, and Uzi. Ess In Symmetric Animal Conflicts With Time Dependent Strategy Sets. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Gorodeisky, Ziv . Evolutionary Stability For Large Populations. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Noam Bar-shai, Rana Samuels, Tamar Keasar Uzi Motro, and Avi Shmida. Flight Durations In Bumblebees Under Manipulation Of Feeding Choices. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Winter, Eyal . Incentives And Discrimination. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Salant, Yuval . Learning The Decisions Of Small Committees. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Thierry Foucault, Ohad Kadan, and Eugene Kandel. Limit Order Book As A Market For Liquidity. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Salant, Yuval . Limited Computational Resources Favor Rationality. Discussion Papers 2003. Web. Publisher's VersionAbstract
' 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.''
Tamar Kugler, Zvika Neeman, Nir Vulkan . Markets Versus Negotiations: An Experimental Investigation. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Sheshinski, Eytan . Note On The Optimum Pricing Of Annuities. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Sheshinski, Eytan . On Atmosphere Externality And Corrective Taxes. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Fiedler, Yaakov Kareev, and Klaus. On The Accentuation Of Contingencies: The Sensitive Research Designer Versus The Intuitive Statistician. Discussion Papers 2003. Web. Publisher's VersionAbstract
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).
Peleg, Hans Keiding, and Bezalel. On The Continuity Of Representations Of Effectivity Functions. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Goldberg, Yair . On The Minmax Of Repeated Games With Imperfect Monitoring: A Computational Example. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Gary Bornstein, Tamar Kugler, and Shmuel Zamir. One Team Must Win, The Other Need Only Not Lose: An Experimental Study Of An Asymmetric Participation Game. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Neyman, Gilad Bavly, and Abraham. Online Concealed Correlation By Boundedly Rational Players. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.
Olivier Gossner, Penelope Hernandez, and Abraham Neyman. Online Matching Pennies. Discussion Papers 2003. Web. Publisher's VersionAbstract
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.