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Publications | The Federmann Center for the Study of Rationality

Publications

2009
Schuster, Amir Perelberg, and Richard. Coordinated Breathing In Bottlenose Dolphins (Tursiops Truncatus) As Cooperation: Integrating Proximate And Ultimate Explanations. Discussion Papers 2009. Web. Publisher's VersionAbstract
In this study, coordinated breathing was studied in 13 common bottlenose dolphins because of its links with spontaneous coordinated behaviors (e.g., swimming, foraging, and playing). A strong link was shown between dyadic coordination levels and age/sex categories when both association patterns and spatial formation are considered. This is consistent with a significant influence of social relationships on cooperating and contrasts with an economic perspective based on immediate material outcomes alone. This cooperation bias is explained by linking proximate processes that evoke performance with ultimate evolutionary processes driven by long-term adaptive outcomes. Proximate processes can include 2 kinds of immediate outcomes: material reinforcements and affective states associated with acts of cooperating that can provide positive reinforcement regardless of immediate material benefits (e.g., when there is a time lag between cooperative acts and material outcomes). Affective states can then be adaptive by strengthening social relationships that lead to eventual gains in fitness.
Zultan, M. Vittoria Levati, and Ro I. Cycles Of Conditional Cooperation In A Real-Time Voluntary Contribution Mechanism. Discussion Papers 2009. Web. Publisher's VersionAbstract
This paper provides a new way to identify conditional cooperation in a real-time version of the standard voluntary contribution mechanism. Our approach avoids most drawbacks of the traditional procedures because it relies on endogenous cycle lengths, which are defined by the number of contributors a player waits before committing to a further contribution. Based on hypothetical distributions of randomly generated contribution sequences, we provide strong evidence for conditionally cooperative behavior. Moreover, notwithstanding a decline in contributions, conditional cooperation is found to be stable over time.
Lehmann, Daniel . Foundations Of Non-Commutative Probability Theory. Discussion Papers 2009. Web. Publisher's VersionAbstract
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way. The mystery presented by the algebraic equations satisfied by (non-commuting) observables that cannot be observed in the same states is elucidated
Aumann, Robert J. . Game Engineering. Discussion Papers 2009. Web. Publisher's VersionAbstract
"Game Engineering" deals with the application of game theoretic methods to interactive situations or systems in which the rules are well defined, or where the designer can himself specify the rules. This talk, which addressed a business-school audience with no specific knowledge of game theory, describes five examples of game engineering: two dealing with auctions, two with traffic systems, and one with arbitration. At the end of the talk there was a Q & A session, which, too, is recorded here.
Lehmann, Aron Matskin, and Daniel. General Matching: Lattice Structure Of The Set Of Agreements. Discussion Papers 2009. Web. Publisher's VersionAbstract
The subset agreement problem generalizes all forms of two-sided matching. Two agents need to agree on some subset of a given
Kalai, Gil . How Quantum Computers Can Fail. Discussion Papers 2009. Web. Publisher's VersionAbstract
We propose and discuss two postulates on the nature of errors in highly correlated noisy physical stochastic systems. The first postulate asserts that errors for a pair of substantially correlated elements are themselves substantially correlated. The second postulate asserts that in a noisy system with many highly correlated elements there will be a strong effect of error synchronization. These postulates appear to be damaging for quantum computers. The paper includes a self-contained description of the model of quantum computers.
Winter, Eyal . Incentive Reversal. Discussion Papers 2009. Web. Publisher's VersionAbstract
By incentive reversal we refer to situations in which an increase of rewards for all agents results in fewer agents exerting effort. We show that externalities among peers may give rise to such intriguing situations even when all agents are fully rational. We provide a necessary and sufficient condition on the organizational technology in order for it to be susceptible to incentive reversal. The condition implies that some degree of complementarity is enough to allow incentive reversal.
Levy, Itai Arieli, and Yehuda (John). Infinite Sequential Games With Perfect But Incomplete Information. Discussion Papers 2009. Web. Publisher's VersionAbstract
Infinite sequential games, in which Nature chooses a Borel winning set and reveals it to one of the players, do not necessarily have a value if Nature has 3 or more choices. The value does exist if Nature has 2 choices. The value also does not necessarily exist if Nature chooses from 2 Borel payoff functions. Similarly, if Player 1 chooses the Borel winning set and does not reveal his selection to Player 2, then the game does not necessarily have a value if there are 3 or more choices; it does have a value if there are only 2 choices. If Player 1 chooses from 2 Borel payoff functions and does not reveal his choice, the game need not have a value either.
Romm, Dror Lellouche, and Assaf. Information Effects Of Jump Bidding In English Auctions. Discussion Papers 2009. Web. Publisher's VersionAbstract
Should an auctioneer start a rising auction from some starting price or set it as a reservation price? Under what circumstances might a bidder find it rational to raise the current offer by a substantial factor instead of making just a small increase above the highest bid? This paper aims to answer both of these questions by exploring the implications of jump bidding over the information sets available to the bidders. Our motivation is to find whether hiding the information about other players' signals might be beneficial for one of the bidders. We first show that it is better for the auctioneer to set a reservation price rather than "jump" to the starting price. We then prove that in a very general setting and when bidders are risk-neutral there exist no equilibrium with jump bidding (in non-weakly dominated strategies). Finally, we demonstrate that jump bidding might be a rational consequence of risk aversion, and analyze the different effects at work.
Gura, Ein-Ya . Insights Into Game Theory: An Alternative Mathematical Experience. Discussion Papers 2009. Web. Publisher's VersionAbstract
Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behavior of competing individuals, firms, and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. The authors use four different topics (college admissions, social justice and majority voting, coalitions and cooperative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.
Winter, Eric D. Gould, and Eyal. Interactions Between Workers And The Technology Of Production: Evidence From Professional Baseball. Discussion Papers 2009. Web. Publisher's VersionAbstract
This paper shows that workers can affect the productivity of their coworkers based on income maximization considerations, rather than relying on behavioral considerations such as peer pressure, social norms, and shame. We show that a worker's effort has a positive effect on the effort of coworkers if they are complements in production, and a negative effect if they are substitutes. The theory is tested using a panel data set of baseball players from 1970 to 2003. The results are consistent with the idea that the effort choices of workers interact in ways that are dependent on the technology of production.
Hellman, Ziv . Iterated Expectations, Compact Spaces, And Common Priors. Discussion Papers 2009. Web. Publisher's VersionAbstract
Extending to infinite state spaces that are compact metric spaces a result previously attained by D. Samet solely in the context of finite state spaces, a necessary and suficient condition for the existence of a common prior for several players is given in terms of the players' present beliefs only. A common prior exists if and only if for each random variable it is common knowledge that all Cesaro means of iterated expectations with respect to any permutation converge to the same value; this value is its expectation with respect to the common prior. It is further shown that compactness is a necessary condition for some of the results.
von Zamir, Bernhard Stengel, and Shmuel. Leadership Games With Convex Strategy Sets. Discussion Papers 2009. Web. Publisher's VersionAbstract
A basic model of commitment is to convert a two-player game in strategic form to a leadership game  with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader s payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.
Sheshinski, Eytan . Longevity And Aggregate Savings. Discussion Papers 2009. Web. Publisher's VersionAbstract
Two salient features of modern economic growth are the rise in aggregate savings rates and the steady increase in life expectancy. This paper links these processes, showing that under certain conditions economic theory supports the hypothesis that increased longevity leads to higher aggregate savings in steady state. The analysis is based on a lifecycle model with uncertain longevity in which individuals choose an optimum consumption path and a retirement age. Conditions on the age-specific pattern of improvements in survival probabilities are shown to ensure that individual savings rise with longevity and that aggregation preserves this result. Population theory (Coale (1972)) is used to link the steady-state age density function and the population's growth rate to individuals' survival probabilities. The importance of a competitive annuity market in avoiding unintended bequests is underscored.
Shapira, Theresa Lant, and Zur. Managerial Reasoning About Aspirations And Expectations. Discussion Papers 2009. Web. Publisher's VersionAbstract
Managerial reasoning about performance targets and subsequent actions can be influenced by whether they focus their attention on expectations of future events or internal efforts to meet organizational goals. This study explores how managers think about expectations and aspirations by examining the semantic similarities and differences between these concepts for practicing managers and economists, the results suggesting subtle differences in how economists and managers reason about aspirations and expectations. For economists, the concept of expectations played a major role and influenced their subsequent thinking about goals and actions while managers conceptually separated factors that were controllable and uncontrollable, the concept of expectation not playing the central role for them. Implications for descriptive and prescriptive models of decision- making are discussed.
Neyman, Abraham . Maximal Variation Of Martingales Of Probabilities And Repeated Games With Incomplete Information, The. Discussion Papers 2009. Web. Publisher's VersionAbstract
The variation of a martingale m[k] of k+1 probability measures p(0),...,p(k) on a finite (or countable) set X is the expectation of the sum of ||p(t)-p(t-1)|| (the L one norm of the martingale differences p(t)-p(t-1)), and is denoted V(m[k]). It is shown that V(m[k]) is less than or equal to the square root of 2kH(p(0)), where H(p) is the entropy function (the some over x in X of p(x)log p(x) and log stands for the natural logarithm). Therefore, if d is the number of elements of X, then V(m[k]) is less than or equal to the square root of 2k(log d). It is shown that the order of magnitude of this bound is tight for d less than or equal to 2 to the power k: there is C>0 such that for every k and d less than or equal to 2 to the power k there is a martingale m[k]=p(0),...,p(k) of probability measures on a set X with d elements, and with variation V(m[k]) that is greater or equal the square root of Ck(log d). It follows that the difference between the value of the k-stage repeated game with incomplete information on one side and with d states, denoted v(k), and the limit of v(k), as k goes to infinity, is bounded by the maximal absolute value of a stage payoff times the square root of 2(log d)/k, and it is shown that the order of magnitude of this bound is tight.
Eyal Winter, Ignacio Garcia-Jurado, Jose Mendez-Naya, and Luciano Mendez-Naya. Mental Equilibrium And Rational Emotions. Discussion Papers 2009. Web. Publisher's VersionAbstract
We introduce emotions into an equilibrium notion. In a mental equilibrium each player "selects" an emotional state which determines the player's preferences over the outcomes of the game. These preferences typically differ from the players' material preferences. The emotional states interact to play a Nash equilibrium and in addition each player's emotional state must be a best response (with respect to material preferences) to the emotional states of the others. We discuss the concept behind the definition of mental equilibrium and show that this behavioral equilibrium notion organizes quite well the results of some of the most popular experiments in the experimental economics literature. We shall demonstrate the role of mental equilibrium in incentive mechaisms and will discuss the concept of collective emotions, which is based on the idea that players can coordinate their emotional states.
Parimal Kanti Bag, Hamid Sabourian, and Eyal Winter. Multi-Stage Voting, Sequential Elimination And Condorcet Consistency. Discussion Papers 2009. Web. Publisher's VersionAbstract
A class of voting procedures based on repeated ballots and elimination of one candidate in each round is shown to always induce an outcome in the top cycle and is thus Condorcet consistent, when voters behave strategically. This is an important class as it covers multi-stage, sequential elimination extensions of all standard one-shot voting rules (with the exception of negative voting), the same one-shot rules that would fail Condorcet consistency. The necessity of repeated ballots and sequential elimination are demonstrated by further showing that Condorcet consistency would fail in all standard voting rules that violate one or both of these conditions.
Zamir, Bezalel Peleg, and Shmuel. On Bayesian-Nash Equilibria Satisfying The Condorcet Jury Theorem: The Dependent Case. Discussion Papers 2009. Web. Publisher's VersionAbstract
We investigate sufficient conditions for the existence of Bayesian-Nash equilibria that satisfy the Condorcet Jury Theorem (CJT). In the Bayesian game Gn among n jurors, we allow for arbitrary distribution on the types of jurors. In particular, any kind of dependency is possible. If each juror i has a constant strategy , si (that is, a strategy that is independent of the size n''''¥i of the jury), such that s=( s1, s2, . . . , sn . . .) satisfies theCJT, then byMcLennan (1998) there exists a Bayesian-Nash equilibrium that also satisfies the CJT. We translate the CJT condition on sequences of constant strategies into the following problem: (**) For a given sequence of binary random variables X = (X1, X2, ..., Xn, ...) with joint distribution P, does the distribution P satisfy the asymptotic part of the CJT ? We provide sufficient conditions and two general (distinct) necessary conditions for (**). We give a complete solution to this problem when X is a sequence of exchangeable binary random variables.
Weisel, Gary Bornstein, and Ori, B. Punishment, Cooperation, And Cheater Detection In. Discussion Papers 2009. Web. Publisher's VersionAbstract
Explaining human cooperation in large groups of non-kin is a major challenge to both rational choice theory and the theory of evolution. Recent research suggests that group cooperation can be explained assuming that cooperators can punish non-cooperators or cheaters. The experimental evidence comes from economic games in which group members are informed about the behavior of all others and cheating occurs in full view. We demonstrate that under more realistic information conditions, where cheating is less obvious, punishment is ineffective in enforcing cooperation. Evidently, the explanatory power of punishment is constrained by the visibility of cheating.