2012
Levy, Yehuda (John) .
“A Discounted Stochastic Game With No Stationary Nash Equilibrium”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe present an example of a discounted stochastic game with a continuum of states, finitely many players and actions, and deterministic transitions, that possesses no measurable stationary equilibria, or even stationary approximate equilibria. The example is robust to perturbations of the payoffs, the transitions, and the discount factor, and hence gives a strong nonexistence result for stationary equilibria. The example is a game of perfect information, and hence it also does not possess stationary extensive-form correlated equilibrium. Markovian equilibria are also shown not to exist in appropriate perturbations of our example.
Hellman, Ziv .
“A Game With No Bayesian Approximate Equilibria”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractSimon (2003) presented an example of a 3-player Bayesian games with no Bayesian equilibria but it has been an open question whether or not there are games with no approximate Bayesian equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states that possesses no approximate Bayesian equilibria, thus resolving the question. As a side benefit we also have for the first time an an example of a 2-player Bayesian game with no Bayesian equilibria and an example of a strategic-form game with no approximate Nash equilibria. The construction makes use of techniques developed in an example by Y. Levy of a discounted stochastic game with no stationary equilibria.
Kareev, Yaakov .
“Advantages Of Cognitive Limitations”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractBeing a product of evolutionary pressures, it would not be surprising to find that what seems to be a limitation of the cognitive system is actually a fine-tuned compromise between a set of competing needs. This thesis is demonstrated using the case of the limited capacity of short-term memory, which is often regarded as the prime example of a cognitive limitation.
Konigsberg, Amir .
“Aesthetic Autonomy”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractThe acquaintance principle (AP) and the view it expresses have recently been tied to a debatesurrounding the possibility of aesthetic testimony, which, plainly put, deals with the questionwhether aesthetic knowledge can be acquired through testimony-typically aesthetic and non-aesthetic descriptions communicated from person to person. In this context a number of suggestions have been put forward opting for a restricted acceptance of AP. This paper is an attempt to restrict AP even more
Schreiber, Amnon .
“An Economic Index Of Relative Riskiness”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractIn their seminal works, Arrow (1965) and Pratt (1964) defined two aspects of risk aversion: absolute risk aversion and relative risk aversion. Based on their definitions, we define two aspects of risk: absolute risk and relative risk. We consider situations in which, by making an investment, an agent exchanges a certain amount of wealth w by a random distributed level of wealth W. In such situations, we define absolute risk as the riskiness of a gamble that is distributed as W-w, and relative risk as the riskiness of a security that is distributed as W/w. We measure absolute risk by the Aumann and Serrano (2008) index of riskiness and relative risk by an equivalent index that we develop in this paper. The two concepts of risk do not necessarily agree on which one of two investments is riskier, and hence they capture two different aspects of risk.
Fabrizio Germano, Peio Zuazo-Garin .
“Approximate Knowledge Of Rationality And Correlated Equilibria”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe extend Aumann's theorem (Aumann, 1987) in deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weakernotion, p-belief of rationality, where agents believe the other agents are rational with probabilities p or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p sufficiently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's theorem (Aumann and Dreze, 2008) on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.
Sergiu Hart, Noam Nisan .
“Approximate Revenue Maximization With Multiple Items”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractMyerson's classic result provides a full description of how a seller can maximize revenue when selling a single item. We address the question of revenue maximization in the simplest possible multi-item setting: two items and a single buyer who has independently distributed values for theitems, and an additive valuation. In general, the revenue achievable from selling two independent items may be strictly higher than the sum of the revenues obtainable by selling each of themseparately. In fact, the structure of optimal (i.e., revenue-maximizing) mechanisms for two itemseven in this simple setting is not understood.In this paper we obtain approximate revenue optimization results using two simple auctions: that of selling the items separately, and that of selling them as a single bundle. Our main results (which are of a "direct sum" variety, and apply to any distributions) are as follows. Selling theitems separately guarantees at least half the revenue of the optimal auction; for identicallydistributed items, this becomes at least 73% of the optimal revenue. For the case of k > 2 items, we show that selling separately guarantees at least a c/log^2 k fraction of the optimal revenue; for identically distributed items, the bundling auction yields at least a c/log k fraction of the optimal revenue.
“Automatic Learning Of Evaluation, With Applications To Computer Chess”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractA new and fast learning method is described in the context of teaching a program to play chess. A theory of the meaning of a position evaluation is developed, and is then confronted with a large collection of games played by masters or other programs. The program learns by fitting its evaluation to better predict the results of the games. The method has been employed by a top-rated program for the past 10 years, and has earned several world championships and successful matches against the world's best grandmasters for the program. The effectiveness of the method is demonstrated by showing its successful prediction of known playing strength of the programs.
Babichenko, Yakov .
“Best-Reply Dynamics In Large Anonymous Games”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe consider small-influence anonymous games with a large number of players $n$ where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most $cn log n$ steps for some constant $c>0$). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least $1-e^-c'n$ for some constant $c'>0$.
Edhan, Omer .
“Continuous Values Of Market Games Are Conic”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe prove that every continuous value on a space of vector measure market games $Q$, containing the space of nonatomic measures $NA$, has the textitconic property, i.e., if a game $vin Q$ coincides with a nonatomic measure $nu$ on a conical diagonal neighborhood then $varphi(v)=nu$. We deduce that every continuous value on the linear space $mathcal M$, spanned by all vector measure market games, is determined by its values on $mathcalLM$ - the space of vector measure market games which are Lipschitz functions of the measures.
Neyman, Abraham .
“Continuous-Time Stochastic Games”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractEvery continuous-time stochastic game with finitely many states and actions has a uniform andlimiting-average equilibrium payoff.
Levy, Yehuda (John) .
“Continuous-Time Stochastic Games Of Fixed Duration”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe study non-zero-sum continuous-time stochastic games, also known as continuous-time Markov games, of fixed duration. We concentrate on Markovian strategies. We show by way of example that equilibria need not exist in Markovian strategies, but they always exist in Markovian public-signal correlated strategies. To do so, we develop criteria for a strategy profile to be an equilibrium via differential inclusions, both directly and also by modeling continuous-time stochastic as differential games and using the Hamilton-Jacobi-Bellman equations. We also give an interpretation of equilibria in mixed strategies in continuous-time, and show that approximate equilibria always exist.
Hellman, Ziv .
“Countable Spaces And Common Priors”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks a common prior but has a common improper prior may or may not have a bounded agreeable bet. The iterated expectations characterisation of the existence of common priors extends almost as is, as a sufficient and necessary condition, from finite spaces to countable spaces, but fails to serve as a characterisation of common improper priors. As a side-benefit of the proofs here, we also obtain a constructive proof of the no betting characterisation in finite spaces.
Micha Mandel, Yosef Rinott .
“Cross-Sectional Sampling, Bias, Dependence, And Composite Likelihood”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractA population that can be joined at a known sequence of discrete times is sampled cross-sectionally, and the sojourn times of individuals in the sample are observed. It is well known that cross-sectioning leads to length-bias, but less well known that it may result also in dependence among the observations, which is often ignored. It is therefore important to understand and to account for this dependence when estimating the distribution of sojourn times in the population.In this paper, we study conditions under which observed sojourn times are independent and conditions under which treating observations as independent, using the product of marginals in spite of dependence, results in proper inference. The latter is known as the Composite Likelihood approach. We study parametric and nonparametric inference based on Composite Likelihood, and provide conditions for consistency, and further asymptotic properties, including normal and non-normal distributional limits of estimators. We show that Composite Likelihood leads to good estimators under certain conditions, and illustrate that it may fail without them. The theoretical study is supported by simulations. We apply the proposed methods to two data sets collected by cross-sectional designs: data on hospitalization time after bowel and hernia surgeries, and data on service times at our university.
“Deludedly Agreeing To Agree”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractWe study conditions relating to the impossibility of agreeing to disagree in models of interactive KD45 belief (in contrast to models of S5 knowledge, which are used in nearly all the agreements literature). Agreement and disagreement are studied under models of belief in three broad settings: non-probabilistic decision models, probabilistic belief revision of priors, and dynamic communication among players. We show that even when the truth axiom is not assumed it turns out that players will find it impossible to agree to disagree under fairly broad conditions.
Moti Michaeli, Daniel Spiro .
“Distribution Of Revealed Preferences Under Social Pressure, The”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractThis paper studies theoretically the aggregate distribution of revealed preferences when heterogeneous individuals make the trade o? between being true to their real opinions and conforming to a social norm. We show that in orthodox societies, individuals will tend to either conform fully or ignore the social norm while individuals in liberal societies will tend to compromise between the two extremes. The model sheds light on phenomena such as polarization, alienation and hypocrisy. We also show that societies with orthodox individuals will be liberal on aggregate unless the social norm is upheld by an authority. This suggests that orthodoxy cannot be maintained under pluralism.
Amos Schurr, Ilana Ritov, Yaakov Kareev Judith Avrahami .
“Effect Of Perspective On Unethical Behavior, The”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractIn two experiments, we explored how the perspective through which individuals view their decisions influences their moral behavior. To do this we employed a computerized "Is that the answer you had in mind?" trivial-pursuit style game. The game challenges individuals' integrity because cheating during play cannot be detected. Perspective, whether local or global, was manipulated: In Experiment 1 the choice procedure was used to evoke a local or an integrative perspective of one's choices, whereas in Experiment 2, perspective was manipulated through priming. Across all the experiments, we observed that when given an incentive to cheat, the adoption of a local perspective increased cheating, as evidenced by overall higher reported success rates. These findings have clear implications for explaining and controlling behavior in other situations (e.g., exercising, dieting) in which the perspective one takes is a matter of choice.
Abba M. Krieger, Ester Samuel-Cahn .
“Generalized Bomber And Fighter Problems: Offline Optimal Allocation Of A Discrete Asset”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractThe classical Bomber problem concerns properties of the optimal allocation policy of arsenal for an airplane equipped with a given number, n, of anti-aircraft missiles, at a distance t > 0 from its destination, which is intercepted by enemy planes appearing according to a homogeneous Poisson process. The goal is to maximize the probability of reaching its destination. The Fighter problem deals with a similar situation, but the goal is to shoot down as many enemy planes as possible. The optimal allocation policies are dynamic, depending upon the times at which the enemy is met. The present paper generalizes these problems by allowing the number of enemy planes to have any distribution, not just Poisson. This implies that the optimal strategies can no longer be dynamic, and are, in our terminology, offline. We show that properties similar to those holding for the classical problems hold also in the present case. Whether certain properties hold that remain open questions in the dynamic version are resolved in the offline version. Since `time' is no longer a meaningful way to parametrize the distributions for the number of encounters, other more general orderings of distributions are needed. Numerical comparisons between the dynamic and offliine approaches are given.
Ofri Raviv, Merav Ahissar, Yonatan Loewenstein .
“How Recent History Affects Perception: The Normative Approach And Its Heuristic Approximation”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractThere is accumulating evidence that prior knowledge about expectations plays an important role in perception. The Bayesian framework is the standard computational approach to explain how prior knowledge about the distribution of expected stimuli is incorporated with noisy observations in order to improve performance. However, it is unclear what information about the prior distribution is acquired by the perceptual system over short periods of time and how this information is utilized in the process of perceptual decision making. Here we address this question using a simple two-tone discrimination task. We find that the contraction bias , in which small magnitudes are overestimated and large magnitudes are underestimated, dominates the pattern of responses of human participants. This contraction bias is consistent with the Bayesian hypothesis in which the true prior information is available to the decision-maker. However, a trial-by-trial analysis of the pattern of responses reveals that the contribution of most recent trials to performance is overweighted compared with the predictions of a standard Bayesian model. Moreover, we study participants performance in a-typical distributions of stimuli and demonstrate substantial deviations from the ideal Bayesian detector, suggesting that the brain utilizes a heuristic approximation of the Bayesian inference. We propose a biologically plausible model, in which decision in the two-tone discrimination task is based on a comparison between the second tone and an exponentially-decaying average of the first tone and past tones. We show that this model accounts for both the contraction bias and the deviations from the ideal Bayesian detector hypothesis. These findings demonstrate the power of Bayesian-like heuristics in the brain, as well as their limitations in their failure to fully adapt to novel environments.
Sergiu Hart, Philip J. Reny .
“Maximal Revenue With Multiple Goods: Nonmonotonicity And Other Observations”.
Discussion Papers 2012. Web.
Publisher's VersionAbstractConsider the problem of maximizing the revenue from selling a number of goods to a single buyer. We show that, unlike the case of one good, when the buyer's values for the goods increase the seller's maximal revenue may well decrease. We also provide a characterization of revenue-maximizing mechanisms (more generally, of "seller-favorable" mechanisms) that circumvents nondifferentiability issues. Finally, through simple and transparent examples, we clarify the need for and the use of randomization when maximizing revenue in the multiple-goods versus the one-good case.