The Predictive Utility of Generalized Expected Utility Theories

Many alternative theories have been proposed to explain violations of expected utility (EU) theory observed in experiments. Several recent studies test some of these alternative theories against each other. Formal tests used to judge the theories usually count the number of responses consistent with the theory, ignoring systematic variation in responses that are inconsistent. We develop a maximum-likelihood estimation method which uses all the information in the data, creates test statistics that can be aggregated across studies, and enables one to judge the predictive utility-the fit and parsimony-of utility theories. Analyses of 23 data sets, using several thousand choices, suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit. The menu is: mixed fanning, prospect theory, EU, and expected value. Which theories are best is highly sensitive to whether gambles in a pair have the same support (EU fits better) or not (EU fits poorly). Our method may have application to other domains in which various theories predict different subsets of choices (e.g., refinements of Nash equilibrium in noncooperative games)

Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin-flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.Comment: published version (5 pages, 3 figures

Heterogeneous Quantal Response Equilibrium and Cognitive Hierarchies

We explore an equilibrium model of games where players’ choice behavior is given by logit response functions, but their payoff responsiveness is heterogeneous. We extend the definition of quantal response equilibrium to this setting, calling it heterogeneous quantal response equilibrium (HQRE), and prove existence under weak conditions. We generalize HQRE to allow for limited insight, in which players can only imagine others with low responsiveness. We identify a formal connection between this new equilibrium concept, called truncated quantal response equilibrium (TQRE), and the Cognitive Hierarchy (CH) model. We show that CH can be approximated arbitrarily closely by TQRE. We report a series of experiments comparing the performance of QRE, HQRE, TQRE and CH. A surprise is that the fi of the models are quite close across a variety of matrix and dominance-solvable asymmetric information betting games. The key link is that in the QRE approaches, strategies with higher expected payoffs are chosen more often than strategies with lower expected payoff. In CH this property is not built into the model, but generally holds true in the experimental data

Resonant coupling of a Bose-Einstein condensate to a micromechanical oscillator

We report experiments in which the vibrations of a micromechanical oscillator are coupled to the motion of Bose-condensed atoms in a trap. The interaction relies on surface forces experienced by the atoms at about one micrometer distance from the mechanical structure. We observe resonant coupling to several well-resolved mechanical modes of the condensate. Coupling via surface forces does not require magnets, electrodes, or mirrors on the oscillator and could thus be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes.Comment: 9 pages, 4 figure

Can Observers Predict Trustworthiness?

We investigate whether experimental subjects can predict behavior in a prisoner's dilemma played on a TV show. Subjects report probabilistic beliefs that a player cooperates, before and after the players communicate. Subjects correctly predict that women and players who make a voluntary promise are more likely to cooperate. They are able to distinguish truth from lies when a player is asked about her intentions by the host. Subjects are to some extent able to predict behavior; their beliefs are 7~percentage points higher for cooperators than for defectors. We also study their Bayesian updating. Beliefs do not satisfy the martingale property and display mean reversion

Game theory of mind

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution

“Economic man” in cross-cultural perspective: Behavioral experiments in 15 small-scale societies

Researchers from across the social sciences have found consistent deviations from the predictions of the canonical model of self-interest in hundreds of experiments from around the world. This research, however, cannot determine whether the uniformity results from universal patterns of human behavior or from the limited cultural variation available among the university students used in virtually all prior experimental work. To address this, we undertook a cross-cultural study of behavior in ultimatum, public goods, and dictator games in a range of small-scale societies exhibiting a wide variety of economic and cultural conditions. We found, first, that the canonical model – based on self-interest – fails in all of the societies studied. Second, our data reveal substantially more behavioral variability across social groups than has been found in previous research. Third, group-level differences in economic organization and the structure of social interactions explain a substantial portion of the behavioral variation across societies: the higher the degree of market integration and the higher the payoffs to cooperation in everyday life, the greater the level of prosociality expressed in experimental games. Fourth, the available individual-level economic and demographic variables do not consistently explain game behavior, either within or across groups. Fifth, in many cases experimental play appears to reflect the common interactional patterns of everyday life

Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories

This article compares classical expected utility (EU) with the more general rank-dependent utility (RDU) models. The difference between the independence condition for preferences of EU and its comonotonic generalization in RDU provides the exact demarcation between EU and rank-dependent models. Other axiomatic differences are not essential. An experimental design is described that tests this difference between independence and comonotonic independence in its most basic form and is robust against violations of other assumptions that may confound the results, in particular the reduction principle and transitivity. It is well known that in the classical counterexamples to EU, comonotonic independence performs better than full-force independence. For our more general choice pairs, however, we find that comonotonic independence does not perform better. This is contrary to our prior expectation and suggests that rank-dependent models, in full generality, do not provide a descriptive improvement over EU. For rank-dependent models to have a future, submodels and choice situations need to be identified for which rank-dependence does contribute descriptively