Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Nonatomic games on Loeb spaces

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.

Multijurisdictional economies, the Tiebout Hypothesis, and sorting

The Tiebout Hypothesis asserts that, when it is efficient to have multiple jurisdictions providing local public goods, then competition between jurisdictions for residents will lead to a near-optimal outcome. Research from cooperative game theory both provides a foundation for the hypothesis and extends the hypothesis to diverse situations where small groups of participants are effective.

Founder-effect speciation theory: failure of experimental corroboration.

The theory of founder-effect speciation proposes that colonization by very few individuals of an empty habitat favors rapid genetic changes and the evolution of a new species. We report here the results obtained in a 10-year-long and large-scale experiment with Drosophila pseudoobscura designed to test the theory. In our experimental protocol, populations are established with variable numbers of very few individuals and allowed to expand greatly for several generations until conditions of severe competition for resources are reached and the population crashes. A few random survivors are then taken to start a new population expansion and thus initiate a new cycle of founding events, population flushes, and crashes. Our results provide no support for the theories proposing that new species are very likely to appear as by-products of founder events.

The vibrational energy flow transition in organic molecules: Theory meets experiment

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907–3915].

Theory for normal and impaired experience-dependent plasticity in neocortex of adult rats

We model experience-dependent plasticity in the cortical representation of whiskers (the barrel cortex) in normal adult rats, and in adult rats that were prenatally exposed to alcohol. Prenatal exposure to alcohol (PAE) caused marked deficits in experience-dependent plasticity in a cortical barrel-column. Cortical plasticity was induced by trimming all whiskers on one side of the face except two. This manipulation produces high activity from the intact whiskers that contrasts with low activity from the cut whiskers while avoiding any nerve damage. By a computational model, we show that the evolution of neuronal responses in a single barrel-column after this sensory bias is consistent with the synaptic modifications that follow the rules of the Bienenstock, Cooper, and Munro (BCM) theory. The BCM theory postulates that a neuron possesses a moving synaptic modification threshold, θM, that dictates whether the neuron's activity at any given instant will lead to strengthening or weakening of its input synapses. The current value of θM changes proportionally to the square of the neuron's activity averaged over some recent past. In the model of alcohol impaired cortex, the effective θM has been set to a level unattainable by the depressed levels of cortical activity leading to “impaired” synaptic plasticity that is consistent with experimental findings. Based on experimental and computational results, we discuss how elevated θM may be related to (i) reduced levels of neurotransmitters modulating plasticity, (ii) abnormally low expression of N-methyl-d-aspartate receptors (NMDARs), and (iii) the membrane translocation of Ca2+/calmodulin-dependent protein kinase II (CaMKII) in adult rat cortex subjected to prenatal alcohol exposure.

Flower color variation: A model for the experimental study of evolution

We review the study of flower color polymorphisms in the morning glory as a model for the analysis of adaptation. The pathway involved in the determination of flower color phenotype is traced from the molecular and genetic levels to the phenotypic level. Many of the genes that determine the enzymatic components of flavonoid biosynthesis are redundant, but, despite this complexity, it is possible to associate discrete floral phenotypes with individual genes. An important finding is that almost all of the mutations that determine phenotypic differences are the result of transposon insertions. Thus, the flower color diversity seized on by early human domesticators of this plant is a consequence of the rich variety of mobile elements that reside in the morning glory genome. We then consider a long history of research aimed at uncovering the ecological fate of these various flower phenotypes in the southeastern U.S. A large body of work has shown that insect pollinators discriminate against white phenotypes when white flowers are rare in populations. Because the plant is self-compatible, pollinator bias causes an increase in self-fertilization in white maternal plants, which should lead to an increase in the frequency of white genes, according to modifier gene theory. Studies of geographical distributions indicate other, as yet undiscovered, disadvantages associated with the white phenotype. The ultimate goal of connecting ecology to molecular genetics through the medium of phenotype is yet to be attained, but this approach may represent a model for analyzing the translation between these two levels of biological organization.

Theory of orientation tuning in visual cortex.

The role of intrinsic cortical connections in processing sensory input and in generating behavioral output is poorly understood. We have examined this issue in the context of the tuning of neuronal responses in cortex to the orientation of a visual stimulus. We analytically study a simple network model that incorporates both orientation-selective input from the lateral geniculate nucleus and orientation-specific cortical interactions. Depending on the model parameters, the network exhibits orientation selectivity that originates from within the cortex, by a symmetry-breaking mechanism. In this case, the width of the orientation tuning can be sharp even if the lateral geniculate nucleus inputs are only weakly anisotropic. By using our model, several experimental consequences of this cortical mechanism of orientation tuning are derived. The tuning width is relatively independent of the contrast and angular anisotropy of the visual stimulus. The transient population response to changing of the stimulus orientation exhibits a slow "virtual rotation." Neuronal cross-correlations exhibit long time tails, the sign of which depends on the preferred orientations of the cells and the stimulus orientation.