Spacing patterns in terebellid polychaetes

Many fresh and coastal waters are becoming increasingly turbid because of human activities, which may disrupt the visually mediated behaviours of aquatic organisms. Shoaling fish typically depend on vision to maintain collective behaviour, which has a range of benefits including protection from predators, enhanced foraging efficiency and access to mates. Previous studies of the effects of turbidity on shoaling behaviour have focussed on changes to nearest neighbour distance and average group‐level behaviours. Here, we investigated whether and how experimental shoals of three‐spined sticklebacks (Gasterosteus aculeatus) in clear (<10 Nephelometric Turbidity Units [NTU]) and turbid (~35 NTU) conditions differed in five local‐level behaviours of individuals (nearest and furthest neighbour distance, heading difference with nearest neighbour, bearing angle to nearest neighbour and swimming speed). These variables are important for the emergent group‐level properties of shoaling behaviour. We found an indirect effect of turbidity on nearest neighbour distances driven by a reduction in swimming speed, and a direct effect of turbidity which increased variability in furthest neighbour distances. In contrast, the alignment and relative position of individuals was not significantly altered in turbid compared to clear conditions. Overall, our results suggest that the shoals were usually robust to adverse effects of turbidity on collective behaviour, but group cohesion was occasionally lost during periods of instability.

We study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. Under Hotelling's assumptions (uniform distribution of consumers, travel cost proportional to distance, inelastic demand of one unit by each consumer) the price-setting subgames possess equilibria in pure strategies for only a limited set of location pairs. Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. (1979)), Hotelling's claim that there is an equilibrium of the two-stage game in which the firms locate close to each other is incorrect. A result of Dasgupta and Maskin (1986) guarantees that each price-setting subgame has an equilibrium in mixed strategies. We first study these mixed strategy equilibria. We are unable to provide a complete characterization of them, although we show that for a subset of location pairs all equilibria are of a certain type. We reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations. At each of a large number of location pairs we have computed approximate solutions to the system of equations. Next, we use our analytical results and computations to study the equilibrium location choices of the firms. There is a unique (up to symmetry) subgame perfect equilibrium in which the location choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market. At this equilibrium, the support of the subgame equilibrium price strategy is the union of two short intervals. Most of the probability weight is in the upper interval, so that this strategy is reminiscent of occasional sales by the firms. We also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations. In fact, in the class of strategy pairs in which the firms use the same mixed strategy over locations, and this strategy is symmetric about 0.5, there is a single equilibrium. In this equilibrium most of the probability weight of the common strategy is between 0.2 and 0.4, and between 0.6 and 0.8. There is a wide range of pure Nash (as opposed to subgame perfect) equilibrium location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close.

We prove an equilibrium existence result for a class of games with an infinite number of strategies. Our theorem generalises an earlier result by Dasgupta and Maskin. We also identify conditions under which the limit of pure-strategy equilibria of a sequence of finite games is an equilibrium for the limit game. We apply this result to obtain new existence results for the multi-firm, i-dimensional version of Hotellings's location game. The techniques used suggest a technique for computing such equilibria. This paper studies games with discontinuous payoffs. Any game with a compact set of strategies can be approximated by a sequence of finite games. We study the correspondence mapping each approximation to the limit game to its mixed-strategy equilibria and identify conditions under which the limit of such equilibria is an equilibrium for the limit game. When payoffs are discontinuous, this property will not hold in general. An equilibrium for the limit game may not exist or, if it does exist, the equilibrium correspondence may not be upper hemi-continuous. The topic is of concern to economists for two, rather different, reasons. The existence question is clearly important in its own right. In many games that interest economists, payoff functions fail to be continuous or even semi-continuous. Standard existence theorems (Debreu (1952), Glicksberg (1950), (1952), etc.), therefore, are inapplicable. Two classical examples are Bertrand's (1883) model of price competition and Hotelling's (1929) model of spatial competition. Recent work on auction theory (see Milgrom-Weber (1982)) and dynamic oligopoly models (surveyed in Fudenberg-Tirole (1983)) has generated many more instances. The second reason for interest in the equilibrium correspondence is pragmatic. Finite games are generally much more tractable than infinite games. When the equilibrium correspondence is upper hemi-continuous, the easiest way to find an equilibrium for an infinite game may be to calculate the equilibria of a sequence of finite games and take limits.1 The seminal paper on games with discontinuous payoffs is Dasgupta-Maskin (DM) (1986a). This paper proves an existence theorem under assumptions that are strictly weaker than DM's. The key difference between our approach and DM's is as follows. DM identify conditions under which the limit of equilibria of any sequence of approximating finite games is an equilibrium for the limit game. These conditions are quite restrictive. They may be violated even though dominant strategy equilibria exist for the limit game. Our approach to the existence problem is different. We consider a given sequence of approximating games and ask when the limit of equilibria for this particular sequence will be an equilibrium for the limit game.2

A Noncooperative Analysis of Hotelling's Location Game

Currencies, competition, and clans

This paper examines Hotelling's model of location with linear transportation cost. Existence of pure strategy subgame perfect equilibria in the infinitely repeated price game with fixed locations is proved. These subgame perfect equilibria have a stick and carrot structure. Given firm locations, there are discount factors sufficiently high that there is a subgame perfect equilibrium with a two-phase structure. Given the discount factors, there are stationary subgame perfect equilibria for a wide range of locations. However, for some pairs of location, no symmetric simple penal code exists, all subgame perfect profiles are nonstationary, and there is only one seller in the market in infinitely many periods.

Why Judges Always Vote

Asymmetric equilibria in spatial competition under weakly concave scoring rules

We investigate how bank competition affects the efficiency of credit allocation, using a model of spatial competition. Our analysis shows that bad loans are more likely the larger the number of banks competing for customers. We study further how many banks will be active if market entry is not regulated. Free entry can induce too much entry and thus too many bad loans compared to the social optimum. Finally we analyse how bank competition affects the restructuring efforts of firms. We find that restructuring has positive externalities which give rise to multiple equilibria, with either much or little restructuring activity.JEL classification: D43, G21, G34, L13, P31, P34.

Structures of NaCl and LiCl aqueous solutions in pores of carbon nanotubes with diameter 1 and 2 nm were evaluated by using X-ray diffraction and molecular dynamics simulations. Water intermolecular distances in carbon nanotubes with 1 and 2 nm pore diameters were more elongated and shortened than bulk water, respectively. Those were results of weakened and strengthened hydrogen bonds. The structures of aqueous solutions in carbon nanotubes were considerably different from water despite tiny amounts of ions in the pores. The nearest neighbour distances in aqueous solutions were rarely changed from that in water system in 1 nm carbon nanotubes pore, while those were longer than water in 2 nm carbon nanotubes pore. On the other hand, the second nearest neighbour distances in aqueous solutions in 1 and 2 nm pore diameter carbon nanotubes were both decreased from those in water in carbon nanotubes. Significant hydration formation and cleavage of hydrogen bonds were thus observed in 2 nm carbon nanotubes pore, because the elongated nearest neighbour and shortened second nearest neighbour distances were observed. Anomalous feature of the unchanged nearest neighbour and shortened second neighbour distances in 1 nm carbon nanotubes pore is the result that water intermolecular distance was much longer than bulk and hydrogen bonds were thus severely separated. Ions might play dominant role to connect hydrogen bonds and of course form hydration shell. Those anomalous structure changes from water to aqueous solution were observed only in extremely narrow carbon nanotubes.

Les modèles de concurrence spatiale à la Hotelling permettent de traiter simultanément deux éléments de la concurrence imparfaite : la différenciation des produits et la discrimination des prix. On montre qu'au-delà d'un certain degré de monopole, la discrimination des prix permet de maximiser les résultats de la firme, notamment lorsque les coûts sont élevés et les coûts marginaux faibles. Certaines productions qui exigent des coûts fixes élevés ne peuvent alors être engagés que si une politique discriminatoire est engagée. Les entreprises ont alors intérêt à se spécialiser dans les activités où elles disposent d'un degré de monopole suffisant pour pratiquer la discrimination.

EXAFS study of atomic structure and relaxation phenomena in amorphous Tb20Fe80

Interpretation of the behavioural dynamics and distribution of herring requires explicit consideration of spatial and temporal scales since no single mechanism can explain the pattern on all scales. High resolution sonar and echosounders were used as our observation tools. The cluster ratio, mean Nearest Neighbour Distance (mean ISD): mean of the average Inter-school Distance (mean ISD) provides a descriptive index linking scales of distribution pattern within and between clusters of schools. It can be used to compare school clustering patterns for surveys made at different places and seasons. Two mesoscale patterns of school clustering were observed, as indicated by the distribution of nearest neighbour distances; one at 0.05–0.3 km revealed by sonar and another at 0.8–2.5 km revealed by echosounder. In general, schools were tightly aggregated, whilst school clusters were patchily distributed. Heightened feeding motivation explains the predominance of relatively small schools and their tendency to be found closer together and more clustered than large schools. Differences in distribution and density of food patches and predators may account to some degree for the observations (1) schools were distributed according to their size; both small and large schools had nearest neighbours of similar size more often than expected, (2) splitting and joining of schools were the most frequently recorded behavioural events. A considerable amount of variation in distribution and dynamics can be accounted for by changes in behaviour associated with diurnal vertical migrations. Some schools apparently did not perform diurnal vertical migrations. We suggest that when profitable, some herring may ‘‘dip in to the fridge’’ (feed in deep, cold water) during the day rather than pursue food on potentially high energy migrations. 1999 International Council for the Exploration of the Sea

Nearest neighbor distances in uniform–random poly-dispersed microstructures

Modal frequencies are widely used as damage-sensitive features in vibration-based unsupervised anomaly detection for full-scale civil structures. However, environmental variations introduce nonlinear and non-Gaussian behaviors in modal frequencies, characterized by multicentricity and substantial variance differences. These behaviors inevitably mask damage-induced frequency shifts, leading to increased false-detection rates and degraded real-time performance. To address this, this paper presents a novel unsupervised framework for early-stage anomaly detection that integrates exponential slow feature analysis (SFA) with just-in-time learning-aided standard K -nearest neighbor metrics. First, nonlinear modal features with minimum temporal variation are extracted from modal frequencies via exponential SFA for dimensionality reduction. Afterward, under the standard measurement criteria, the Euclidean squared distances between each sample in the entire training set and its nearest neighbors are computed. The standard distance for each neighbor is then modeled, with the number of neighbors automatically selected through Bayesian optimization and cross-validation. The primary purpose of this step is to ensure that the nearest neighbor distances between samples under different environmental conditions and damage conditions including abrupt anomalies or gradual degradations, are measured on a consistent scale, thereby minimizing environmental variability. After that, a robust detection indicator is derived from the mean of squared nearest neighbor distances and combined with kernel density estimation to determine an online detection threshold for outliers. The results indicate the proposed method effectively mitigates strong environmental variability without prior environmental measurements and accurately identifies anomalies in bridge modal frequencies with negligible false-positive and false-negative errors.