Peter D. Sozou

ON HYPERBOLIC DISCOUNTING AND UNCERTAIN HAZARD RATES

The value of a future reward should be discounted where there is a risk that the reward will not be realized. If the risk manifests itself at a known, constant hazard rate, a risk–neutral recipient should discount the reward according to an exponential time–preference function. Experimental subjects, however, exhibit short–term time preferences that differ from the exponential in a manner consistent with a hazard rate that falls with increasing delay. It is shown here that this phenomenon can be explained by uncertainty in the underlying hazard. The time–preference function predicted by this analysis can be calculated by means of either (i) a direct superposition method, or (ii) Bayesian updating of the expected hazard rate. The observed hyperbolic time–preference function is consistent with an exponential prior distribution for the underlying hazard rate. Sensitivity of the predicted time–preference function to variation in the probability distribution of the underlying hazard rate is explored.

Augmented discounting: interaction between ageing and time–preference behaviour

Discounting occurs when an immediate benefit is systematically valued more highly than a delayed benefit of the same magnitude. It is manifested in physiological and behavioural strategies of organisms. This study brings together life–history theory and time–preference theory within a single modelling framework. We consider an animal encountering reproductive opportunities as a random process. Under an external hazard, optimal life–history strategy typically prioritizes immediate reproduction at the cost of declining fertility and increasing mortality with age. Given such ageing, an immediate reproductive reward should be preferred to a delayed reward because of both the risk of death and declining fertility. By this analysis, ageing is both a consequence of discounting by the body and a cause of behavioural discounting. A series of models is developed, making different assumptions about external hazards and biological ageing. With realistic ageing assumptions (increasing mortality and an accelerating rate of fertility decline) the time–preference rate increases in old age. Under an uncertain external hazard rate, young adults should also have relatively high time–preference rates because their (Bayesian) estimate of the external hazard is high. Middle–aged animals may therefore be the most long term in their outlook.

Pensions and retirement savings: cluster analysis of consumer behaviour and attitudes

Purpose - The aim of this article is to obtain a better understanding of peoples motivation and behaviour with respect to provision for their retirement. Design/methodology/approach - This study examines variation in behaviour and attitudes towards pensions and retirement saving among consumers of financial service products, using data from a questionnaire survey. Findings - A cluster analysis indicates that consumers can be divided into six clusters, with distinctive demographic, economic, behavioural and attitudinal traits for each cluster. Of particular interest is the finding that members of two of the clusters reported a general tendency to be in debt in the short term, whilst at the same time putting money away for retirement through either a company pension or voluntary regular saving. Research limitations/implications - The data set is composed of people who enquired about products offered by the financial services industry. This makes the findings by definition relevant to marketing pensions and retirement savings products to this set of people. It is not clear to what extent they apply to the population as a whole; this would be a useful further study. Originality/value - The key contribution of this study is that the identification of target groups could ultimately lead to enhanced abilities for pension providers to develop customised pension and saving products for those groups.

Costly but worthless gifts facilitate courtship

What are the characteristics of a good courtship gift? We address this question by modelling courtship as a sequential game. This is structured as follows: the male offers a gift to a female; after observing the gift, the female decides whether or not to accept it; she then chooses whether or not to mate with the male. In one version of the game, based on human courtship, the female is uncertain about whether the male intends to stay or desert after mating. In a second version, there is no paternal care but the female is uncertain about the males quality. The two versions of the game are shown to be mathematically equivalent. We find robust equilibrium solutions in which mating is predominantly facilitated by an ‘extravagant’ gift which is costly to the male but intrinsically worthless to the female. By being costly to the male, the gift acts as a credible signal of his intentions or quality. At the same time, its lack of intrinsic value to the female serves to deter a ‘gold-digger’, who has no intention of mating with the male, from accepting the gift. In this way, an economically inefficient gift enables mutually suitable partners to be matched.

To age or not to age

According to the antagonistic pleiotropy theory of ageing, natural selection has favoured genes conferring short–term benefits to the organism at the cost of deterioration in later life. The ‘disposable soma’ theory expresses this as a life–history strategy in which somatic maintenance is below the level required to prevent ageing, thus enabling higher immediate fertility. It has been argued that a non–ageing strategy will always be bettered by a low but non–zero rate of ageing, because the costs of such ageing will be felt only in the distant future when they are of negligible importance. Here, we examine this argument critically. We find that a non–ageing strategy will be locally optimal if, in the presence of ageing, the onset of deterioration is sufficiently rapid or early. Conversely, ageing will be optimal if deterioration is sufficiently slow or late. As the temporal profile of ageing changes from one of steady deterioration to one involving a sudden loss of vitality after a period of little or no decline, the conditions for a non–ageing strategy to be locally optimal become progressively more stringent. But for all forms of profile considered, conditions can be found for which a strategy involving no ageing is locally optimal.

Flocking behaviour of passerines: a dynamic model for the non-reproductive season

SummaryThe behaviour of a small male passerine bird over a typical winter day is studied by a dynamic programming model. The bird can be either unpaired or paired; an unpaired bird can forage in a flock, forage alone or sing to attract a mate. Foraging increases his reserves, while singing reduces them. The optimal policy and the expected behaviour of birds depend both on time and reserves. The model predicts that birds will flock, especially in the morning, if flocking birds find more food (“foraging efficiency”), and also more flocking can be expected when the predation risk is lower in a flock (“antipredator benefit”). Where flocking gives lower variance in food intake, with the same mean (“reduced variance benefit”), birds with low reserves at the end of the day choose to forage alone (high variance option), while otherwise they are risk-averse and forage in a flock. The cost of flocking increases with time in a day and with the probability of mate attraction through singing. Decisions inevitably involve trade-offs. Where flocking results in antipredator benefit, but also lower foraging gain, birds with low reserves forage alone, but birds with high reserves flock.

Non-linear point distribution modelling using a multi-layer perceptron

Objects of the same class sometimes exhibit variation in shape. This shape variation has previously been modelled by means of point distribution models (PDMs) in which there is a linear relationship between a set of shape parameters and the positions of points on the shape. A polynomial regression generalization of PDMs, which succeeds in capturing certain forms of non-linear shape variability, has also been described. Here we present a new form of PDM, which uses a multi-layer perceptron to carry out non-linear principal component analysis. We compare the performance of the new model with that of the existing models on two classes of variable shape: one exhibits bending, and the other exhibits complete rotation. The linear PDM fails on both classes of shape; the polynomial regression model succeeds for the first class of shapes but fails for the second; the new multi-layer perceptron model performs well for both classes of shape. The new model is the most general formulation for PDMs which has been proposed to date.

Individual and social discounting in a viscous population.

Social discounting in economics involves applying a diminishing weight to community-wide benefits or costs into the future. It impacts on public policy decisions involving future positive or negative effects, but there is no consensus on the correct basis for determining the social discount rate. This study presents an evolutionary biological framework for social discounting. How an organism should value future benefits to its local community is governed by the extent to which members of the community in the future are likely to be its kin. Trade-offs between immediate and delayed benefits to an individual or to its community are analysed for a modelled patch-structured iteroparous population with limited dispersal. It is shown that the social discount rate is generally lower than the individual (private) discount rate. The difference in the two rates is most pronounced, in ratio terms, when the dispersal level is low and the hazard rate for patch destruction is much smaller than the individual mortality rate. When decisions involve enforced collective action rather than individuals acting independently, social investment increases but the social discount rate remains the same.

A general non-linear method for modelling shape and locating image objects

Objects of the same class often exhibit variation in shape. This shape variation has previously been modelled by means of point distribution models (PDMs) in which there is a linear relationship between a set of shape parameters and the positions of points on the shape. Here we present a new form of PDM, which uses a multilayer perceptron (MLP) to carry out nonlinear principal component analysis. We demonstrate that MLP-PDMs can model the shape variability in classes of object for which the linear model fails. We describe the use of MLP-PDMs in image search and present quantitative results for a practical application (face recognition), demonstrating the ability to locate image structures accurately starting from a very poor initial approximation to their pose and shape.

Ydenberg's model of fledging time. A comment

Ydenberg (1989) presents a model for the timing of fledging in the Alcidae, based on the fitness consequences of fledging at a given mass. The model goes beyond previous suggestions based on predation (Cody 1971) or food availability (e.g., Lack 1968, Sealy 1973, Birkhead 1977) in providing a framework that includes both growth and mortality. (For a general theoretical treatment of growth and mortality in a deterministic context see Ludwig and Rowe [1990].) Ydenberg uses dynamic programming (D.P.) to solve the problem; we show that the problem can be solved with a direct method. We also explore the sensitivity of the optimal fledging time t* to various aspects of the model as applied to the Common Murre or Guillemot, Uria aalge.