Reward Variables Research Articles

Optimality of index policies for a sequential sampling problem

Consider the following sequential sampling problem: at each time, a choice must be made between obtaining an independent sample from one of a set of random reward variables or stopping the sampling. Sampling a random variable incurs a random cost at each time. The objective of the problem is to maximize the expected nett difference between the largest sample reward obtained before stopping and the accumulated costs incurred while sampling. In this paper, the authors prove that the optimal feedback strategies for this problem are index policies and provide an explicit expression for the optimal expected reward from any state. The problem is motivated by search methods for global optimization problems where the cost of computation is explicitly incorporated into the objective.

Assessing Specification Errors in Stochastic Discount Factor Models

ABSTRACTIn this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage‐free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

Assessing Specification Errors in Stochastic Discount Factor Models

In this paper we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on x2 statistics associated with null hypothesis that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

Algorithms for the generation of state-level representations of stochastic activity networks with general reward structures

Stochastic Petri nets (SPNs) and extensions are a popular method for evaluating a wide variety of systems. In most cases, their numerical solution requires generating a state-level stochastic process, which captures the behavior of the SPN with respect to a set of specified performance measures. These measures are commonly defined at the net level by means of a reward variable. In this paper, we discuss issues regarding the generation of state-level reward models for systems specified as stochastic activity networks (SANs) with "step-based reward structures". Step-based reward structures are a generalization of previously proposed reward structures for SPNs and can represent all reward variables that can be defined on the marking behavior of a net. While discussing issues related to the generation of the underlying state-level reward model, we provide an algorithm to determine whether a given SAN is "well-specified" A SAN is well-specified if choices about which instantaneous activity completes among multiple simultaneously-enabled instantaneous activities do not matter, with respect to the probability of reaching next possible stable markings and the distribution of reward obtained upon completion of a timed activity. The fact that a SAN is well specified is both a necessary and sufficient condition for its behavior to be completely probabilistically specified, and hence is an important property to determine.

Reward model solution methods with impulse and rate rewards: an algorithm and numerical results

Reward models have become an important method for specifying performability models for many types of systems. Many methods have been proposed for solving reward models, but no method has proven itself to be applicable over all system classes and sizes. Furthermore, specification of reward models has usually been done at the state level, which can be extremely cumbersome for realistic models. We describe a method to specify reward models as stochastic activity networks (SANs) with impulse and rate rewards, and a method by which to solve these models via uniformization. The method is an extension of one proposed by de Souza e Silva and Gail in which impulse and rate rewards are specified at the SAN level, and solved in a single model. Furthermore, we propose a new technique for discarding paths in the uniformized process whose contribution to the reward variable is minimal, which greatly reduces the time and space required for a solution. A bound is calculated on the error introduced by this discarding, and its effectiveness is illustrated through the study of the performability and availability of a degradable multi-processor system.

Utility maximization and melioration: Internalities in individual choice

AbstractHow do people go about choosing between alternatives in relatively simple settings? This study explores some of the variables that past work suggests may be relevant. Volunteer subjects worked for money in six procedures in which the probability of a payment from either of two alternatives was 1.0, but the rate of pay (i.e. the speed with which a payment was delivered or the size of the payment) interacted with the subjects recent allocation of choices, which we define as the ‘internalities’. Because of the internalities, choosing the currently more profitable alternative did not maximize total earnings. Subjects were more likely to fail to maximize when the interaction between present pay and past choices was spread over longer sequences of choices, or when the reward variable was the speed, rather than the value, of each payment. Subjects often disregarded the internalities and were instead guided by the current yields of the two alternatives, which is a frequently observed tendency, called ‘melioration’, in experiments on choices by animals. The tendency toward melioration was only partially counteracted by explicit instructions on how to maximize earnings. We discuss a theoretical framework for melioration that postulates both motivational and cognitive sources.

Constant vs. Variable Risk‐Aversion in Foraging Bananaquits

Recent foraging theories predict that risk—averse foragers will trade off increases in mean reward against increases in reward variability. Different formulations of this trade—off have been proposed, with some models assuming constant risk—aversion and others assuming decreasing risk—aversion. A detailed analysis of indifference curves (when a forager shows equal preference for certain mean—variance combinations) can theoretically be used to discriminate between models. We follow the analysis of previous workers by equating decreasing risk—aversion with the predictions of the z—score model because those predictions suggest indifference curves that can be discriminated from the constant risk—aversion of the variance discounting model. Experiments conducted with captive Bananaquits (Coereba flaveola) foraging on nectar in an artificial floral patch indicate that they show a simple mean—variance trade—off. Bananaquit foraging behavior was consistent with the constant risk—aversion of the variance—discounting model, but was significantly different from decreasing risk—aversion represented by the z—score model.

Pollination Biology of Montane Plants: Relationship Between Rate of Nectar Production and Standing Crop

Rates of floral nectar production and volumes of standing crops of floral nectar were measured for eight species of Colorado montane plants. Although significant positive correlations exist between the two variables, the magnitudes of the coefficients are not very great. This surprising result may be due to the large variability in rate of nectar production within each species. The patterns suggest that pollinators, by responding to standing crop volumes, may not exert very strong selective pressure on rate of floral nectar production. All species examined had similarly variable patterns of standing crop indicating that pollinators encounter a wide range of reward variability while collecting nectar, regardless of which plant species is being visited. INTRODUCTION It has become increasingly obvious in recent years that successful plant reproduction occurs not only as a function of the frequency of pollinator visitation but of subtler aspects of pollinator behavior as well (e.g, Pyke, 1981; Waser, 1983; Zimmerman, 1988). Not all combinations of matings, for example, yield equal results. Price and Waser (1979) and Waser and Price (1983) have found that optimal outcrossing distances exist for both Delphinium nelsonii and Ipomopsis aggregata; pollen moving this distance before landing on a stigma has a higher probability of producing more, high-quality seeds than does pollen arriving from either a shorter or longer distance. Also, a growing body of literature suggests that pollinator flight distances, and thus, ultimately, the distances pollen grains are carried, are significantly influenced by the amount of nectar reward received from flowers by pollinators (e.g., Pyke, 1978a; Heinrich, 1979; Zimmerman, 1982; Galen and Plowright, 1985; Zimmerman and Cook, 1985). Therefore the possibility exists that pollinators might provide selective pressure on plants to produce optimal quantities of floral nectar (Zimmerman, 1988). The concept that rate of floral nectar production by plants might be under selective pressure from pollinators is certainly not novel (Pyke, 1981; Pyke and Waser, 1981; Pleasants, 1983; Pleasants and Chaplin, 1983). Nectar production in a number of species has been found to have high heritability (Pedersen, 1953; Hawkins, 1971; Teuber and Barnes, 1978, 1979; Teuber et al., 1980, 1983) and to respond quickly to artificial selection (Hawkins, 1971). Although both of these characteristics are necessary if pollinators are to provide the selective force necessary to influence rate of nectar production, a third condition must also be met. Selection will operate only if a significant, positive relationship exists between rate of nectar production and standing crop of nectar. From the perspective of pollinators, standing crop is the more important of the two values because it, more directly, reflects the nature of the reward received. Standing crops, however, are determined both by the rate of nectar production and by the foraging behavior of pollinators. Surprisingly, not a single study has examined the relationship between rate of floral nectar production and the volume of standing crop of nectar found in flowers. It is certainly reasonable to expect that a significant positive relationship between nectar production and standing crop will exist. What is important from an evolutionary standpoint, however, is the strength of that relationship. Selection pressure on rate of nectar production cannot be very great when the two variables are only weakly linked. A weak correlation can arise in at least two manners. First, if high per flower visitation

How constant is the constant of risk-aversion?

We describe an experiment designed to distinguish between two models of risk-sensitive feeding behaviour: the variance discounting model and the z-score model. The variance discounting model assumes that mean reward levels do not affect preferences over reward variability, but the z-score model assumes that mean reward levels do affect preferences over variability. We presented two choices to feeding rufous hummingibrds, Selaphoruous rufus. One alternative had a higher mean and a higher variance than the other. After measuring preference, we increased the mean of both alternatives by adding the same amount to all possible outcomes. The variance discounting model predicts that such a general shift should not change preferences, but the z-score model predicts that preferences will change. Our results support the z-score model. The variance discounting model's assumption of constant risk-aversion fails.

REPRODUCTION IN POLEMONIUM: PATTERNS AND IMPLICATIONS OF FLORAL NECTAR PRODUCTION AND STANDING CROPS

Patterns of floral nectar production and standing crop were measured in four populations of the herbaceous perennial plant species Polemonium foliosissimum. Contrary to prediction (Pleasants, 1983), individual flowers in this mass‐flowering species were found to produce equivalent nectar volumes every day of their lives. Alternative methods of increasing the reward variability presented to pollinators are evaluated for P. foliosissimum and the relationship between that variability and risk‐aversive foraging by pollinators is discussed. Significant spatial and temporal variability in rate of nectar production was found. Populations separated by approximately 200 m exhibited different rates. Nectar production declined significantly as a function of time of the flowering season in two populations but not in a third. In spite of such variability, individual plants showed consistency in production both within a single blooming season and across successive seasons. Because of the variability found in the present study, care should be taken to design appropriate sampling protocols in future nectar studies. Patterns of standing nectar crop were consistent with those expected if pollinators were using an area‐restricted searching pattern.

Reproduction in Polemonium: Patterns and Implications of Floral Nectar Production and Standing Crops

Patterns of floral nectar production and standing crop were measured in four populations of the herbaceous perennial plant species Polemonium foliosissimum. Contrary to prediction (Pleasants, 1983), individual flowers in this mass-flowering species were found to produce equivalent nectar volumes every day of their lives. Alternative methods of increasing the reward variability presented to pollinators are evaluated for P. foliosissimum and the relationship between that variability and risk-aversive foraging by pollinators is discussed. Significant spatial and temporal variability in rate of nectar production was found. Populations separated by approximately 200 m exhibited different rates. Nectar production declined significantly as a function of time of the flowering season in two populations but not in a third. In spite of such variability, individual plants showed consistency in production both within a single blooming season and across successive seasons. Because of the variability found in the present study, care should be taken to design appropriate sampling protocols in future nectar studies. Patterns of standing nectar crop were consistent with those expected if pollinators were using an area-restricted searching pattern.

Risk aversion in hand-reared bananaquits

To study risk aversion in hand-reared bananaquits (Coereba flaveola) we placed individuals in a cage with a 1 m2 floral board having a random array of 85 yellow and 85 red artificial flowers. Flowers of one color were filled with the same quantity of nectar (constant flowers), whereas flowers of the other color were filled with variable quantities of nectar (variable flowers). The constant and variable flowers had identical mean contents, only their variances differed. After three presentations, the constant flowers were made variable and vice versa to control for color preferences. Naive foragers tended to avoid variable flowers. The degree of risk aversion was influenced by previous experience, the relative variability of the variable flowers, and flower color. Variable flowers having similar coefficients of variation, but different reward variables (volume or concentration) resulted in similar levels of risk aversion. Within single foraging episodes the following was observed: sequences of constant flowers increased while sequences of variable flowers remained similar to random foraging; the probability of revisiting a constant flower was higher than revisiting a variable flower; the average amount of nectar consumed from constant and variable flowers was similar within the assessment periods (prior to favoring constant flowers); the proportion of visits falling below the mean expected reward during the assessment period or its inverse (the proportion visited with at least the equivalent of the mean) may be a cue used for risk aversion; risk aversion persisted through long foraging bouts despite changed nectar distributions suggesting that the bananaquits did not track resource distributions well within foraging bouts.

Foraging juncos: interaction of reward mean and variability

Recent stochastic theories of feeding strategy propose that a risk-averse forager will trade off increases in reward variability against increases in average reward. We show that two models of risk-aversion (variance discounting and the z-score model) imply different forms for this interaction of mean and variability. Variance discounting suggests constant risk-aversion, since the effect of reward variance on expected fitness is assumed to be independent of the mean. The z-score model suggests decreasing risk-aversion, since the effect of a given level of reward variance on expected fitness is assumed to decrease as the mean increases. We report two series of experiments with dark-eyed juncos ( Junco hyemalis). Each series investigated the mean-variability trade-off under physiological conditions promoting risk-aversion; reward sizes were generally greater in the second series. The results clearly indicate a trade-off, but within a series the data do not discriminate between the two models' predictions. Comparing the two series suggests that the juncos' level of aversion to reward variability decreases after an overall increment in environmental profitability.

Sex Discrimination and Rewards in a Public Comprehensive University

Baldridge, Cutis, Ecker, and Riley (1978) posit that differences in academic rewards for men and women faculty are largely due to differences in the type of employing institution, with males being employed in more prestigious institutions than females. To examine their hypothesis that sex differences do not exist in a single type of institution, we construct four regression models, one each for the rewards of type of appointment, tenure, rank, and salary. Twenty-three background characteristics including sex, work activities, and productivity variables are used as predictors. Reward variables which theoretically precede in time the reward being analyzed are also included as predictors of that reward. Data were collected from personnel files, institutional records, interviews with administrators, and faculty questionnaires. The analyses produced four strong but heterogeneous models of faculty rewards. Thus, there is no single academic reward structure; rather, four different reward structures exist. The heterogeneity of variables within the models demonstrates the need to develop multi-level, multi-trait models of rewards drawing from social, psychological, group, and organizational characteristics. Of the four rewards, only salary differs by sex; thus, our findings partially support Baldridge and associates' hypothesis. Males are paid significantly more than their female counterparts. Male and female salary models differ, with males being more likely to receive rewards for achieved characteristics than females.

White-crowned sparrows (Zonotrichia leucophrys): foraging preferences in a risky environment

White-crowned sparrows were presented with a series of two-choice experiments. Mean rewards were the same in each experiment, but the standard deviations differed. When fed at a rate faster than that minimally required to meet daily costs, the birds most often preferred the reward with the lower standard deviation. However, when the same birds could expect an energy deficiency, they most often preferred the greater standard deviation. For each sparrow and each mean reward level, I attempted to construct a preference ranking based on experimental pairwise comparisons of all elements of a set of reward probability distributions. The birds usually mostpreferred the minimal or maximal standard deviation, depending on whether they avoided or favored reward variability. However, in a few cases either an intermediate standard deviation was most-preferred, or a bird exhibited inconsistency in its preferences.

Effects of Reward on Creativity in College Students of Two Levels of Ability

This study investigated the effects of reward on the creativity of 80 college students. Subjects at two levels of cognitive ability were assigned to either a rewarded or nonrewarded condition for group administration of two subtests of the Torrance Tests of Creative Thinking (Figural Form B). Differences were obtained as a function of reward, task, and subject variables. On the Picture Completion task, the nonrewarded group performed better than the rewarded group, especially on the flexibility measure. On the Circles task, reward led to a decrement in performance for students of high ability but facilitated the performance of students low in ability. The findings suggest that tangible incentives may have a detrimental effect on creativity in certain contexts.

A Causal Analysis of Environment-Reward-Satisfaction Linkages for the Sales Representative

A causal model that postulated linkages of organizational environmental variables, reward variables, and satisfaction for sales representatives was investigated. Findings indicated that the usual assumptions concerning an organization's inability to contribution to intrinsic rewards may not hold.

Multivariate Analyses of Factors Affecting Work Role Centrality of Occupational Categories

This paper presents a theory concerning work-role centrality and its relationship with a number of variables related to the individual's background, orientation, role strains, job rewards, and career characteristics. It is examined empiricallyfor seven occupational categories in Israel. Occupations are found to vary in their work-role centrality and in the variables hypothesized to relate to it, and the general validity of our model is supported by the results. Stepwise multiple regressions of the independent variables upon work-role centrality explained between 30 and 70% of the variance within the occupational categories. Job reward variables, especially intrinsic rewards, have strongest explanatory weight, but in each occupational category a somewhat different configuration of independent variables emerges.

Wage Differentials in São Paulo's Labor Force

SummaryTo explain the variation in the salaries of specialized workers in São Paulo's industries of transformation, we have used a model made up of five variables: the person's occupational preparation, the influence he may exert within the company because of his occupation, his age, his seniority in the company, and his time on the job.The data obtained for the total sample show clearly that the status of the worker within the company (occupational influence) as well as his occupational preparation and age, are powerful partial determinants of salary levels in São Paulo. On the whole, training is the most powerful of these variables because it has a strong direct effect on wages and because it has an indirect effect on wages through its impact on occupational influence level. Variables indicating experience in the company (seniority) and in the present job are almost negligible. The results suggest the presence of a modern industrial structure where one's technical preparation and position in the company are closely related and where these factors weigh far more heavily than experience on the job and in the company.Except for age, the viable variables used here are special cases of major status dimension: wealth (wages); power (occupational influence); informational status (occupatibnal preparation or education). Occupational prestige was also investigated and, in a stepwise regression, was found useless as a determinant of wages. In this research we explore, possibly for the first time, the use of a power variable, occupational influence, as a determinant of a reward variable, hourly wages. Though theoretically promising, power has previously been remarkably resistant to empirical analysis. Although our use of occupational influence has been successful, the introduction of new variables is always risky. We hope that others will conduct studies leading either to refinements in the use of this and similar indicators or to their rejection.Also, recent publications report only a small effect of most known variables on individual income differentials in the United States. Perhaps adding occupational influence might help. It is worth repeating that in the present data‐set, this variable alone explains just about as much variance in hourly wages (23 per cent) as a set of 13 repressors does on job income (27 per cent) in data analyzed by Spaeth. The whole set of five variables is, of course, more effective here, with 36 per cent of the variance explained. These differences may be due to many factors. It would seem that education may be more influential in Brazil—or at least in this sample —than in the United States. Clearly, educated personnel are in shorter supply than in the United States, and the relative rewards may be greater. If this is true, the rewards for education should decrease as Brazil's education system improves.In any case, by its clear elimination of job experience and seniority, and its strong support for occupational training, occupational influence level, and age, we hope the present work may add to the growing body of evidence regarding the determinants of wage differentials, especially in Brazil and perhaps in other dynamic third world sectors.

The relationship between training methods and reward variables in brightness discrimination learning.

The relationship between training methods and reward variables in brightness discrimination learning.