Existence of perfect equilibria in a class of multigenerational stochastic games of capital accumulation

In this paper we introduce a model of multigenerational stochastic games of capital accumulation where each generation consists of m different players. The main objective is to prove the existence of a perfect stationary equilibrium in an infinite horizon game. A suitable change in the terminology used in this paper provides (in the case of perfect altruism between generations) a new Nash equilibrium theorem for standard stochastic games with uncountable state space.     

Delay discounting of cocaine by rhesus monkeys.

The present, subjective value of a reinforcer typically decreases as a function of the delay to its receipt, a phenomenon termed delay discounting. Delay discounting, which is assumed to reflect impulsivity, is hypothesized to play an important role in drug abuse. The present study examined delay discounting of cocaine injections by rhesus monkeys. Subjects were studied on a discrete-trials task in which they chose between 2 doses of cocaine: a smaller, immediate dose and a larger, delayed dose. The immediate dose varied between 0.012 and 0.4 mg/kg/injection, whereas the delayed dose was always 0.2 mg/kg/injection and was delivered after a delay that varied between 0 and 300 s in different conditions. At each delay, the point at which a monkey chose the immediate and delayed doses equally often (i.e., the ED50) provided a measure of the present, subjective value of the delayed dose. Dose-response functions for the immediate dose shifted to the left as delay increased. The amount of the immediate dose predicted to be equal in subjective value to the delayed dose decreased as a function of the delay, and hyperbolic discounting functions provided good fits to the data (median R2 = .86). The current approach may provide the basis for an animal model of the effect of delay on the subjective value of drugs of abuse. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Discounting of past outcomes.

Drug use, abuse, and addiction are common behavioral manifestations of impulsiveness. A useful and popular laboratory analogue of impulsiveness is temporal discounting. Temporal discounting refers to the reduction in the present, subjective value of outcomes that are temporally distant in the future. The extensive literature on temporal discounting indicates hyperbolic discounting, the magnitude effect, and the sign effect. It is possible that the same principles may apply to other dimensions of psychological distance, including past temporal distance. The purpose of the present study was to examine the possibility that outcomes in the past are discounted hyperbolically and at a similar rate to outcomes in the future. The magnitude and sign effects were also examined in past discounting. Indifference points of college students were determined from a paper-and-pencil questionnaire of future and past discounting. The results demonstrate that humans discount temporally distant past outcomes similarly to future outcomes. Discounting of the future and past are qualitatively and quantitatively similar; discounting of past outcomes is orderly, hyperbolic, and consistent with most empirical observations from studies of future discounting, including the magnitude and sign effects. The present study indicates that the discounting of past outcomes is a quantifiable phenomenon, and the results are similar to observations from the established future-discounting literature. Past discounting may be of use in the study of drug-dependent and other impulsive populations. Implications of a relationship between future and past discounting are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Moderate drug use and delay discounting: A comparison of heavy, light, and never smokers.

Delay discounting was examined in light smokers (10 or fewer cigarettes per day) and compared with previously published delay discounting data for heavy and never smokers. Participants evaluated several hypothetical outcomes: money gains and loses ($10, $100, and $1,000), health gains and losses (durations of improved and impoverished health subjectively equivalent to $1,000), cigarette gains and losses (amounts subjectively equivalent to $1,000), and potentially real rewards ($10 and $100). Light smokers discounted money significantly more than never smokers, but light smokers did not differ from heavy smokers. The 3 groups did not statistically differ in discounting of health consequences. Similarly, the 2 smoking groups were not found to differ in discounting of cigarettes. Like heavy smokers, light smokers discounted cigarettes significantly more than money and health. Several significant, positive correlations were found between smoking rate and various discounting measures in the heavy smokers but not in the light smokers. Several previous findings were replicated, helping to validate the present results: the sign effect (greater discounting of gains than losses), the magnitude effect (greater discounting of smaller rewards), reliability of discounting measures over time, and the consistency of hypothetical and potentially real rewards. These data suggest that even moderate levels of drug use may be associated with high delay discounting levels. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Dynamic pricing for multiple class deterministic demand fulfillment

We consider how a firm should allocate inventory to multiple customer classes that differ based on the price they pay and their willingness to incur delay in fulfillment of their demand. The problem is set in a deterministic demand, economic-order-quantity-like environment with holding, backorder, lost demand and setup costs. The firm either fulfills demand or offers a price discount to induce the demand to wait for fulfillment from the next reorder. We determine the optimal policy and discuss how changes in various parameters affect profitability, customer service, and operational measures such as order frequency and base stock levels. We compare the results to a policy that only rations inventory without dynamic discounting and to a policy that only provides discounts. Through the comparison, we observe that dynamic pricing can be seen as a combination of a pricing mechanism which determines demand and an allocation mechanism that differentiates between customer classes, serving each ones needs. We show that if lower-value customers are distinguished by accepting reduced service, it is possible that both high and low-value customer classes see better levels of service under the optimal policy than under a discounting only policy. In addition we demonstrate the applicability of the results to a stochastic version of the problem.     

Price discounts for increased profitability under partial backordering

If some, but not all, customers are willing to wait for an out‐of‐stock product to become available, sellers may be able to increase their profits by offering a price discount to increase the number of backordered demands rather than losing those sales. We modify an existing model for the deterministic economic order quantity with partial backordering by making the backordering percentage a function of the size of the discount. We combine results about the optimal solution for a partial backordering model with a fixed backorder percentage and a search procedure to determine whether offering a discount is optimal and, if so, how large the discount should be to maximize profit.     

A behavioral economic analysis of texting while driving: Delay discounting processes

The purpose of the present study was to examine an impulsive decision-making process underlying texting while driving from a behavioral economic perspective. A sample of 108 college students completed a novel discounting task that presented participants with a hypothetical scenario in which, after receiving a text message while driving, they rated the likelihood of replying to a text message immediately versus waiting to reply for a specific period of time. Participants also completed a delay discounting task in which they made repeated hypothetical choices between obtaining a larger amount of money available after a delay and an equal or lesser amount of money available immediately. The results show that the duration of the delay is a critical variable that strongly determines whether participants choose to wait to reply to a text message, and that the decrease in the likelihood of waiting as a function of delay is best described by a hyperbolic delay discounting function. The results also show that participants who self-reported higher frequency of texting while driving discounted the opportunity to reply to a text message at greater rates, whereas there was no relation between the rates of discounting of hypothetical monetary rewards and the frequency of texting while driving. The results support the conclusion that texting while driving is fundamentally an impulsive choice.     

Non-constant discounting and differential games with random time horizon

Previous results on non-constant discounting in continuous time are extended to the field of deterministic differential games with a stochastic terminal time. A dynamic programming equation is derived for problems with general time inconsistent preferences and random duration. Different cooperative and non-cooperative solution concepts for differential games with random duration are analyzed. The results are illustrated by solving the cake-eating problem describing the classical model of management of a nonrenewable resource.     

Pecunia olet: The role of incidental disgust in the ultimatum game.

We address the role of the incidental emotion of disgust in the Ultimatum Game. Participants had to choose whether or not to accept a ? offer from a ?0 pot made by another participant; 120 were in a room where a disgusting smell was released and 120 were in a room with no particular smell. Acceptance rates were higher in the room with the disgusting smell. The effect was mainly carried by the male participants who also reported more disgust with the disgusting smell and judged the offer as less unfair than females. We propose a spontaneous discounting explanation. Acceptance rates were higher in the room with the disgusting smell because participants misattributed the disgust induced by the offer to the ambient disgusting smell. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Personal relative deprivation, delay discounting, and gambling.

Several lines of research have provided evidence for a relation between personal relative deprivation and gambling. Despite this knowledge, little is known about possible psychological mechanisms through which personal relative deprivation exerts its influence on gambling. The authors of this research sought to examine one such mechanism: the desire for immediate rewards. Using complementary approaches to studying psychological mechanisms, they tested in four studies the general hypothesis that personal relative deprivation translates into gambling urges and behavior in part via increased desires for immediate, even if smaller, rewards. Study 1 showed that an experimental manipulation of personal relative deprivation increased participants' preferences for smaller-sooner over larger-later rewards during a delay-discounting task. Studies 2 and 3 showed that a decreased willingness to delay gratification led to increased gambling behavior. Study 4 showed that preferences for smaller-sooner over larger-later rewards statistically mediated the relation between self-reported personal relative deprivation and gambling urges among a community sample of gamblers. The implications and potential applications of these findings are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)