The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also (...) from “residual” consumption in the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one). (shrink)

Intertemporal choice involves deciding between smaller, sooner and larger, later rewards. People tend to prefer smaller rewards that are available earlier to larger rewards available later, a phenomenon referred to as temporal or delay discounting. Despite its ubiquity in human and non-human animals, temporal discounting is subject to considerable individual differences. Here, we provide a critical narrative review of this literature and make suggestions for future work. We conclude that temporal discounting is associated with key socio-economic and health-related (...) variables. Regarding personality, large-scale studies have found steeper temporal discounting to be associated with higher levels of self-reported impulsivity and extraversion; however, effect sizes are small. Temporal discounting correlates negatively with future-oriented cognitive styles and inhibitory control, again with small effect sizes. There are consistent associations between steeper temporal discounting and lower intelligence, with effect sizes exceeding those of personality or cognitive variables, although socio-demographic moderator variables may play a role. Neuroimaging evidence of brain structural and functional correlates is not yet consistent, neither with regard to areas nor directions of effects. Finally, following early candidate gene studies, recent Genome Wide Association Study (GWAS) approaches have revealed the molecular genetic architecture of temporal discounting to be more complex than initially thought. Overall, the study of individual differences in temporal discounting is a maturing field that has produced some replicable findings. Effect sizes are small-to-medium, necessitating future hypothesis-driven work that prioritizes large samples with adequate power calculations. More research is also needed regarding the neural origins of individual differences in temporal discounting as well as the mediating neural mechanisms of associations of temporal discounting with personality and cognitive variables. (shrink)

This paper reports the results of a series of experiments examining intertemporal choice. The paper makes three contributions: First, it presents a new analytic device, the intertemporal choice triangle, which is analogous to the Marschak--Machina choice triangle used in the analysis of choice under risk. Second, we have developed a new experimental design based on the intertemporal choice triangle which allows subjects greater flexibility in making choices, and which allows the researcher to (...) make more subtle inferences, than are possible with designs previously employed. Subjects are able to create their most-preferred outcome in each choice situation by choosing a constrained linear combination of two extreme options. Third, our results show that while subjects do not typically maximize present value, they are significantly influenced break by present value considerations. We refer to this finding as it present value-seeking behavior. We find only weak evidence of several previously documented intertemporal choice anomalies in our framework. (shrink)

According to Chen's Linguistic Savings Hypothesis, our native language affects our economic behavior. We present three studies investigating how cross-linguistic differences in the grammaticalization of future-time reference affect intertemporal choices. In a series of decision scenarios about finance and health issues, we let speakers of altogether five languages that represent FTR with increasing strength, that is, Chinese, German, Danish, Spanish, and English, choose between hypothetical sooner-smaller and later-larger reward options. While the LSH predicts a present-bias that increases with FTR-strength, (...) our decision makers preferred later-larger options and this future-bias increased with FTR-strength. In multiple regressions, the FTR-strength effect persisted when controlled for socioeconomic and cultural differences. We discuss why our findings deviate from the LSH and ask in how far the FTR-strength effect represents a habitual constitution of linguistic relativity or an instance of online decision framing. (shrink)

Models of intertemporal choice draw on three evaluation rules, which we compare in the restricted domain of choices between smaller sooner and larger later monetary outcomes. The hyperbolic discounting model proposes an alternative-based rule, in which options are evaluated separately. The interval discounting model proposes a hybrid rule, in which the outcomes are evaluated separately, but the delays to those outcomes are evaluated in comparison with one another. The tradeoff model proposes an attribute-based rule, in which both outcomes (...) and delays are evaluated in comparison with one another: People consider both the intervals between the outcomes and the compensations received or paid over those intervals. We compare highly general parametric functional forms of these models by means of a Bayesian analysis, a method of analysis not previously used in intertemporal choice. We find that the hyperbolic discounting model is outperformed by the interval discounting model, which, in turn, is outperformed by the tradeoff model. Our cognitive modeling is among the first to offer quantitative evidence against the conventional view that people make intertemporal choices by discounting the value of future outcomes, and in favor of the view that they directly compare options along the time and outcome attributes. (shrink)

Intertemporal choice requires one to decide between smaller sooner and larger later payoffs and is captured by discount rates. Across two preregistered experiments testing three language pairs (Polish vs. English, Spanish, and German; Experiment 1) and with incentivized participants (Experiment 2), we found no evidence that using a foreign language decreased the strength or increased the consistency of intertemporal choices. On the contrary, there was some evidence of stronger discounting when a foreign language was used. We confirmed (...) prior findings that more reflective individuals discount less strongly but observed that they were just as (un)affected by using foreign language as less reflective individuals. Thus, we provide preliminary evidence that the foreign language effect is robust to individual differences in cognitive reflection. (shrink)

Intertemporal choice requires one to decide between smaller sooner and larger later payoffs and is captured by discount rates. Across two preregistered experiments testing three language pairs (Polish vs. English, Spanish, and German; Experiment 1) and with incentivized participants (Experiment 2), we found no evidence that using a foreign language decreased the strength or increased the consistency of intertemporal choices. On the contrary, there was some evidence of stronger discounting when a foreign language was used. We confirmed (...) prior findings that more reflective individuals discount less strongly but observed that they were just as (un)affected by using foreign language as less reflective individuals. Thus, we provide preliminary evidence that the foreign language effect is robust to individual differences in cognitive reflection. (shrink)

The life-cycle theory of saving behavior (Modigliani, 1988) suggests that humans strive towards an equal intertemporal distribution of wealth. However, behavioral life-cycle theory (Shefrin & Thaler, 1988) proposes that people use self-control heuristics to postpone wealth until later in life. According to this theory, people use a system of cognitive budgeting known as mental accounting. In the present study it was found that mental accounts were used differently depending on if the income change was positive or negative. This was (...) shown both in a representative nationwide sample of households and in a student sample. Respondents were more willing to cut down on their propensity to consume when faced with an income decrease than to raise it when the income increased. Furthermore, contrary to the predictions of behavioral life-cycle theory, it was found that the respondents adjusted their propensity to consume the most when the income increases or decreases took place immediately. Hence, it is suggested that theories of intertemporal choice (e.g., Loewenstein, 1988; Loewenstein & Prelec, 1992) provide a better account of the data than does the behavioral lifecycle theory. (shrink)

An interesting phenomenon called “hidden opportunity cost of time effect” was detected in intertemporal choices. The majority of our participants preferred the smaller but sooner (SS) option to the larger but later (LL) option if opportunity cost was explicit. However, a higher proportion of participants preferred the LL to SS option if opportunity cost was hidden. This shift violates the invariance principle and opens a new way to encourage future-oriented behavior. By simply mentioning the ‘obvious’ opportunity cost of alternatives, (...) decision makers can be more informed in prioritizing their long-term goals rather than short-term goals. (shrink)

The ability to delay rewards is one of the most useful qualities one may wish to develop. People who possess this quality achieve more successful careers, display better interpersonal skills and are less vulnerable to psychopathology, obesity or addictions. In the present online studies, we investigated the extent to which delay-of-reward behaviors in female participants can be improved by observing others mastering it. We developed an intertemporal choice (IC) paradigm in which participants had to make fictitious choices between (...) sooner smaller rewards and later bigger ones (e.g. $150 in one week vs $170 in 4 weeks). In Study 1 (N = 186), we found that participants who delayed more had higher socioeconomic statuses and were less likely to procrastinate, smoke or develop obesity. In Study 2 (N = 178), we exposed female participants to a role model who, faced with intertemporal choices, chose most of the time the delayed option. Results showed that, although participants were only asked to memorize the model’s decisions, they tended to choose the delayed option more often after than before exposure to the model. In Study 3 (N = 148), we found that the direction of the influence depended on the model’s behavior: Our female participants delayed more after having seen a high delay than a low delay model. In Study 4 (N = 370), we confirmed the effect of modeling on intertemporal choices in comparison to a control condition and showed that this effect was still significant three months after exposure to the model. Altogether, these results speak in favor of a high efficacy of modeling to develop self-control in women. (shrink)

Despite various studies examining intertemporal choice with hypothetical rewards due to problematic real reward delivery, there remains no substantial evidence on the effect of the incentives on the decision confidence and cognitive process in intertemporal choice and no comprehensive exploration on the loss domain. Hence, this study conducts an eye-tracking experiment to examine the effect of incentive approach and measure participants' decision confidence using a between-subject design in both gain and loss domains. Results replicated previous findings (...) which show incentives do not affect intertemporal choice in the gain domain. In contrast, in the loss domain, participants in the incentivized group were more likely to choose the larger-later options than those in the non-incentivized group. Furthermore, the decision confidence and the mean fixation duration differed between the incentivized and non-incentivized groups in both gain and loss domains. These findings allow for a better understanding of the effect of incentives on intertemporal choice and provide valuable information for the design of incentives in future intertemporal experiments. (shrink)

The purpose of this study is to explore the influence of consumers’ choice deferral behavior on their intertemporal choice preference. The empirical study shows that consumers’ choice deferral behavior can significantly affect their intertemporal decision preference through the level of hopefulness. Compared with non-choice deferral behavior, choice deferral behavior can improve the level of consumers’ sense of hopefulness, which then makes them prefer larger-longer interests in intertemporal decision-making. The effect of consumers’ sense (...) of hopefulness on their intertemporal choice preference is moderated by their perceived information integrity. When the perceived information integrity is low, the effect of hopefulness on intertemporal decision preference will be enhanced, but when the perceived information integrity is high, the effect of hopefulness on intertemporal decision preference will not be affected. In addition, the theoretical and practical significance of this study and the prospect of future research are also discussed. (shrink)

Two experiments with undergraduates as subjects were carried out with the aim of replicating and extending previous results showing that the implication of the behavioral life-cycle hypothesis (H. M. Shefrin & R. H. Thaler, 1988) that people classify assets in different mental accounts (current income, current assets, and future income) may explain how consumption choices are influenced by temporary income changes. In both experiments subjects made fictitious choices between paying for a good in cash or according to a more expensive (...) installment plan after they had received an income which was either less, the same, or larger than usual. In Experiment 1 subjects were supposed to have savings so that the total assets were equal, whereas in Experiment 2 the total assets varied. The results of both experiments supported the role of mental accounts in demonstrating that subjects were unwilling to pay in cash after an income decrease even though they had access to saved money. Thus, in effect they chose to pay more for the good than they had to. Indicating a need for further refinement of the concept of mental account, choices to pay in cash after an income decrease tended to be more frequent when the consumption and savings motives were compatible than when they were incompatible. Furthermore, increasing the total assets made subjects more willing to pay in cash after an income decrease. (shrink)

People make different choices depending on which decision is the default option. In intertemporal choices, the default option is typically imposed externally. For example, people expect more for delaying the gain than are willing to pay for accelerating the future gain over the same period. We claim that apart from the external default, people’s choices are also influenced by the internal default such as the time perspective resulting in the reference point in the present. By manipulating the congruency between (...) the internal and external defaults, we show that incongruence between defaults decreases the strength of discounting of gains, but not of losses. (shrink)

Introduction George Loewenstein, Daniel Read, and Roy F. Baumeister P _L sychology and economics have a classic love-hate relationship. ...

People often feel that a period of time becomes longer when it is described in more detail or cut into more segments, which is known as the time unpacking effect. The current study aims to unveil how time unpacking manipulation impacts intertemporal decision making and whether the gain-loss valence of choices moderates such impacts. We recruited 87 college students and randomly assigned them to the experimental conditions to complete a series of intertemporal choice tasks. The subjective values (...) of the delayed choices were calculated for each participant and then analyzed. The results showed that participants perceived longer time delays and higher subjective values on the delayed gains in the time unpacking conditions than in the time packing conditions. These results suggest that time unpacking manipulation not only impacts time perception but also other factors, which in turn, influence the valuation of delayed outcomes and thereby intertemporal choices. The results are discussed in comparison to previous studies to highlight the complexity of the mechanism underlying the effect of time unpacking on intertemporal decision making. (shrink)

Intertemporal choice is the study of how people make choices about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in time. Most choices require decision-makers to trade off costs and benefits at different points in time. These decisions may be about savings, work effort, (...) education, nutrition, exercise, health care and so forth. Since early in the twentieth century, economists have analyzed intertemporal decisions using the discounted utility model, which assumes that people evaluate the pleasures and pains resulting from a decision in much the same way that financial markets evaluate losses and gains, exponentially 'discounting' the value of outcomes according to how delayed they are in time. Discounted utility has been used to describe how people actually make intertemporal choices and it has been used as a tool for public policy. Policy decisions about how much to spend on research and development, health and education all depend on the discount rate used to analyze the decision. (shrink)

Lewis ascribes the stubborn persistence of addictions to habit, itself a normal process that does not imply lack of responsiveness to motivation. However, he suggests that more dynamic processes may be involved, for instance that “our recurrently focused brains inevitably self-organize.” Given hyperbolic delay discounting, a reward-seeking internal marketplace model describes two processes, also normal in themselves, that may give rise to the “deep attachment” to addictive activities that he describes: People learn to interpret current choices as test cases for (...) how they can expect to choose in the future, thus recruiting additional incentive against a universal tendency to temporarily prefer smaller, sooner to larger, later rewards. However, when this incentive is not enough, the same interpretation creates incentive to abandon the failed area, leading to the abstinence violation effect and a localized weak will. Normal human value does not come entirely, or even mainly, from expectation of external rewards, but is generated endogenously in imagination. Hyperbolic discounting provides an account of how we learn to cultivate the hedonic importance of occasions for endogenous reward by building appetite. In this account, expectations of the far future have to be rewarded endogenously if they are be as important as currently rewarded alternatives; and this importance is prone to collapse. Both will and hedonic importance are recursive and thus hard to study by controlled experiment, but do represent modelable, reward-based hypotheses about the dynamic nature of habit. (shrink)

To the extent that acting fairly is in an individual's long-term interest, short-term impulses to cheat present a self-control problem. The only effective solution is to interpret the problem as a variant of repeated prisoner's dilemma, with each choice as a test case predicting future choices. Moral choice appears to be the product of a contract because it comes from self-enforcing intertemporal cooperation.

This paper proposes a novel account of why intertemporal decisions tend to display impatience: People pay more attention to the opportunity costs of choosing larger, later rewards than to the opportunity costs of choosing smaller, sooner ones. Eight studies show that when the opportunity costs of choosing smaller, sooner rewards are subtly highlighted, people become more patient, whereas highlighting the opportunity costs of choosing larger, later rewards has no effect. This pattern is robust to variations in the choice (...) task, to the participant population, and is observed for both incentivized and hypothetical choices. We argue that people are naturally aware of the opportunity costs associated with delayed rewards, but pay less attention to those associated with taking smaller, sooner ones. We conclude by discussing implications for theory and policy. (shrink)

We agree with Ainslie's general approach to intertemporal choices and self-control. However, we argue that a concept of “will” is superfluous in explaining tradeoffs between SS (smaller and sooner) and LL (larger and later) rewards in a framework of temporal goal setting and goal aggregation. We provide an alternative framework of reference point-dependent tradeoffs between SS and LL options.

We report results of an experiment testing for present-value maximization in intertemporal income choice. Two-thirds of subjects did not maximize present value. Through a series of experimental manipulations that impose costs on non-present value maximizers, we are able to reduce the level of violations substantially. We find, however, that a sizeable proportion of subjects continue to systematically violate present-value principles. Our interpretation is that these subjects either cannot or choose not to distinguish between t income and t expenditure (...) in making their choices. Self-management, bounded rationality, and sequence preference are suggested as possible explanations for such behavior. (shrink)

Intentional change when viewed as making a risky or intertemporal choice with evolutionary relevance helps us understand its successes and its failures. To promote future-oriented ecological rationality requires establishing a linkage between nongenetic, cultural, and symbolic selections and genetic adaptations. Coupled with biophilic instinct, intentional conservation is more likely to prevail against evolved desires of environmental exploitation.

Psychologists have a long tradition of studying human behavior, strengths and weaknesses, biases and limitations. Economists have constructed normative frameworks that capture the most important elements of human decision-making and developed powerful tools to determine individual and strategic choices in a variety of situations. Only recently have their strengths been combined and economic models enriched with key ingredients found in psychological studies.This volume covers four of the most important themes in this interdisciplinary field: feelings, inconsistencies, limitations and biases. Each chapter (...) contributes to a more comprehensive and accurate modelling and description of human behavior. Its four parts cover: the origins, formation, and evolution of beliefs; consistency, commitment, and intertemporal separability of dynamic choices; attention, preference formation, and risk evaluation in limited cognition; and affective behaviour, specifically the role of emotions in decision making. (shrink)

Psychologists have a long tradition of studying human behavior, strengths and weaknesses, biases and limitations. Economists have constructed normative frameworks that capture the most important elements of human decision-making and developed powerful tools to determine individual and strategic choices in a variety of situations. Only recently have their strengths been combined and economic models enriched with key ingredients found in psychological studies.This volume covers four of the most important themes in this interdisciplinary field: feelings, inconsistencies, limitations and biases. Each chapter (...) contributes to a more comprehensive and accurate modelling and description of human behavior. Its four parts cover: the origins, formation, and evolution of beliefs; consistency, commitment, and intertemporal separability of dynamic choices; attention, preference formation, and risk evaluation in limited cognition; and affective behaviour, specifically the role of emotions in decision making. (shrink)

Despite Fisher's (1930) psychological intuitions of and the formal treatment given by Yaari (1965, Review of Economic Studies 32, 137), the intertemporal model of choice is mainly a model with certain lifetime. The purpose of this paper is to reconsider this assumption, starting from a very simple two-period model of choice with lifetime uncertainty. We examine the comparative statics of the model at the first two orders and replace the concept of `pure time preference' by taking into (...) account the subjective treatment of the probability of survival. (shrink)

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group R\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

When faced with intertemporal choices, which have consequences that unfold over time, we often discount the future, preferring smaller immediate rewards often at the expense of long-term benefits. How psychologically connected one feels to one’s future self-influences such temporal discounting. Psychological connectedness consists in sharing psychological properties with past or future selves, but connectedness comes in degrees. If one feels that one is not psychologically connected to one’s future self, one views that self like a different person and is (...) less likely to wait for the future reward. Increasing perceived psychological connectedness to one’s future self may lead to more far-sighted decisions. Episodic prospection may help in this regard. Episodic prospection is our ability to ‘pre-experience’ the future by mentally simulating it, drawing on information from episodic memory and other sources. Episodic memory and prospection are thought to involve a special form of consciousness, which underpins the capacity to appreciate the connection between one’s past, present, and future selves. Simulating the future self through prospection may increase felt psychological connectedness and support future-oriented decision-making. Yet this is where a puzzle arises. The imagery of episodic memory and prospection is perspectival: often one views the visualised scenario from a detached perspective, seeing oneself from-the-outside as if viewing another person. The aim of this paper is to characterise how the perspectival imagery of prospection relates to psychological connectedness, and to show that even though such imagery involves a detached perspective it can still be used to help reward one’s future self. (shrink)

Recent evidence on intertemporal choice suggests that decision-makers may exhibit both increasing and decreasing impatience simultaneously, called inverse-S discounting. This paper introduces trichotomic discounted utility to model inverse-S discounting. Under trichotomic discounted utility the decision-maker distinguishes between short-term delays, medium-term delays, and long-term delays. Exponential discounting holds within each category, but not necessarily across each category. We provide preference foundations for trichotomic discounted utility in the timed outcomes framework and in the consumption streams framework. The key axiom is (...) a weakening of the time consistency axiom that allows for both increasing and decreasing impatience. We also consider a weak, local version of time consistency, and show that this plausible condition is satisfied only by discount functions with exponential “pieces”. (shrink)