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A prominent theme in behavioural contract theory is the study of present-biased agents represented through quasi-hyperbolic discounting. In a model of competitive credit provision, we study an alternative to this framework in which the…

Theoretical Economics · Economics 2026-02-11 Siddharth Chatterjee , Daniel F. Garrett

People often face trade-offs between costs and benefits occurring at various points in time. The predominant discounting approach is to use the exponential form. Central to this approach is the discount rate, a unique parameter that…

Theoretical Economics · Economics 2024-08-13 Bach Dong-Xuan , Philippe Bich

As the capabilities of artificial agents improve, they are being increasingly deployed to service multiple diverse objectives and stakeholders. However, the composition of these objectives is often performed ad hoc, with no clear…

Machine Learning · Computer Science 2023-10-03 Silviu Pitis

The well-known theorem of Dybvig, Ingersoll and Ross shows that the long zero-coupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the…

General Finance · Quantitative Finance 2015-09-29 Dorje C. Brody , Lane P. Hughston

Present bias, the tendency to overvalue immediate rewards while undervaluing future ones, is a well-known barrier to achieving long-term goals. As artificial intelligence and behavioral economics increasingly focus on this phenomenon, the…

Computer Science and Game Theory · Computer Science 2024-09-18 Yasunori Akagi , Hideaki Kim , Takeshi Kurashima

In economics and psychology, delay discounting is often used to characterize how individuals choose between a smaller immediate reward and a larger delayed reward. People with higher delay discounting rate (DDR) often choose smaller but…

Artificial Intelligence · Computer Science 2017-03-27 Tao Ding , Warren K. Bickel , Shimei Pan

The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting. Exponential discounting has a well-established axiomatic foundation originally developed…

Economics · Quantitative Finance 2017-02-10 Nina Anchugina

A dynamic model of collective consumption and saving decisions made by a finite number of agents with constant but different discount rates is developed. Collective utility is a weighted sum of individual utilities with time-varying utility…

Optimization and Control · Mathematics 2018-07-18 Luis A. Alcala

This paper proposes a new reinforcement learning with hyperbolic discounting. Combining a new temporal difference error with the hyperbolic discounting in recursive manner and reward-punishment framework, a new scheme to learn the optimal…

Machine Learning · Computer Science 2021-06-04 Taisuke Kobayashi

How much should you receive in a week to be indifferent to \$ 100 in six months? Note that the indifference requires a rule to ensure the similarity between early and late payments. Assuming that rational individuals have low accuracy, then…

General Economics · Economics 2020-03-02 José Cláudio do Nascimento

Time-inconsistent preferences, where agents favor smaller-sooner over larger-later rewards, are a key feature of human and animal decision-making. Quasi-Hyperbolic (QH) discounting provides a simple yet powerful model for this behavior, but…

Machine Learning · Computer Science 2025-09-09 S. R. Eshwar

This paper empirically analyzes how individual characteristics are associated with risk aversion, loss aversion, time discounting, and present bias. To this end, we conduct a large-scale demographically representative survey across eight…

General Economics · Economics 2022-05-12 Thomas Meissner , Xavier Gassmann , Corinne Faure , Joachim Schleich

The literature on bandit learning and regret analysis has focused on contexts where the goal is to converge on an optimal action in a manner that limits exploration costs. One shortcoming imposed by this orientation is that it does not…

Machine Learning · Computer Science 2017-05-01 Daniel Russo , David Tse , Benjamin Van Roy

Value [4][5] is typically modeled using a continuous representation (i.e., a Real number). A discrete representation of value has recently been postulated [6]. A quantized representation of probability in the brain was also posited and…

Neurons and Cognition · Quantitative Biology 2020-09-17 James Tee , Desmond P. Taylor

In this paper, we investigate the effects of applying generalised (non-exponential) discounting on a long-run impulse control problem for a Feller-Markov process. We show that the optimal value of the discounted problem is the same as the…

Optimization and Control · Mathematics 2024-04-22 Damian Jelito , Łukasz Stettner

This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…

Optimization and Control · Mathematics 2011-07-25 Ivar Ekeland , Oumar Mbodji , Traian A. Pirvu

Discounting is an important dimension in multi-agent systems as long as we want to reason about strategies and time. It is a key aspect in economics as it captures the intuition that the far-away future is not as important as the near…

Artificial Intelligence · Computer Science 2023-05-25 Munyque Mittelmann , Aniello Murano , Laurent Perrussel

By embedding uncertainty into time, we obtain a conjoint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility that accommodates arbitrary state and outcome spaces. In doing so, we provide a novel and…

Theoretical Economics · Economics 2024-03-25 Lorenzo Bastianello , Vassili Vergopoulos

Empirical research often cites observed choice responses to variation that shifts expected discounted future utilities, but not current utilities, as an intuitive source of information on time preferences. We study the identification of…

Econometrics · Economics 2020-05-28 Jaap H. Abbring , Øystein Daljord

Many popular policy gradient methods for reinforcement learning follow a biased approximation of the policy gradient known as the discounted approximation. While it has been shown that the discounted approximation of the policy gradient is…

Machine Learning · Computer Science 2023-01-10 Chris Nota