Abstract
This paper shows the interaction between probabilistic and delayed rewards. In decision- making processes, the Expected Utility (EU) model has been employed to assess risky choices whereas the Discounted Utility (DU) model has been applied to intertemporal choices. Despite both models being different, they are based on the same theoretical principle: the rewards are assessed by taking into account the sum of their utilities and some similar anomalies have been revealed in both models. The aim of this paper is to characterize and consider particular cases of the Time Trade-Off (PPT) model and show that they correspond to the EU and DU models. Additionally, we will try to build a PTT model starting from a discounted and an expected utility model able to overcome the limitations pointed out by Baucells and Heukamp.
Highlights
The main objective of this paper is to present the Probability and Time Trade-Off Model [1] as an accurate framework where risk and intertemporal decisions can be separately considered
The possibility of reversing the process is provided, i.e., obtaining a Probability and Time Trade-Off (PTT) model starting from an Expected Utility (EU) and a Discounted Utility (DU) model
This paper has dealt with the classical problem of the possible relationship between the DU and the EU models but treated from the joint perspective of the PTT model
Summary
The main objective of this paper is to present the Probability and Time Trade-Off Model [1] as an accurate framework where risk and intertemporal decisions can be separately considered.The methodology used in this paper consists of considering some particular cases of the PTT model and show that they correspond to EU and DU models. Due to the fact that most real-world decisions are made on alternatives which are both uncertain and delayed [4], there is a growing interest in understanding and modelling how risk and delay interact in the individual behavior. A discount function in the context of the PTT model is a continuous real-valued map V ( x, p, t), defined on M, which is strictly increasing with respect to the first and second components, and strictly decreasing according to the third. It satisfies that V ( x, 1, 0) = x, for every x ∈ X.
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