Abstract
The framework of this paper is intertemporal choice, which traditionally has been studied with preference relations and discount functions. However, the interest of econophysics in this topic makes time become a central magnitude. Therefore, the aim of this paper is to introduce the concept of delay function and, by using this tool, to analyze the concept of impatience and the different types of inconsistency. In behavioral finance, consistency is correlated with the concept of symmetry because, in this case, the indifference between two rewards does not change when the same delay is added to their respective availability dates. Moreover, we have shown the way to derive a discount (respectively, delay) function starting from the expression of its corresponding delay (respectively, discount) function by requiring some suitable conditions for this construction. Finally, we have deduced the concept of instantaneous variation rate and Prelec’s measure of inconsistency in terms of the delay function.
Highlights
Intertemporal choice involves making decisions between several alternatives whose monetary amounts take place at different instants of time
This paper analyzed the concept of impatience and the different types of inconsistency from the point of view of a delay function
It is well known that intertemporal choice can be treated by means of discount functions or, alternatively, with preference relations, but in this paper, we derived the expression of the discount function, underlying the process of intertemporal choice, starting from the concept of delay function
Summary
Intertemporal choice involves making decisions between several alternatives whose monetary amounts take place at different instants of time. The reduction through time of temperature in a system or the decrease of individuals in an organism can be described in the same way as the loss of acquisitive power suffered by a monetary unit (i.e., temporal discounting) In this context, Cajueiro [8] demonstrated that the q-exponential function, present in the deformed algebra inspired in the Tsallis’ nonextensive thermodynamics, could be used to model discount functions in intertemporal choices. Recent studies by Takahashi et al [24] used Tsallis’ statistics-based econophysics to show that the q-exponential discount function may continuously parameterize a subject’s consistency in intertemporal choice This result was generalized by Cruz and Muñoz [25] to any discount function, based on the deformed algebra developed in the Tsallis’ nonextensive thermostatistics.
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