Discounted and Expected Utility from the Probability and Time Trade-Off Model

Abstract

This paper shows the interaction between probabilistic and delayed rewards. In decisionmaking 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.On the other hand, the decision-making under uncertainty involves alternatives whose rewards differ in relation to the probability of being received (the choice between "a smaller reward, to be received with greater probability, and a larger one, but less likely") [3].Both kinds of decisions have been traditionally analyzed by using two main systems of calculation: the Discounted Utility model and the Expected Utility theory which describe the present value of delayed rewards and the actuarial value of risky rewards, respectively. Both models are simple, widely accepted, and with a similar structure, since they use the same theoretical principle: the rewards are assessed by the sum of their utilities [6,7]. In the decision-making process, individuals choose the alternative which maximizes their current utility value (denoted by U 0 ).As seen in Table 1, DU and EU are the basic models employed in the decision-making process which represent the rational choice over time and under risk, respectively.

An economic lens to understanding antimicrobial resistance: disruptive cases to livestock and wastewater management in Australia

“…delayed response to treatment and uncertainty whether the antibiotic will be effective in the future). Antibiotic effectiveness in the mastitis example can be viewed as a utility and potentially assessed using discounting utility model enabling discounting of the future (Rambaud and Pérez 2020). Here, antibiotic effectiveness within each time periods is additively separable, so we can write utility in period t aswhere x and y are the variables that impact antibiotic effectiveness in period t and u is the felicity function.…”