Advanced Utility Theory extends the basic principles of utility theory, which is a cornerstone of microeconomic theory, to more complex scenarios involving risk, uncertainty, and multi-dimensional preferences. It provides a framework for understanding how individuals make choices under conditions where outcomes are not certain and involves advanced concepts beyond the standard utility maximization.
1. Foundations of Utility Theory
Utility theory, in its basic form, assumes that individuals make choices to maximize their satisfaction or “utility” from a set of available alternatives. Utility functions represent preferences over a set of goods or outcomes, with the idea that individuals choose the option that provides the highest utility.
2. Expected Utility Theory
Expected Utility Theory (EUT) is an extension that deals with decision-making under uncertainty. It suggests that when faced with risky choices, individuals evaluate options based on the expected utility, which is the weighted average of the utilities of all possible outcomes, with weights corresponding to their probabilities.
The expected utility E[U]E[U] of a decision dd with outcomes x1,x2,…,xnx_1, x_2, ldots, x_n and their respective probabilities p1,p2,…,pnp_1, p_2, ldots, p_n is given by:
E[U(d)]=∑i=1npiU(xi)E[U(d)] = sum_{i=1}^n p_i U(x_i)
where:
- U(xi)U(x_i) is the utility of outcome xix_i.
- pip_i is the probability of outcome xix_i.
3. Von Neumann-Morgenstern Utility Theory
Von Neumann-Morgenstern Utility Theory is a specific formulation of expected utility theory that provides axioms for rational decision-making under risk. It establishes that preferences over risky prospects can be represented by a utility function if they satisfy certain axioms such as completeness, transitivity, independence, and continuity. This framework allows for the comparison of risky choices and the derivation of utility functions that reflect individual risk preferences.
4. Prospect Theory
Prospect Theory, developed by Daniel Kahneman and Amos Tversky, addresses some of the anomalies observed in traditional utility theory. It introduces concepts such as:
- Value Function: This function captures the perceived value of gains and losses rather than final wealth levels. It is typically concave for gains and convex for losses, reflecting diminishing sensitivity.
- Loss Aversion: Individuals experience losses more intensely than gains of the same magnitude.
- Probability Weighting: People tend to overestimate the likelihood of rare events and underestimate the likelihood of common events.