Prospect theory

Prospect theory is a behavioral economic theory that describes the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are known. The theory states that people make decisions based on the potential value of losses and gains rather than the final outcome, and that people evaluate these losses and gains using certain heuristics. The model is descriptive: it tries to model real-life choices, rather than optimal decisions, as normative models do.

The theory was created in 1979 and developed in 1992 by Daniel Kahneman and Amos Tversky as a psychologically more accurate description of decision making, compared to the expected utility theory. In the original formulation, the term prospect referred to a lottery. The paper "Prospect Theory: An Analysis of Decision under Risk" (1979) has been called a "seminal paper in behavioral economics".

The theory describes the decision processes in two stages:

The formula that Kahneman and Tversky assume for the evaluation phase is (in its simplest form) given by:

where ${\displaystyle V}$ is the overall or expected utility of the outcomes to the individual making the decision, ${\displaystyle x_{1},x_{2},\ldots ,x_{n}}$ are the potential outcomes and ${\displaystyle p_{1},p_{2},\dots ,p_{n}}$ their respective probabilities and ${\displaystyle v}$ is a function that assigns a value to an outcome. The value function that passes through the reference point is s-shaped and asymmetrical. Losses hurt more than gains feel good (loss aversion). This differs from expected utility theory, in which a rational agent is indifferent to the reference point. In expected utility theory, the individual does not care how the outcome of losses and gains are framed. The function ${\displaystyle \pi }$ is a probability weighting function and captures the idea that people tend to overreact to small probability events, but underreact to large probabilities. Let ${\displaystyle (x,p;y,q)}$ denote a prospect with outcome ${\displaystyle x}$ with probability ${\displaystyle p}$ and outcome ${\displaystyle y}$ with probability ${\displaystyle q}$ and nothing with probability ${\displaystyle 1-p-q}$. If ${\displaystyle (x,p;y,q)}$ is a regular prospect (i.e., either ${\displaystyle p+q<1}$, or ${\displaystyle x\geq 0\geq y}$, or ${\displaystyle x\leq 0\leq y}$), then:

...
Wikipedia