Regret is a negative emotion with a powerful social and reputational component, and is central to how humans learn from experience and to the human psychology of risk aversion.
Conscious anticipation of regret creates a feedback loop that transcends regret from the emotional realm—often modeled as mere human behavior—into the realm of the rational choice behavior that is modeled in decision theory.
Regret theory is a model in theoretical economics simultaneously developed in 1982 by Graham Loomes and Robert Sugden,[1] David E. Bell,[2] and Peter C.
This regret term is usually an increasing, continuous and non-negative function subtracted to the traditional utility index.
These type of preferences always violate transitivity in the traditional sense,[5] although most satisfy a weaker version.
[6] This form of regret inherits most of desired features, such as holding right preferences in face of first order stochastic dominance, risk averseness for logarithmic utilities and the ability to explain Allais paradox.
To better preface, regret aversion can be seen through fear by either commission or omission; the prospect of committing to a failure or omitting an opportunity that we seek to avoid.
[7] Regret, feeling sadness or disappointment over something that has happened, can be rationalized for a certain decision, but can guide preferences and can lead people astray.
Several experiments over both incentivized and hypothetical choices attest to the magnitude of this effect.
Experiments in first price auctions show that by manipulating the feedback the participants expect to receive, significant differences in the average bids are observed.
This in turn allows for the possibility of regret and if bidders correctly anticipate this, they would tend to bid higher than in the case where no feedback on the winning bid is provided in order to decrease the possibility of regret.
In decisions over lotteries, experiments also provide supporting evidence of anticipated regret.
For example, when faced with a choice between $40 with certainty and a coin toss that pays $100 if the outcome is guessed correctly and $0 otherwise, not only does the certain payment alternative minimizes the risk but also the possibility of regret, since typically the coin will not be tossed (and thus the uncertainty not resolved) while if the coin toss is chosen, the outcome that pays $0 will induce regret.
Anticipated regret tends to be overestimated for both choices and actions over which people perceive themselves to be responsible.
[12][13] People are particularly likely to overestimate the regret they will feel when missing a desired outcome by a narrow margin.
In one study, commuters predicted they would experience greater regret if they missed a train by 1 minute more than missing a train by 5 minutes, for example, but commuters who actually missed their train by 1 or 5 minutes experienced (equal and) lower amounts of regret.
[12] Besides the traditional setting of choices over lotteries, regret aversion has been proposed as an explanation for the typically observed overbidding in first price auctions,[14] and the disposition effect,[15] among others.
This differs from the standard minimax approach in that it uses differences or ratios between outcomes, and thus requires interval or ratio measurements, as well as ordinal measurements (ranking), as in standard minimax.
Suppose an investor has to choose between investing in stocks, bonds or the money market, and the total return depends on what happens to interest rates.
However, if interest rates fell then the regret associated with this choice would be large.
A mixed portfolio of about 11.1% in stocks and 88.9% in the money market would have ensured a return of at least 2.22; but, if interest rates fell, there would be a regret of about 9.78.
In this example, the problem is to construct a linear estimator of a finite-dimensional parameter vector
The regret is defined to be the difference between the MSE of the linear estimator that doesn't know the parameter
Instead, the concept of regret can be used in order to define a linear estimator with good MSE performance.
and the derivative is equated to 0 getting Then, using the Matrix Inversion Lemma Substituting this
Although this problem appears difficult, it is an instance of convex optimization and in particular a numerical solution can be efficiently calculated.
[18][19] Camara, Hartline and Johnsen[20] study principal-agent problems.
The Principal commits to a policy, then the agent responds, and then the state of nature is revealed.
Based on this assumption, they develop mechanisms that minimize the principal's regret.
Collina, Roth and Shao[21] improve their mechanism both in running-time and in the bounds for regret (as a function of the number of distinct states of nature).