Ambiguity aversion

Last updated

In decision theory and economics, ambiguity aversion (also known as uncertainty aversion) is a preference for known risks over unknown risks. An ambiguity-averse individual would rather choose an alternative where the probability distribution of the outcomes is known over one where the probabilities are unknown. This behavior was first introduced through the Ellsberg paradox (people prefer to bet on the outcome of an urn with 50 red and 50 black balls rather than to bet on one with 100 total balls but for which the number of black or red balls is unknown).

Contents

There are two categories of imperfectly predictable events between which choices must be made: risky and ambiguous events (also known as Knightian uncertainty). Risky events have a known probability distribution over outcomes while in ambiguous events the probability distribution is not known. The reaction is behavioral and still being formalized. Ambiguity aversion can be used to explain incomplete contracts, volatility in stock markets, and selective abstention in elections (Ghirardato & Marinacci, 2001).

The concept is expressed in the English proverb: "Better the devil you know than the devil you don't."

Difference from risk aversion

The distinction between ambiguity aversion and risk aversion is important but subtle. Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative and its expected value. Ambiguity aversion applies to a situation when the probabilities of outcomes are unknown (Epstein 1999) and it is defined through the preference between risky and ambiguous alternatives, after controlling for preferences over risk.

Using the traditional two-urn Ellsberg choice, urn A contains 50 red balls and 50 blue balls while urn B contains 100 total balls (either red or blue) but the number of each is unknown. An individual who prefers a certain payoff strictly smaller than $10 over a bet that pays $20 if the color of a ball drawn from urn A is guessed correctly and $0 otherwise is said to be risk averse but nothing can be said about her preferences over ambiguity. On the other hand, an individual who strictly prefers that same bet if the ball is drawn from urn A over the case where the ball is drawn from urn B is said to be ambiguity averse but not necessarily risk averse.

A real world consequence of increased ambiguity aversion is the increased demand for insurance because the general public are averse to the unknown events that will affect their lives and property (Alary, Treich, and Gollier 2010).

Causes

Unlike risk aversion, which is primarily attributed to decreasing marginal utility, there is no widely accepted main cause for ambiguity aversion. The many possible explanations include different choice mechanisms, behavioral biases and differential treatment of compound lotteries; this in turn explains the lack of a widespread measure of ambiguity aversion.

Maxmin expected utility

In their 1989 paper, Gilboa and Schmeidler [1] propose an axiomatic representation of preferences that rationalizes ambiguity aversion. An individual that behaves according to these axioms would act as if having multiple prior subjective probability distributions over the set of outcomes and chooses the alternative that maximizes the minimum expected utility over these distributions. In the Ellsberg example, if an individual has a set of subjective prior probabilities of a ball drawn from urn B being red ranging between, for example, 0.4 and 0.6, and applies a maxmin choice rule, she will strictly prefer a bet on urn A over a bet on urn B since the expected utility she assigns to urn A (based on an assumed 50% probability of the predicted color) is greater than the one she assigns to urn B (based on the worst-case 40% probability of the predicted color).

Choquet expected utility

David Schmeidler [2] also developed the Choquet expected utility model. Its axiomatization allows for non-additive probabilities and the expected utility of an act is defined using a Choquet integral. This representation also rationalizes ambiguity aversion and has the maxmin expected utility as a particular case.

Compound lotteries

In Halevy (2007) [3] the experimental results show that ambiguity aversion is related to violations of the Reduction of Compound Lotteries axiom (ROCL). This suggests that the effects attributed to ambiguity aversion may be partially explained by an inability to reduce compound lotteries to their corresponding simple lotteries or some behavioral violation of this axiom.

Gender difference

Women are more risk averse than men.[ citation needed ] One potential explanation for gender differences is that risk and ambiguity are related to cognitive and noncognitive traits on which men and women differ. Women initially respond to ambiguity much more favorably than men, but as ambiguity increases, men and women show similar marginal valuations of ambiguity. Psychological traits are strongly associated with risk but not to ambiguity. Adjusting for psychological traits explains why a gender difference exists within risk aversion and why these differences are not a part of ambiguity aversion. Since psychological measures are related to risk but not to ambiguity, risk aversion and ambiguity aversion are distinct traits because they depend on different variables (Borghans, Golsteyn, Heckman, Meijers, 2009.)

A framework that allows for ambiguity preferences

Smooth ambiguity preferences are represented as:

Experiments testing ambiguity in games

Battle of the Sexes Game with Ambiguity
Player 2
Player 1
LeftMiddleRight
Top
0
0
100
300
x
50
Bottom
300
100
0
0
x
55

Kelsey and le Roux (2015) [4] report an experimental test of the influence of ambiguity on behaviour in a Battle of Sexes game which has an added safe strategy, R, available for Player 2 (see Table). The paper studies the behaviour of subjects in the presence of ambiguity and attempts to determine whether subjects playing the Battle of Sexes game prefer to choose an ambiguity safe option.

The value of x, which is the safe option available to Player 2, varies in the range 60-260. For some values of x, the safe strategy (option R) is dominated by a mixed strategy of L and M, and thus would not be played in a Nash equilibrium. For some higher values of x the game is dominance solvable. The effect of ambiguity-aversion is to make R (the ambiguity-safe option) attractive for Player 2. R is never chosen in Nash equilibrium for the parameter values considered. However it may be chosen when there is ambiguity. Moreover, for some values of x, the games are dominance solvable and R is not part of the equilibrium strategy. [5]

During the experiment, the Battle of Sexes games were alternated with decision problems based on the 3-ball Ellsberg urn. In these rounds, subjects were presented with an urn containing 90 balls, of which 30 were Red, and the remainder an unknown proportion of Blue or Yellow, and asked to pick a colour to bet on. The payoff attached to Red was varied in order to obtain an ambiguity threshold. Alternating experiments on urns and games had the dual aim of erasing the short term memory of subjects, and providing an independent measure of subjects' ambiguity-attitudes.

It was found that R is chosen quite frequently by subjects. While the Row Player randomises 50:50 between her strategies, the Column Player shows a marked preference for avoiding ambiguity and choosing his ambiguity-safe strategy. Thus, the results provide evidence that ambiguity influences behaviour in the games.

One surprising feature of the results was that the links between choices in the single person decision and those in the games was not strong. Subjects appeared to perceive a greater level of ambiguity in a two-person coordination game, than a single person decision problem. More generally the results suggested that perceptions of ambiguity and even attitudes to ambiguity depend on context. Hence it may not be possible to measure ambiguity-attitude in one context and use it to predict behaviour in another.

Ambiguity and learning

Given the salience of ambiguity in economic and financial research, it is natural to wonder about its relation with learning and its persistence over time. The long-run persistence of ambiguity clearly depends on the way the inter-temporal ambiguity is modeled. If the decision-maker incorporate new information according to a natural generalization of Bayes' rule entailing a set of priors (rather than a unique prior) on a given prior support; then Massari-Newton (2020) [6] and Massari-Marinacci (2019) [7] show that long-run ambiguity is not a possible outcome of the multiple prior-learning models with convex prior support (i.e., positive Lebegue measure) and provide sufficient conditions for ambiguity to fade away when the prior support is not convex, respectively.

See also

Related Research Articles

<span class="mw-page-title-main">Risk aversion</span> Economics theory

In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome.

<span class="mw-page-title-main">Prospect theory</span> Theory of behavioral economics

Prospect theory is a theory of behavioral economics, judgment and decision making that was developed by Daniel Kahneman and Amos Tversky in 1979. The theory was cited in the decision to award Kahneman the 2002 Nobel Memorial Prize in Economics.

<span class="mw-page-title-main">Decision theory</span> Branch of applied probability theory

Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses the tools of expected utility and probability to model how individuals should behave rationally under uncertainty. It differs from the cognitive and behavioral sciences in that it is prescriptive and concerned with identifying optimal decisions for a rational agent, rather than describing how people really do make decisions. Despite this, the field is important to the study of real human behavior by social scientists, as it lays the foundations for the rational agent models used to mathematically model and analyze individuals in fields such as sociology, economics, criminology, cognitive science, and political science.

The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour.

In decision theory, subjective expected utility is the attractiveness of an economic opportunity as perceived by a decision-maker in the presence of risk. Characterizing the behavior of decision-makers as using subjective expected utility was promoted and axiomatized by L. J. Savage in 1954 following previous work by Ramsey and von Neumann. The theory of subjective expected utility combines two subjective concepts: first, a personal utility function, and second a personal probability distribution.

In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk. The concept acknowledges some fundamental degree of ignorance, a limit to knowledge, and an essential unpredictability of future events.

In decision theory, the Ellsberg paradox is a paradox in which people's decisions are inconsistent with subjective expected utility theory. John Maynard Keynes published a version of the paradox in 1921. Daniel Ellsberg popularized the paradox in his 1961 paper, "Risk, Ambiguity, and the Savage Axioms". It is generally taken to be evidence of ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks.

Howard Raiffa was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and Harvard Kennedy School at Harvard University. He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. He helped found and was the first director of the International Institute for Applied Systems Analysis.

The Allais paradox is a choice problem designed by Maurice Allais to show an inconsistency of actual observed choices with the predictions of expected utility theory. The Allais paradox demonstrates that individuals rarely make rational decisions consistently when required to do so immediately. The independence axiom of expected utility theory, which requires that the preferences of an individual should not change when altering two lotteries by equal proportions, was proven to be violated by the paradox.

The ambiguity effect is a cognitive tendency where decision making is affected by a lack of information, or "ambiguity". The effect implies that people tend to select options for which the probability of a favorable outcome is known, over an option for which the probability of a favorable outcome is unknown. The effect was first described by Daniel Ellsberg in 1961.

<span class="mw-page-title-main">Cumulative prospect theory</span> Behavioral model of risky decision-making

In behavioral economics, cumulative prospect theory (CPT) is a model for descriptive decisions under risk and uncertainty which was introduced by Amos Tversky and Daniel Kahneman in 1992. It is a further development and variant of prospect theory. The difference between this version and the original version of prospect theory is that weighting is applied to the cumulative probability distribution function, as in rank-dependent expected utility theory but not applied to the probabilities of individual outcomes. In 2002, Daniel Kahneman received the Nobel Memorial Prize in Economic Sciences for his contributions to behavioral economics, in particular the development of CPT.

The rank-dependent expected utility model is a generalized expected utility model of choice under uncertainty, designed to explain the behaviour observed in the Allais paradox, as well as for the observation that many people both purchase lottery tickets and insure against losses.

A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical mechanics and potential theory, but found its way into decision theory in the 1980s, where it is used as a way of measuring the expected utility of an uncertain event. It is applied specifically to membership functions and capacities. In imprecise probability theory, the Choquet integral is also used to calculate the lower expectation induced by a 2-monotone lower probability, or the upper expectation induced by a 2-alternating upper probability.

<span class="mw-page-title-main">Risk</span> Possibility of something bad happening

In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value, often focusing on negative, undesirable consequences. Many different definitions have been proposed. One international standard definition of risk is the "effect of uncertainty on objectives".

David Schmeidler was an Israeli mathematician and economic theorist. He was a Professor Emeritus at Tel Aviv University and the Ohio State University.

In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature. The elements of a lottery correspond to the probabilities that each of the states of nature will occur,. Much of the theoretical analysis of choice under uncertainty involves characterizing the available choices in terms of lotteries.

Itzhak Gilboa is an Israeli economist with contributions in decision theory. After obtaining his BA in Mathematics and Economics from Tel Aviv University, he earned his Ph.D. in 1987 under the supervision of David Schmeidler. He currently holds professorship positions at HEC Paris and Reichman University.

Risk aversion is a preference for a sure outcome over a gamble with higher or equal expected value. Conversely, rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking behavior.

Edi Karni is an Israeli born American economist and decision theorist. Karni is the Scott and Barbara Black Professor of Economics at Johns Hopkins University. He is a Fellow of the Econometric Society and an Economic Theory Fellow of the Society for the Advancement of Economic Theory.

The uncertainty effect, also known as direct risk aversion, is a phenomenon from economics and psychology which suggests that individuals may be prone to expressing such an extreme distaste for risk that they ascribe a lower value to a risky prospect than its worst possible realization.

References

  1. ↑ Gilboa, I.; Schmeidler, D. (1989). "Maxmin expected utility with non-unique prior" (PDF). Journal of Mathematical Economics. 18 (2): 141–153. doi:10.1016/0304-4068(89)90018-9.
  2. ↑ Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica: Journal of the Econometric Society, 571-587.
  3. ↑ Halevy, Y. (2007). "Ellsberg revisited: An experimental study". Econometrica. 75 (2): 503–536. doi:10.1111/j.1468-0262.2006.00755.x. JSTOR   4501998.
  4. ↑ David Kelsey; Sara le Roux (11 January 2015). "An Experimental Study on the Effect of Ambiguity in a Coordination Game" (PDF). Saraleroux.weebly.com. Retrieved 7 March 2022.
  5. ↑ Kelsey, David; Le Roux, Sara (2015). "An experimental study on the effect of ambiguity in a coordination game" (PDF). Theory and Decision. 79 (4): 667–688. doi:10.1007/s11238-015-9483-2. hdl:10871/16743. S2CID   56396384.
  6. ↑ Massari, Filippo; Newton, Jonathan (2020-09-01). "When does ambiguity fade away?". Economics Letters. 194: 109404. doi:10.1016/j.econlet.2020.109404. hdl: 11585/847657 . ISSN   0165-1765.
  7. ↑ Marinacci, Massimo; Massari, Filippo (2019-10-01). "Learning from ambiguous and misspecified models". Journal of Mathematical Economics. 84: 144–149. doi:10.1016/j.jmateco.2019.07.012. ISSN   0304-4068.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.