James G. March and Zur Shapira, Variable Risk Preferences and the Focus of Attention, Psychological Review, 1992, Vol. 99, No. 1 172-183

Empirical studies have shown that:

* threats to survival have lead to both risk taking and risk aversion

* slack increases risk taking

* risk averse above an aspiration level and risk taking below it

* risk taking affected by perception of resources (less risks with resources held long time).

* managers take more risk with org resources than own

* risk takers think success due to skills rather than luck (nature is favorable to them)

Random walk models of risk taking

Individuals begin with a supply of resources and accumulate or deplete resources over time by sequence of independent draws from a distribution of possibilities.

Unreliability is variability that is relatively involuntary and risk is variability that is voluntary. In reality action is a mixture of the two.

They set up their decision model so that:

* when resources are above a reference point risk increases monotonically with distance from point.

* risk taken increases monotonically with distance below the reference point

Risk can be varied by changing variance or changing investment size. They also include a survival point (exhausted resources) as a second reference point.

Model 0: Fixed Risk

Assume s is fixed for all .

Estimated return = (Rt - k)/t (Rt is accumulated resources, k is initial stake)

Model 1: Survival Reference Point

Level of risk depends on distance from survival point

St = (Rt-1 + Et)/D(p*d)

D(P*d) is the standard deviate of normal distribution associated with p*d, probability that the draw will wipe our resources and end in death. This keeps the probability of death constant over all periods.

Model 2: Aspiration Reference Point

If Rt-1 >= Lt-1 then st = (Rt-1 + Et)/D(p*f)

If Rt-1 < Lt-1 then st = (Rt-1 + Et + q)/D(p*s)

Lt is the aspiration level at t, q is the distance above the aspiration level that is deemed "safe", p*f is the probability that a draw in this period will bring cumulated resources below the aspiration level. p*s is the probability that a draw will bring cumulated resources to at least q above the aspiration level. P*s and p*f are both less than 0.5). If cumulated resources are above the aspiration level, it sets variability to keep the probability of falling below the aspiration level constant. If resources are below the aspiration level, it sets the variability so that the probability of exceeding the aspiration level by a fixed amount is fixed.

Model 3: Shifting focus

In this case the risk taker attends to survival or aspiration level, but not both.

a is the learning parameter for adjusting the aspiration level so:

Lt = aRt-1 + (1-a)Lt-1

Consistency with Empirical Data

Some people in the model will average returns higher than expected and thus will overestimate the mean. Others will underestimate the mean. Since the process differentially eliminates those with negative experience, it produces a positive bias in expectations.

The mixed model (3) suggests that people below their aspiration level are split into two unstable groups. One focuses on survival, another focuses on aspiration. They lead to different levels of risk taking. People above the aspiration level are split into two groups -- one who focuses on far distant chances of death and those focused on near danger of falling below aspirations.

Resource Accumulation and Adaptive Aspirations

Resource accumulation by survivors

Using simulation they find that:

* Model one tends to trap most risk takers near the survival point

* Models 2 and 3 generate gains in performance over time. Risk taking is dependent on past history and tends to increase.

People who are above the mean over time overestimate the expected return and tend to take more risk than if they correctly predicted their resources. Also, increasing aspiration levels tends to decrease risk taking.

Starting with a heterogeneous performance distribution tends to eliminate those with negative performance more and you end up with higher average risk taking.

Effects of the Rate of Aspiration Adjustment

Adjusting aspiration level tends to constrain risk taking. Slower adjustments of aspiration levels increases average risk taking over time.

One could also assume that aspirations adjust based on the performance of others. If e (0<e1) where e=0 for the best performer and e=1 for the worst, then the aspiration updating function becomes:

Lt = acR't-1 + a(1-c)Rt-1 + (1-a)Lt-1

where R' is the accumulated resources of the comparison risk taker at t

c is the fraction of weight assigned to other-comparison than self-comparison.

It appears that rapid adjustment in this case leads to higher levels of risk taking than slow aspiration adjustment.

Focus-of-Attention Effects

Depending on the level of resources and the separation between survival point and aspiration level, focus on either survival or aspiration can have a big effect on risk taking.

Effects of Varying Probalistic Attention to Survival

By varying the % of people who focus on the survival point (and also varying aspiration adj rate) we see that for %50 focus slower adj of aspiration leads to higher risk taking. High % levels lead to low risk taking which leads to low levels of accumulated resources which reinforce low levels of risk taking. Low % levels link risk taking to aspiration levels and reduce risk taking.

But for moderate % levels attention is directed to survival point when resources are high (keeping risk taking high) and attended to aspiration point when resources are low (keeping risk taking high).

Effects of Alternative Attention-Allocation Rules

Probably people switch between survival and aspiration level in other ways.

Model 3 Variant A: Relative Distance

In this variant the probability of attending to survival or aspiration is inversely related to the person's distance from them.

Model 3 Variant B; Learning from experience

In this case attention is the result of simple trial and error learning. Success decreases the chance of a change in focus, failure increases the chance for a change in focus. In simpler terms, whenever current cumulated resources fail to achieve the current aspiration, the focus shifts. Whenever cumulated resources exceed aspiration level, focus of attention remains the same.

The results show that because resources and aspirations rise over time, Variant A leads to less focus on survival point over time. An experience based focus (B) tends to lead to more focus on the survival point over time. This leads to higher risk taking especially when resources are plentiful.

Unlike the probabilistic version, Variants A and B lead to the elimination of low-risk takers. The probabilistic Model 3 tends to eliminate high risk takers. In variants A&B risk takers with high values of a are less likely to survive, because with these rules slow adaptation tends to lead to low risk taking early (when most deaths occur) and relatively large risk taking later.

Risk Taking and Survival in Renewing Populations

Differential Survival Over Time

Assume a population of risk takers whose model doesn't change over time. Every risk taker who fails is replaced by a new person with stake k. We assume that the birth of a person of a particular type is some mix of the current proportion found in the population and the current share of resources by that type.

This represents the trade-off between protecting survival by reducing risk and strengthening reproductive capability by taking risks successfully. If the replacement probability of a certain type is dependent on the number of survivors, low risk-taking will give higher reproduction rates. If it is a function of share of resources, high risk taking will produce higher reproduction rates.

Looking at the five selection models, If replacment depends on numbers of survivors, Model 1 (survival focus) is favored, especially when aspirations adjust slowly (causing more risk taking). If it depends on resources, Model 1 people tend to be eliminated.

Aspiration levels that are upwardly other-referential tend to increase risk taking, resource accumulation by survivors, and rate of failure of risk-takers following the aspiration-level models. Therefore, the consequence of emphasizing other rather than self-referential behavior depends on the replacement rules. When replacement depends on resources other-referential tend to strengthen the posisiton of two-reference point risk taking.

Differential Survival When Relative Resource Position Matters

Suppose that survival depended not only on resource >0 but also being in the top v percent of the population. This almost makes the zero point irrelevant.

In this case, a focus on the zero point doesn't help in the long run. In the short term focus on survival helps but it lags in the long-term over shifting-focus models.

This if relative position matters, a focus on adaptive aspiration level is strongly favored over a focus on survival. This is true even when replacement rules emphasize numbers rather than resources. Also the 3A and 3B variants (rule-based focus shifting) tend to be more successful than the probabilistic shifting.

Concluding Remarks

The models show that:

* survivors tend to have substantial resources, high aspirations, and postive bias in mean estimation

* rate of aspiration adjustment to experience is a significant factor in determining risk preference

* when self-referential, slow adjustment leads to higher risk taking

* when other-referential, fast adaptation leads to higher risk taking

This analysis suggest that there are survival advantages to variable risk taking oriented to adaptive aspiration levels.