Concepts in Decision Making

Concepts in Decision Making

Three Models of Decision Making:

In every one of the following models the decision maker knows t= he (prior) probabilities of the natural states. However, the models differ in the = degree to which the decision maker knows the actual state or capable of predicting= it with some probability of success.

Notice, there can be more complicated decision process= es where the

Model 1: Decision Making under Perfect Information

The decision maker has a Perfect Information of the (a= ctual) Natural <= st1:PlaceType w:st=3D"on">State, prior to choosing the action.

Model 2: Decision Making with Sampling (External) Information.

The deci= sion maker has no Perfect Information on the Natural<= /st1:PlaceName> State, but possesses External In= formation that Forecasts the Natura= l State, prior to cho= osing the action.

This external informati= on is also commonly referred to as sampling information, because it is often based on statistical sampling. For example, by sampling the earth one= may predict if there is oil in the ground or not, prior to deciding whether to = dig for oil or not.

The external (sampling) information provides prediction of the natural state.

The words SAMPLING and EXT= ERNAL are simply synonymous.

Model 3: No Perfect Information and No Sampling (External) Information.

The decision maker has neither Perfect Information nor= even External (Sampling) Information on the Natural State. The decision maker has no choice b= ut to choose his act without external information and then face the natural state with its consequences.

More Compl= icated Models

Notice, typically, the decision making process is more complex than that depicted in the above models. Specifically, in class we dealt wit= h a model where the decision maker has the opportunity to choose between acquir= ing external (sampling) information (Model 2), or not acquiring it and still ac= ting (model 1), or even not acting from the start (e.g., canceling the project),= in the same decision making problem. &nb= sp; See for example, many of the problems in chapter 5 from Q. 20 and on= . However, comprehension of the above models ( 1 through 3) may completely clarify the handling of more complex models, as the above models are the building block= s of all other models.

Ranking the Models when Information= is Free

It is clear that a decision maker will prefer situatio= n with more free information. More f= ree information implies a better decision making process, with a higher maximum expected payoff.

So if full information and external information are free, the decision maker prefers model 1 (Full Information) over Model 2 (Sampling (external) Information) over Model 3 (No Information).

Example:

Let the Maximum Expected Monetary Payoffs of the three models under cost= less (free) information be

$1500 for Perfect info (Model 1)

$1300 for Sampling (External) Info (Model 2)

$1000 for No Info (Model 3)

Considering that initially the decision maker has no information, (Model 3).

Then:

EVPI the Expected Value of (free) Perfect Information = is,

$1500- $100= 0 =3D $500.

Attaining free Perfect Information would have increase= d the decision maker’s maximum expected payoff from $1000 to $1500, i.e., by $500.

And similarly,

EVSI the Expected Value of (free) Sampling (external) Information is,

$1300-$1000= =3D $300.

Attaining free Sampling (external) Information would h= ave increased the decision maker’s maximum expected payoff from $1000 to $1300, i.e., by $300.

The Case w= here the Sampling (External) Information is Not Free=

In case, the information is not free, we have t= o take into account its cost. In the= above example, if the sampling (external) information costs $100, the net gain fr= om the external sampling information will be lower than $300 by $100. Specifically, after subtracting the cost of the external information, we obtain,

ENGSI, the Expected Net Gain of Sampling (External) Information is,

$300 - $100= =3D $200.

The Expected Net Gain of Sampling Information is simpl= y, the Expected Value of Sampling Information less the cost of acquiring it.

Additional re= mark for the interested, beyond the required course material:.

Notice, that if the cost of the external information w= ould have been $300 there would have been no expected net gain from acquiring the external information,

$300 - $300 =3D 0.

A decision maker seeking a maximum expected monetary p= ayoff would be indifferent between acquiring the information and not acquiring it= , as it would obtain the same net maximum expected payoff of $1000.

Furthermore, if the cost of the external information w= ould have been higher, say, $400, there will be an expected net loss of $100 from acquiring it. The value of the Expected Net Gain of Sa= mpling Information is,

$300 - $400 =3D -100.

In this case the decision maker should not acquire the external information. <= /p>

Nevertheless, it is quite interesting to note that empirically, it has been observed that decision makers tend to acquire exte= rnal information, even when the acquisition is not profitable. Perhaps, because decision makers o= ften tend to be risk averters and associate a reduction in risk with the attaini= ng of extra information.