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Decision Theory Professor Ahmadi Learning Objectives Structuring the decision problem and decision trees Types of decision making environments: Decision making under uncertainty when probabilities are not known Decision making under risk when probabilities are known

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Choice Theory Professor Ahmadi

Learning Objectives Structuring the choice issue and choice trees Types of choice making situations: Decision making under vulnerability when probabilities are not known Decision making under danger when probabilities are known Expected Value of Perfect Information Decision Analysis with Sample Information Developing a Decision Strategy Expected Value of Sample Information

Types Of Decision Making Environments Type 1: Decision Making under Certainty . Chief know without a doubt (that is, with assurance) result or outcome of each choice option. T ype 2: Decision Making under Uncertainty. Chief has no data at all about different results or conditions of nature. Sort 3: Decision Making under Risk . Leader has some learning with respect to likelihood of event of every result or condition of nature.

Decision Trees A choice tree is an ordered representation of the choice issue. Every choice tree has two sorts of hubs; round hubs compare to the conditions of nature while square hubs relate to the choice options. The branches leaving every round hub speak to the distinctive conditions of nature while the branches leaving every square hub speak to the diverse choice options. Toward the end of every appendage of a tree are the adjustments achieved from the arrangement of branches making up that appendage.

Decision Making Under Uncertainty If the leader does not know with sureness which condition of nature will happen, then he/she is said to be settling on choice under vulnerability . The five normally utilized criteria for choice making under instability are: the idealistic methodology (Maximax) the moderate methodology (Maximin) the minimax misgiving methodology ( Minimax lament) Equally likely ( Laplace standard) Criterion of authenticity with ï¡ ( Hurwicz basis )

Optimistic Approach The hopeful methodology would be utilized by a hopeful leader. The choice with the biggest conceivable result is picked. In the event that the result table was as far as expenses, the choice with the most minimal expense would be picked.

Conservative Approach The traditionalist methodology would be utilized by a moderate chief. For every choice the base result is recorded and afterward the choice comparing to the most extreme of these base adjustments is chosen. (Henceforth, the base conceivable result is amplified .) If the result was as far as expenses, the greatest expenses would be resolved for every choice and after that the choice relating to the base of these most extreme expenses is chosen. (Subsequently, the most extreme conceivable expense is minimized .)

Minimax Regret Approach The minimax misgiving methodology requires the development of a misgiving table or an open door misfortune table . This is finished by ascertaining for every condition of nature the contrast between every result and the biggest result for that condition of nature. At that point, utilizing this misgiving table, the greatest misgiving for every conceivable choice is recorded. The choice picked is the one comparing to the greatest's base second thoughts .

Example: Marketing Strategy Consider the accompanying issue with two choice options (d 1 & d 2 ) and two conditions of nature S 1 (Market Receptive) and S 2 (Market Unfavorable) with the accompanying result table speaking to benefits ( $1000): States of Nature s 1 s 3 d 1 20 6 Decisions d 2 25 3

Example: Optimistic Approach An idealistic leader would utilize the hopeful methodology. All we truly need to do is to pick the choice that has the biggest single worth in the result table. This biggest quality is 25, and subsequently the ideal choice is d 2 . Most extreme Decision Payoff d 1 20 choose d 2 d 2 25 greatest

Example: Conservative Approach A moderate chief would utilize the traditionalist methodology. List the base result for every choice. Pick the choice with the most extreme of these base settlements. Least Decision Payoff pick d 1 d 1 6 most extreme d 2 3

Example: Minimax Regret Approach For the minimax subtracting so as to misgive methodology, first figure a misgiving table every result in a section from the biggest result in that segment. The subsequent misgiving table is: s 1 s 2 Maximum d 1 5 0 5 d 2 0 3 3 minimum Then, select the choice with least lament.

Example: Equally Likely (Laplace) Criterion Equally likely , additionally called Laplace , paradigm discovers choice option with most elevated normal result. To start with figure normal result for each option. At that point pick elective with most extreme normal result. Normal for d 1 = (20 + 6)/2 = 13 Average for d 2 = (25 + 3)/2 = 14 Thus, d 2 is chosen

Example: Criterion of Realism (Hurwicz) Often called weighted normal , the model of authenticity (or Hurwicz ) choice rule is a trade off in the middle of hopeful and a cynical choice. Initially, select coefficient of authenticity , a , with a worth somewhere around 0 and 1. At the point when an is near 1, chief is idealistic about future, and when an is near 0, leader is negative about future. Result = a x (greatest result) + (1-a ) x (least result) In our sample let ï¡ = 0.8 Payoff for d 1 = 0.8*20+0.2*6=17.2 Payoff for d 2 = 0.8*25+0.2*3=20.6 Thus, select d2

Decision Making with Probabilities Expected Value Approach If probabilistic data in regards to the conditions of nature is accessible, one may utilize the normal Monetary worth (EMV) approach (otherwise called Expected Value or EV) . Here the normal return for every choice is computed by summing the result's results under every condition of nature and the likelihood of the individual condition of nature happening. The choice yielding the best expected return is picked.

Expected Value of a Decision Alternative The normal estimation of a choice option is the whole of weighted settlements for the choice option. The normal worth (EV) of choice option d i is characterized as: where: N = the quantity of conditions of nature P ( s j ) = the likelihood of condition of nature s j V ij = the result comparing to choice elective d i and condition of nature s j

Example: Marketing Strategy Expected Value Approach Refer to the past issue. Accept the market's likelihood being responsive is known not 0.75. Utilize the normal financial quality rule to focus the ideal choice.

Expected Value of Perfect Information Frequently data is accessible that can enhance the likelihood gauges for the conditions of nature. The normal estimation of flawless data (EVPI) is the increment in the normal benefit that would come about if one knew with conviction which condition of nature would happen. The EVPI gives an upper bound on the normal estimation of any example or review data .

Expected Value of Perfect Information EVPI Calculation Step 1: Determine the ideal return relating to every condition of nature. Step 2: Compute the normal estimation of these ideal returns. Step 3: Subtract the EV of the ideal choice from the sum decided in step (2).

Example: Marketing Strategy Expected Value of Perfect Information Calculate the normal worth for the best activity for every condition of nature and subtract the EV of the ideal choice. EVPI= .75(25,000) + .25(6,000) - 19,500 = $750

Decision Analysis With Sample Information Knowledge of test or study data can be utilized to reexamine the likelihood gauges for the conditions of nature. Before getting this data, the likelihood gauges for the conditions of nature are called former probabilities . With learning of contingent probabilities for the results or pointers of the specimen or study data, these former probabilities can be modified by utilizing Bayes' Theorem . The results of this investigation are called back probabilities .

Posterior Probabilities Posterior Probabilities Calculation Step 1: For every condition of nature, duplicate the former likelihood by its contingent likelihood for the marker - this gives the joint probabilities for the states and pointer. Step 2: Sum these joint probabilities over all states - this gives the negligible likelihood for the marker. Step 3: For every state, separate its joint likelihood by the minor likelihood for the marker - this gives the back likelihood dispersion.

Expected Value of Sample Information The normal estimation of test data (EVSI) is the extra expected benefit conceivable through learning of the specimen or review data. EVSI Calculation Step 1: Determine the ideal choice and its normal return for the conceivable results of the specimen utilizing the back probabilities for the conditions of nature. Step 2: Compute the normal estimation of these ideal returns. Step 3: Subtract the EV of the ideal choice acquired without utilizing the specimen data from the sum decided in step (2).

Efficiency of Sample Information Efficiency of test data is the proportion of EVSI to EVPI. As the EVPI gives an upper bound to the EVSI, proficiency is dependably a number somewhere around 0 and 1.

Refer to the Marketing Strategy Example It is known from past experience that of the considerable number of situations when the business sector was open, a think-tank anticipated it in 90 percent of the cases. (In the other 10 percent, the