Decision Theory 9 All Payoff and Regret Criteria in one case

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#OperationsResearch #Math #Statistics #DecisionTheory #DecisionMaking #Maximax #Maximin #Payoff #Regret #FreeLecture #FreeStudy #Solution • Decision making under uncertainty - • These problems deals with the selection of a course of action when we do not know with certainty the results each alternative action will yield. In fact these are the problems frequently faced in real life as we usually can have an expected figure of outcome of future events and rarely have definitive results of future outcomes. • We can study these problems under two heads: • (a) Decision making under uncertainty without use of probability • (b) Decision making under uncertainty using probability. • Decision-making under uncertainty without use of probability - There are several criteria, which do not require the assignment of probabilities in order to reach a decision. The common non-probabilistic criteria are: • Maximax Payoff Criteria [i.e. maximum of the maximum payoffs]: To use the Maximax rule, we determine the maximum payoff associated with each action and choose the action that corresponds to the maximum of these maximum payoffs. Thus the name Maximax. • The easiest way to apply the Maximax criterion is to find the maximum payoff in the entire table and choose the action corresponding to that payoff. • Note that the Maximax criterion ignores all information in the payoff table except the maximum value. That is, no state of nature except that associated with the maximum payoff and the other payoffs is considered. • Maximin Payoff Criteria [i.e. maximum of the minimum payoffs]: • To use the Maximin criterion, we determine the minimum payoff associated with each action and select the action that corresponds to the Maximum of these minimum payoffs. • Note that the Maximin criterion ignores all information except the minimum payoffs corresponding to each action. That is, no other states of nature except those corre¬sponding to the minimum payoffs are considered. • Furthermore, the size of the difference between the minimum payoffs and the other payoffs is given no weight in determining which action to take. The Maximin criteri¬on is conservative because it is based on the assumption that the least favourable state of nature will occur where profits can be maximized. • Horwich principle: • Horwich principle can be interpreted as a compromise between the optimistic approach of maxi-max principle and the pessimistic approach of maxi-min principle. According to this principle co-efficient of optimism (α) is selected and it is multiplied by the maximum value of an act. The minimum value of that act is multiplied by [1 - α]. The sum of these two products is obtained for the act. For all the acts the sum of products are similarly found out. The act giving the maximum sum of products is selected as the best act according to Horwich principle. • i.e. for any act: α[Maximum payoff] + [1 - α] [Minimum payoff] • Laplace principle: • In this method equal probabilities are assigned to different states of nature. In other words the average pay-offs of different acts are found out. The act, for which the average pay-off is the maximum, is selected as the best act according to this principle. • Minimin Regret Criterion [i.e. minimum of the minimum regrets]: Under this criterion we first make a regret table, and select the minimum regret row, out of which the action corresponding to the minimum regret is chosen. Conceptually it is a corollary of the maxim ax payoff criteria, but the result obtained by the two methods may be different. • A payoff table can be converted into opportunity loss table as follows: • 1. Find the maximum payoff in a state of nature. The opportunity loss associated with this payoff is 0. • 2. The opportunity loss associated with any other payoff in the column/row of this state of nature is found by subtracting that payoff from the maximum payoff in the column/row of the state of nature. • Minimax Regret Criterion [i.e. minimum of the maximum regrets]: • To use this criterion, first, we have to make an opportunity loss table, then find the maximum regret for each strategy/act/action/alternative, and select the strategy/act/action/alternative that has minimum of the maximum regret values. • Decision Theory, Statistical Decision Making, State of Nature, Maximax, Maximin, Horwich, Laplace, Minimin Regret Criterion, Minimax Regret Criterion, Statistics, Operations Research, MBA, MCA, BE, CA, CS, CWA, CMA, CPA, CFA, BBA, BCom, MCom, BTech, MTech, CAIIB, FIII, Graduation, Post Graduation, BSc, MSc, BA, MA, Diploma, Production, Finance, Management, Commerce, Engineering , Grade-11, Grade- 12 • www.prashantpuaar.com

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