Payoff_ 7.ppt
- 1. What is Payoff? Payoff means return. Payoff occurs as a result of some unexpected events. Matrix means rectangular array of some numbers placed within brackets. So, payoff is the amount of profit that a decision maker wants or expects under different conditions of uncertainty and for taking different strategies and when it is expressed in a systematic array of numbers within brackets it is called payoff matrix.
- 2. Significance of payoff matrix in business: A businessman conducts his business under different conditions of uncertain environment. The economic conditions are also different in different environments such as boom, depression, recession, slump etc. A businessman takes different strategies to earn profit under different economic conditions. Thus a businessman can be aware of the outcomes of different strategies taken under various economic conditions through payoff matrix.
- 3. For conceptualizing about decision making process payoff matrix converts the decision making process into formal: 1) Description of objectives. 2) Selection of payoffs. 3) Evaluation of alternative payoffs , and 4) Selection from among the alternative strategies. In addition to this, payoff matrix plays a great role in game theory. A player knows not only his own list of possible courses of action but also of his opponents. We can also consider the payoffs under different stages of the product like cycle.
- 4. Procedure of decision making: Decisions are taken under three conditions. The strategy to be taken by a decision maker depends on the conditions of (a) certainty (b) risk, and (c) uncertainty. The payoff matrix of different strategies taken under different economic conditions is discussed below: States of nature Alternative Strategies Boom(N1) Recovery(N2) Recession(N3) Depresion(N4) S1 6 6 6 4 S2 25 7 7 -15 S3 20 20 7 -1 S4 19 16 9 -2 S5 20 15 15 -3
- 5. Decision Making Under Certainty: Under conditions of certainty a decision maker is fully aware of what will happen in future. Consequently, the matrix becomes a one column matrix and the decision maker takes that strategy that yields the highest payoff. In our above example, if the decision maker becomes certain that boom economic condition (N1) will prevail then he will take S2 strategy. If he is assured that the economy is recovering then he will take S3 strategy. If the economic condition is in the Recession (N3) stage then he will take S5 strategy and in case of depression he will take S1 strategy.
- 6. Decision Making Under Risk: In this case, each alternative strategy yields a definite outcome and the probability of each outcome is known to the decision maker i.e., the probability of outcome can be guessed beforehand and the decision maker can prepare a distribution of different strategy’s payoffs. Criterion for Decision Making Under Risk: Under this method the payoff is multiplied by the expected probability and the strategy with the highest expected value is taken. For example, if the decision maker thinks that the probability of happening Boom is 20% Recovery-65%, Recession-10%, and Depression is 5% then the strategy to be taken is determined by the following way:
- 7. Here the expected value of S4 is calculated as follows: E(S(4) = 0.20*19+0.65*16+0.10*9+0.05*(-2) =15.00 and the expected value of each strategy is done the same way. Here S3 strategy shows the highest expected payoff. So, S3 strategy is to be taken. But if any two strategies show the same expected payoff then the standard deviation of them is calculated. Then the strategy is taken on the basis of desire of risk taking.
- 8. Decision Making Under Uncertainty: There are 4 criteria for decision making under uncertainty which are as follows: •The Wald Decision Criterion •The Hurwicz Alpha Decision Criterion •The Savage Decision Decision Criterion, also called the minimax regret. •The Laplace Decision Criterion. Wald Decision Criterion : This decision making process is called the process of the pessimists. This is also called the most conservative method. Murphy’s Law is fully effective here. Under this method the worst outcome of each strategy is chosen first. Then the highest of them is taken as the selected strategy.
- 9. Example of Wald Decision Criterion Alternative Strategies States of nature Criterion N1 N2 N3 N4 Maximin Minimax S1 6 6 6 4 4 6 S2 25 7 7 -15 -15 25 S3 20 20 7 -1 -1 20 S4 19 16 9 -2 -2 19 S5 20 15 15 -3 -3 20 Here S1 strategy is acceptable because among the maximin, S1 strategy yields the highest payoff.
- 10. The Hurwicz Alpha Decision Criterion: Under this method the maximum value of weighted estimated payoff is taken. Then element of weight is the coefficient of optimism which is expressed by alpha (α). The highest payoff is multiplied by alpha. Then the lowest payoff is multiplied by (1- α). These two products are added. The strategy with the highest added value is selected. The following formula is used: di = αMi + (1- α) m
- 11. Hurwicz Alpha Decision Criterion Alternative Strategies Mi α αMi m 1- α (1- α)m d S1 6 .7 4.2 4 0.3 1.2 5.4 S2 25 .7 17.5 -15 0.3 -4.5 13.0 S3 20 .7 14.0 -1 0.3 -0.3 13.7* S4 19 .7 13.3 -2 0.3 -0.6 12.7 S5 20 .7 14.0 -3 0.3 -0.9 13.1 Here S3 strategy should be accepted because it yields the highest payoff.
- 12. The Savage Decision Criterion: This method is also called the maximum regret criterion. Under this method steps are taken to reduce the regret i.e. steps are taken to reduce the opportunity cost of wrong decision. At first a regret matrix is constructed from the payoff matrix. Each cell value of column is deducted from the highest value of a column to get the regret. The difference must be the absolute value. The regret matrix is calculated in the following manner:
- 13. Alternati ve Strategy Payoff Matrix Regret Matrix Maximum Regret N1 N2 N3 N4 N1 N2 N3 N4 S1 6 6 6 4 19 14 9 0 19 S2 25 7 7 -15 0 13 8 19 19 S3 20 20 7 -1 5 0 8 5 8 S4 19 16 9 -2 6 4 6 6 6 S5 20 15 15 -3 5 5 0 7 7 Here S4 strategy should be accepted because it reduces to the minimum the maximum punishment of wrong assumption about the state of nature. The Savage Decision Criterion:
- 14. The Laplace Decision Criterion: This method is also called the Bayes Criterion. According to this method if the probability of occurring an event is unknown we should think that the probability of occurring any event is equal. The strategy with the highest expected payoff is accepted. In our previous example, the expected value of S1, S2, S3, S4, and S5 are 22/4, 24/4, 46/4, 42/4 and 47/4. So, S5 strategy should be accepted.
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