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# Chapter 5R

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### Chapter 5R

1. 1. Chapter 5R ISDS 2001 - Matt Levy
2. 2. Introduction Our decision analyses in Chapter 4R primarily discussed consequences or payoff in terms of monetary value. Using probability information about the outcomes of chance events, we deemed the best decision as the one with the best payoff. But what about decisions that need to take into account other intangibles such as risk, public view, etc? The long term view of Wall Street firms is a great example of this. This leads to the definition of utility. This chapter looks at two (separate) topics: The meaning of utility and game theory.
3. 3. Utility Definition : The total worth of a particular outcome; it reflects the decision maker's attitude toward a collection of factors such as profit, loss, and risk. Utility becomes extremely important as payoffs become extreme and/or there is an increased exposure to downside risk. The book gives a great example of Atlanta-based Swofford Real Estate. Using a pure EV approach, decision alternative 1 looks clearly like the best alternative. But if Swofford can't afford to lose even 30K because it might drive the company out of business -- then d3 is the only way to go. This possible extreme consequence factors into our utility that we can use to factor into monetary outcomes to make optimal decisions.
4. 4. Utility and Decision Making If we are strictly talking about the utility of money, we can use the following steps Use the following step to follow the example on pages 155-158 . Steps: 1. Develop a payoff table using monetary values 2. Identify the best and worst payoff values in the table and assign each a utility value, with U(best payoff) > U(worst payoff) 3. For every other monetary value M in the original payoff table, do the following to determine its utility value a. Define the lottery: The best payoff is obtained with the probability p. Worst payoff (1-p) b. Determine the value of p such that the decision maker is indifferent between a guaranteed payoff M and the lottery defined in step 3(a). c. Calculate the utility of M as follows: U(M) = pU(best payoff) + (1-p)U(worst payoff) 4. Convert the payoff table from monetary values to utility values. 5. Apply the expected utility approach to the utility table from step 4 and select the decision alternative with the highest expected utility.
5. 5. Utility: Other Considerations Risk Avoiders v. Risk Takers In the case of Swofford, our president was viewed as a risk avoider. Hence decision 3 (no investment) became the best alternative. A risk taker is one who would choose the lottery over a better guaranteed payoff. Hence decision 2 might be a better alternative in this case (see p. 161) We can also have a risk neutral decision maker The following slide shows the utility functions for each type of decision maker.
6. 6. Utility: Other Considerations If risk neutral - monetary value and utility value will always lead to identical recommendations. If our decision maker is risk neutral, the trick lies in finding a risk neutral range that yields the highest payoff within that range. We have to do our best to assess levels of reasonableness, then the decision with the best monetary value can be used.
7. 7. End of Part I of Chapter 5R Read the section. Do the problems On to Game Theory!
8. 8. Game Theory In decision analysis, a decision maker seeks an optimal decision after considering the possible outcomes of one or more chance events. In game theory , two or more decision makers are called players and compete as adversaries against each other. Each player selects a strategy independent of knowledge of the other players strategy. In this section we discuss two-person zero sum games -- where the gain for one is equal to the loss of the other.
9. 9. Game Theory Example: Competing for Market Share What are the optimal strategies for the two companies. Company A uses a maximin approach, while Company B uses a minimax approach. A pure strategy is defined as when the maximin = minimax.
10. 10. End of Chapter 5R Look at the examples and homework!