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MBA201a: Decision Analysis

MBA201a: Decision Analysis. Decision tree basics: begin with no uncertainty. Basic setup: Trees run left to right chronologically. Decision nodes are represented as squares. Possible choices are represented as lines (also called branches).

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MBA201a: Decision Analysis

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  1. MBA201a: Decision Analysis

  2. Decision tree basics: begin with no uncertainty Basic setup: • Trees run left to right chronologically. • Decision nodes are represented as squares. • Possible choices are represented as lines (also called branches). • The value associated with each choice is at the end of the branch. Example: deciding where to eat lunch Japanese North Side Greek Burritos South Side Thai MBA201a - Fall 2009

  3. Assigning values to the nodes involves defining goals. Example: deciding where to eat lunch Taste versus Speed Japanese 4 1 North Side Greek 3 2 Burritos 1 4 South Side Thai 2 3 MBA201a - Fall 2009

  4. To solve a tree, work backwards, i.e. right to left. Example: deciding where to eat lunch Speed Japanese 1 North Side Value =2 Greek 2 Value =4 Burritos 4 South Side Value =4 Thai 3 MBA201a - Fall 2009

  5. Decision making under uncertainty • Chance nodes are represented by circles. • Probabilities along each branch of a chance node must sum to 1. Example: a company deciding whether to go to trial or settle a lawsuit Win [p=0.6] Go to trial Lose [p= ] Settle MBA201a - Fall 2009

  6. Solving a tree with uncertainty: • The expected value (EV) is the probability-weighted sum of the possible outcomes: pwinx win payoff + plosex lose payoff • In this tree, “Go to trial” has a cost associated with it that “Settle” does not. • We’re assuming the decision-maker is maximizing expected values. Win [p=0.6] $0 Go to trial EV= -$.5M Lose [p=0.4] -$8M EV= Settle -$4M MBA201a - Fall 2009

  7. Decision tree notation Probabilities (above the branch) Expected value of chance node (or certainty equivalent) Terminal values corresponding to each branch (the sum of payoffs along the branch). Chance nodes (circles) Win [p=0.6] -$.5M $0 Go to trial EV= -$3.2M -$3.7M -$.5M Lose [p=0.4] -$8.5M -$8M EV= -$3.7M Decision nodes (squares) Settle -$4m -$4M -$4M Value of optimal decision Running total of net expected payoffs (below the branch) Payoffs (below the branch) MBA201a - Fall 2009

  8. Decision analysis & decision trees Why is decision analysis a useful tool? • The process of doing the analysis, i.e. writing down a decision tree, forces you to make explicit what your goals are, what elements are within your control, and what risks are outside your control. • It keeps you from getting confused when there are contingent decisions. • It helps you figure out when gathering more information will be valuable. The basic idea: look forwards, reason backwards. Decision trees are the tool used to do decision analysis. MBA201a - Fall 2009

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