1. MBA201a: Decision Analysis

2. Professor WolframMBA201a - Fall 2009 Page 1 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. North Side South Side Japanese Greek Burritos Thai Example: deciding where to eat lunch

3. Professor WolframMBA201a - Fall 2009 Page 2 Assigning values to the nodes involves defining goals. Example: deciding where to eat lunch Taste versus Speed 4 3 1 2 1 2 4 3 North Side South Side Japanese Greek Burritos Thai

4. Professor WolframMBA201a - Fall 2009 Page 3 To solve a tree, work backwards, i.e. right to left. Example: deciding where to eat lunch Speed 1 2 4 3 North Side South Side Japanese Greek Burritos Thai Value =4 Value =2

5. Professor WolframMBA201a - Fall 2009 Page 4 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 Go to trial Settle Win [p=0.6] Lose [p= ]

6. Professor WolframMBA201a - Fall 2009 Page 5 Solving a tree with uncertainty: –The expected value (EV) is the probability-weighted sum of the possible outcomes: p win x win payoff + p lose x 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. Go to trial Settle Win [p=0.6] Lose [p=0.4] -$4M -$8M $0 -$.5M EV=

7. Professor WolframMBA201a - Fall 2009 Page 6 Decision tree notation Go to trial Settle Win [p=0.6] Lose [p=0.4] -$4M -$8M $0 -$.5M -$4m -$8.5M -$.5M EV= -$3.2M EV= -$3.7M Value of optimal decision Chance nodes (circles) Terminal values corresponding to each branch (the sum of payoffs along the branch). Probabilities (above the branch) Payoffs (below the branch) Decision nodes (squares) -$3.7M -$4M Running total of net expected payoffs (below the branch) Expected value of chance node (or certainty equivalent)

8. Professor WolframMBA201a - Fall 2009 Page 7 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.