MBA 201 a Decision Analysis Decision tree basics

MBA 201 a: Decision Analysis

Decision tree basics: begin with no uncertainty Basic setup: Example: deciding where to eat lunch – Trees run left to right chronologically. Japanese North Side – Possible choices are represented as lines (also called branches). Greek Burritos South Side Thai Professor Wolfram – Decision nodes are represented as squares. – The value associated with each choice is at the end of the branch. MBA 201 a - Fall 2009 Page 1

Assigning values to the nodes involves defining goals. Example: deciding where to eat lunch Taste Japanese versus Speed 4 1 3 2 1 4 2 3 North Side Greek Burritos South Side Thai Professor Wolfram MBA 201 a - Fall 2009 Page 2

To solve a tree, work backwards, i. e. right to left. Example: deciding where to eat lunch Speed Japanese North Side 1 Value =2 Greek 2 Value =4 Burritos South Side Value =4 Thai Professor Wolfram 4 3 MBA 201 a - Fall 2009 Page 3

Decision making under uncertainty Example: a company deciding whether to go to trial or settle a lawsuit Win [p=0. 6] Go to trial – Chance nodes are represented by circles. – Probabilities along each branch of a chance node must sum to 1. Lose [p= ] Settle Professor Wolfram MBA 201 a - Fall 2009 Page 4

Solving a tree with uncertainty: Win [p=0. 6] Go to trial -$. 5 M $0 EV= -$8 M -$4 M – We’re assuming the decisionmaker is maximizing expected values. Settle Professor Wolfram pwinx win payoff + plosex lose payoff – In this tree, “Go to trial” has a cost associated with it that “Settle” does not. Lose [p=0. 4] EV= – The expected value (EV) is the probability-weighted sum of the possible outcomes: MBA 201 a - Fall 2009 Page 5

Decision tree notation Chance nodes (circles) Expected value of chance node (or certainty equivalent) Probabilities (above the branch) Win [p=0. 6] $0 Go to trial -$3. 7 M -$. 5 M EV= -$3. 2 M Lose [p=0. 4] Decision nodes (squares) -$8 M EV= -$3. 7 M Settle Professor Wolfram -$8. 5 M -$4 m -$4 M Value of optimal decision -$. 5 M Terminal values corresponding to each branch (the sum of payoffs along the branch). -$4 M Running total of net expected payoffs (below the branch) Payoffs (below the branch) MBA 201 a - Fall 2009 Page 6

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. Professor Wolfram MBA 201 a - Fall 2009 Page 7