The decision tree
Deciding when the future is uncertain: decision and chance nodes, expected value, rolling the tree back, the value of perfect information, then the maximin, maximax, Laplace and minimax-regret criteria when there are no probabilities.
- 27 cards
- 5 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- Scenarios
A few cards from the deck
Decision tree (decision analysis): what is it?
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A diagram that lays out, in the order of time, the choices to make, the random events and the payoffs, so that the possible strategies can be compared.
A square marks a choice that is ours and a circle marks an event we do not control; each leaf carries the final payoff of its path.
A chance node has two branches: a payoff of 100 with probability 0.3 and a payoff of −20 with probability 0.7. What value comes up to this node?
- 16
- 40
- 80
- 30
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16
0.3 × 100 + 0.7 × (−20) = 30 − 14 = 16. The plain average (40) forgets the probabilities, so does the sum (80), and 30 forgets the negative branch.
In a decision tree, a … marks a decision node and a … marks a chance node.
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In a decision tree, a square marks a decision node and a circle marks a chance node.
Probabilities are written on the branches leaving a circle and they sum to 1; branches leaving a square carry none, since we are the ones who choose.
Expected value: what is it?
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The average of the payoffs weighted by their probabilities: the sum, over the possible outcomes, of probability times payoff.
0.6 × 200 + 0.4 × 20 = 128: it is neither 200 nor 20, but what one would win on average by repeating the decision very many times.