Payoff table
Payoff table is a matrix showing the profit or cost outcome of each decision option under every possible state of nature, used to choose under uncertainty via maximin or expected value.
See it move
A payoff table lists profit for each option against each demand state. Choosing between Low and Medium output under weak or strong demand: Low output pays €40,000 under weak demand and €45,000 under strong demand. Medium output pays €25,000 under weak demand but €70,000 under strong demand. A cautious maximin decision-maker picks Low, protecting the €40,000 worst case, while expected value can favour Medium instead.
The formula
Variables
- Expected value of the decision option (€)
- Probability of state of nature i (probability)
- Payoff under state i for the chosen option (€)
Weighs every possible outcome of a decision option by its probability, giving one comparable figure per option.
Check yourself
A firm is choosing between two production plans under three possible demand states. Plan A yields profits of €20,000 (weak demand), €35,000 (moderate demand) and €50,000 (strong demand). Plan B yields a constant €30,000 under all three states. The probabilities of weak, moderate and strong demand are 0.3, 0.4 and 0.3. Using expected value, which plan should the firm choose, and what is its expected value?