Regret
Difference between the best possible payoff and the one you got.
Formula
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Example
Minimax-regret decision rules minimise the worst possible regret.
How it works
Regret measures how much you missed out on by not choosing the best option for the situation that actually occurred. It is found by subtracting the payoff you received from the highest payoff you could have received, so a regret of 0 means you made the best possible choice in hindsight. This idea comes from comparing each decision against a perfect benchmark, which helps decision-makers judge how costly an error really was.
When to use it
Use regret when comparing choices under uncertainty, especially if you want to measure the opportunity cost of a decision after the outcome is known. It is common in game theory, economics, operations research, and decision analysis.
Worked example, step by step
A company had three bidding strategies for a contract. If demand turns out high, the best payoff would have been $120,000 and the company’s chosen strategy gives $95,000. Regret = u* - u = 120,000 - 95,000 = 25,000. So the regret is $25,000. This means the company earned $25,000 less than the best possible outcome for that demand scenario.
Common mistakes to avoid
- Subtracting in the wrong order and getting a negative regret
- Using the best payoff from all scenarios instead of the best payoff for the actual outcome
- Confusing regret with total loss rather than the gap from the best available payoff
Did You Know?
Regret minimisation drives some of the strongest poker-playing AIs ever built.
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