Decision Analysis, Utility, and Game Theory
This domain tests decisions under risk and strategic interaction. Expect decision trees, expected monetary value, expected value of perfect and sample information, risk attitudes, utility, dominant strategies, Nash equilibrium, mixed strategies, and zero-sum games.
Core rules
- Fold back a decision tree from terminal payoffs using probabilities and maximizing expected value at decision nodes.
- EVPI equals expected payoff with perfect information minus the best expected value without it.
- EVSI is usually less than EVPI because sample information is imperfect.
- Expected utility, not expected monetary value, represents risk aversion.
- A Nash equilibrium is a strategy profile where no player gains by unilateral deviation; it need not be Pareto efficient.
Worked example
An investor chooses Invest or Not. Invest pays 100 in a high state with probability 0.6 and -40 in a low state with probability 0.4. Not pays 0. EMV(Invest)=0.6(100)+0.4(-40)=60-16=44, so Invest is preferred to 0. With perfect information, the investor would invest only in the high state and earn expected 0.6(100)+0.4(0)=60. EVPI=60-44=16. A risk-averse investor might still reject Invest if utility of -40 is sufficiently severe.
Traps
Confusing EVPI with EVSI, equating expected monetary value with expected utility, assuming a Nash equilibrium is socially best, and ignoring mixed strategies when no pure equilibrium exists.
Key points
- Roll back decision trees correctly.
- EVPI uses perfect information.
- EVSI reflects imperfect information.
- Utility captures risk attitude.
- Nash equilibrium requires no profitable unilateral deviation.