EVPI

360. EVPI

Expected Value of Perfect Information (EVPI) — how much more you’d earn by knowing the state of nature in advance. The upper bound on what information is worth.

360.1. Definition

Let ${EMV}^{*} = {max}_{𝑖} EMV (𝑎_{𝑖})$ — best expected value under uncertainty.

With perfect information (you know $𝑠_{𝑗}$ before deciding): pick the best act for each state. Expected value:

EV under PI = \sum_{𝑗} 𝑝_{𝑗} max_{𝑖} 𝑉_{𝑖 𝑗}

(Note: $max$ inside the sum vs $max$ of sums — perfect info lets you tailor act to state.)

EVPI = EV under PI - {EMV}^{*}

360.2. Example

From EMV example:

	$𝑠_{1}$ (high)	$𝑠_{2}$ (low)
$𝑎_{1}$ (big)	$80$	$- 10$
$𝑎_{2}$ (small)	$40$	$20$
$𝑎_{3}$ (no build)	$0$	$0$
Best in this state	$80$ ( $𝑎_{1}$ )	$20$ ( $𝑎_{2}$ )

$EV under PI = 0.6 \cdot 80 + 0.4 \cdot 20 = 48 + 8 = 56$

${EMV}^{*} = 44$ (from $𝑎_{1}$ )

$EVPI = 56 - 44 = 12$

So perfectly knowing the market state in advance is worth $12$ M to this decision.

360.3. Why it’s an upper bound

Real information sources (market research, pilot tests, expert forecasts) are imperfect — they update probabilities but don’t reveal the state directly. The value of imperfect information (EVSI) is always less than EVPI:

EVSI \leq EVPI

If EVPI itself is small, no information is worth much — don’t bother investing in market research.

360.4. Usage

Set a budget for information gathering: $EVPI = 12$ M means no research is worth more than $12$ M
Identify high-stakes uncertainties: high EVPI signals where uncertainty matters most
Drive sensitivity analysis: if EVPI is low, the decision is robust to uncertainty about that state

360.5. Decomposition by uncertainty

If there are multiple sources of uncertainty (demand and exchange rate), you can compute EVPI for each separately, or jointly. They’re not additive in general.

360.6. See also

EVSI — value of imperfect information
EMV
Decision Trees