Expected value of perfect information

In decision theory, the expected value of perfect information (EVPI) is the price that one would be willing to pay in order to gain access to perfect information. A common discipline that uses the EVPI concept is health economics. In that context and when looking at a decision of whether to adopt a new treatment technology, there is always some degree of uncertainty surrounding the decision, because there is always a chance that the decision turns out to be wrong. The expected value of perfect information analysis tries to measure the expected cost of that uncertainty, which “can be interpreted as the expected value of perfect information (EVPI), since perfect information can eliminate the possibility of making the wrong decision” at least from a theoretical perspective.

The problem is modeled with a payoff matrix R_ij in which the row index i describes a choice that must be made by the payer, while the column index j describes a random variable that the payer does not yet have knowledge of, that has probability p_j of being in state j. If the payer is to knowing the value of j, the best choice is the one that maximizes the expected monetary value:

where

is the expected payoff for action i i.e. the expectation value, and

is choosing the maximum of these expectations for all available actions. On the other hand, with perfect knowledge of j, the player may choose a value of i that optimizes the expectation for that specific j. Therefore, the expected value given perfect information is

where ${\displaystyle p_{j}}$ is the probability that the system is in state j, and ${\displaystyle R_{ij}}$ is the pay-off if one follows action i while the system is in state j. Here ${\displaystyle (\max _{i}R_{ij}),\,}$ indicates the best choice of action i for each state j.

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