Question

You have developed a new video game that you can self-publish, or auction off to publishers. If you auction it off, you estimate there is a 50% chance you will net $20,000, and a 50% chance you will net $30,000. If you self-publish, you will have initial costs of $7,000. You estimate there is a 30% chance your game will gross $45,000, a 40% chance your game will gross $35,000, and a 30% chance your game will gross $10,000. As an expected value maximizer, you make the optimal decision to auction off your game and you expect to net $25,000. Genie Analytics offers to provide perfect information to you. How much are you willing to pay? That is, what is EVPI?

Answer 1

The EVPI is the difference between the EV with perfect information and the best EV without perfect information. In this scenario, the maximum amount you would be willing to pay for perfect information is $13,000. This is because the EV with perfect information is $38,000 (self-publishing) minus the EV without perfect information of $25,000 (auctioning).

Step-by-step explanation:

The Expected Value of Perfect Information (EVPI) is the maximum amount a decision-maker should be willing to pay for having perfect information before making a decision. To calculate the EVPI for the video game auctioning scenario, we first consider the expected values (EV) from each option without perfect information. Auctioning the game has an EV of $25,000, which represents a 50% chance of netting $20,000 plus a 50% chance of netting $30,000. When self-publishing, the expected net income is calculated by subtracting the initial costs from the expected gross values, based on their respective probabilities: (0.3 × ($45,000 - $7,000)) + (0.4 × ($35,000 - $7,000)) + (0.3 × ($10,000 - $7,000)) = $11,400 + $11,200 + $900 = $23,500. Therefore, without perfect information, the best decision is to auction, with an EV of $25,000.

With perfect information, the decision-maker could always choose the option with the highest outcome, which would be the best scenario for each decision. To calculate the EV with perfect information (EVwPI), we consider the highest possible net gain from each option. For auctioning, the highest net gain is $30,000, and for self-publishing, it is $45,000 - $7,000 = $38,000. Thus, EVwPI is $38,000 because we'd always choose the higher amount. The EVPI is then the difference between EVwPI and the best EV without perfect information: $38,000 - $25,000 = $13,000. This $13,000 represents the maximum amount one should be willing to pay for perfect information.