You’re ignoring that with probability 1/4 agent ends up in room B.n that case you don’t get to decide but you get to collect reward. Which is 3 for (the other agent) guessing T, or 0 for (the other agent) guessing H.
So basically guessing H is increasing your own expected reward at the expense of the other agent’s expected reward (before you actually went to a room you didn’t know if you’ll be an agent which gets to decide or not so your expected reward also included part of expected reward for agent which doesn’t get an opportunity to make a guess).
That’s not important at all. The agents in rooms A1 and A2 themselves would do better to choose tails than to choose heads. They really are being harmed by the information.
It’s totally important. The knowledge that you get paid for guessing T in the cases you’re never asked the question is extremely relevant here. It changes the EV from 1⁄3 * 3 = 1 to 1⁄3 * 3 + 1⁄4 * 3 = 1.75.
No, it doesn’t. There is no 1⁄4 chance of anything once you’ve found yourself in Room A1.
You do acknowledge that the payout for the agent in room B (if it exists) from your actions is the same as the payout for you from your own actions, which if the coin came up tails is $3, yes?
You’re ignoring that with probability
1/4agent ends up in roomB.n that case you don’t get to decide but you get to collect reward. Which is3for (the other agent) guessingT, or0for (the other agent) guessingH.So basically guessing
His increasing your own expected reward at the expense of the other agent’s expected reward (before you actually went to a room you didn’t know if you’ll be an agent which gets to decide or not so your expected reward also included part of expected reward for agent which doesn’t get an opportunity to make a guess).That’s not important at all. The agents in rooms A1 and A2 themselves would do better to choose tails than to choose heads. They really are being harmed by the information.
It’s totally important. The knowledge that you get paid for guessing T in the cases you’re never asked the question is extremely relevant here. It changes the EV from 1⁄3 * 3 = 1 to 1⁄3 * 3 + 1⁄4 * 3 = 1.75.
No, it doesn’t. There is no 1⁄4 chance of anything once you’ve found yourself in Room A1.
You do acknowledge that the payout for the agent in room B (if it exists) from your actions is the same as the payout for you from your own actions, which if the coin came up tails is $3, yes?