Not having read that part of planecrash, the solution I immediately thought of, just because it seemed so neat, was that if offered a fraction p of the money, accept with probability p. The other player’s expectation is p(1−p), maximised at p=1/2. Is Eliezer’s solution better than mine, or mine better than his?
One way in which Eliezer’s is better is that mine does not have an immediate generalisation to all threat games.
Your solution works! It’s not exploitable, and you get much more than 0 in expectation! Congrats!
Eliezer’s solution is better/optimal in the sense that it accepts with the highest probability a strategy can use without becoming exploitable. If offered 4⁄10, you accept with p=40%; the optimal solution accepts with p=83% (or slightly less than 5⁄6); if offered 1⁄10, it’s p=10% vs. p=55%. The other player’s payout is still maximized at 5, but everyone gets the payout a lot more often!
Not having read that part of planecrash, the solution I immediately thought of, just because it seemed so neat, was that if offered a fraction p of the money, accept with probability p. The other player’s expectation is p(1−p), maximised at p=1/2. Is Eliezer’s solution better than mine, or mine better than his?
One way in which Eliezer’s is better is that mine does not have an immediate generalisation to all threat games.
Your solution works! It’s not exploitable, and you get much more than 0 in expectation! Congrats!
Eliezer’s solution is better/optimal in the sense that it accepts with the highest probability a strategy can use without becoming exploitable. If offered 4⁄10, you accept with p=40%; the optimal solution accepts with p=83% (or slightly less than 5⁄6); if offered 1⁄10, it’s p=10% vs. p=55%. The other player’s payout is still maximized at 5, but everyone gets the payout a lot more often!