For what it’s worth, here’s the answers given by UDT:
1) If there was apriori probability P<1 that you would need the $100 to survive later on, you should pay up, because it trades certain death for death with probability P.
2) If there was apriori probability P<1 that the driver would cheat and get away with it, you should pay up, because it trades certain death for death with probability P.
3) If there was apriori probability P<1 that the driver would drive you for free, but in the desert you had to say “yes” or “no” without asking the driver any questions, you should pay up, because it trades death with probability 1-P for certain life.
These seem true (with some caveats) given that the driver is following a fixed policy. But UDT might pay up less of the time if it thinks it can affect the driver’s policy. In case 1, UDT might refuse to pay up for bargaining reasons (this is more clear if the amount is “all of your life savings” rather than $100). In case 2, I’m not sure how the mechanics of the driver cheating would work, but if the driver is less likely to cheat if UDT does not pay up when it predicts the driver to cheat, then perhaps UDT will not pay up if it predicts the driver to cheat.
There’s a broader difficulty here which is that UDT is not well-defined in multi-agent problems (with multiple UDT agents).
Like Jessica said, not well-defined. UDT only solves games where all players have the same utility function, it pretty much just extends utility maximization to games with copies. I’m not sure that general game theory with bargaining can ever be reduced to decision theory, or at least it will take some new idea which is most likely orthogonal to UDT. I spent a lot of time trying to find such an idea and failed.
For what it’s worth, here’s the answers given by UDT:
1) If there was apriori probability P<1 that you would need the $100 to survive later on, you should pay up, because it trades certain death for death with probability P.
2) If there was apriori probability P<1 that the driver would cheat and get away with it, you should pay up, because it trades certain death for death with probability P.
3) If there was apriori probability P<1 that the driver would drive you for free, but in the desert you had to say “yes” or “no” without asking the driver any questions, you should pay up, because it trades death with probability 1-P for certain life.
These seem true (with some caveats) given that the driver is following a fixed policy. But UDT might pay up less of the time if it thinks it can affect the driver’s policy. In case 1, UDT might refuse to pay up for bargaining reasons (this is more clear if the amount is “all of your life savings” rather than $100). In case 2, I’m not sure how the mechanics of the driver cheating would work, but if the driver is less likely to cheat if UDT does not pay up when it predicts the driver to cheat, then perhaps UDT will not pay up if it predicts the driver to cheat.
There’s a broader difficulty here which is that UDT is not well-defined in multi-agent problems (with multiple UDT agents).
How does bargaining work in UDT? Are there any posts on this?
Like Jessica said, not well-defined. UDT only solves games where all players have the same utility function, it pretty much just extends utility maximization to games with copies. I’m not sure that general game theory with bargaining can ever be reduced to decision theory, or at least it will take some new idea which is most likely orthogonal to UDT. I spent a lot of time trying to find such an idea and failed.
In 3, if P is high enough then it can be worth refusing to pay.
Yeah.