(Didn’t you also give up your ability to meaningfully talk about the PD, by the way?)
No, in PD each agent knows where it is and what utility value it gets. In PD with identical players the problem might be similar if it’s postulated that the two agents get different utilities.
Identical agents can’t get different utilities in the internal sense of what’s referred by their decision problems (and any other sense is decision-theoretically irrelevant, since the agent can’t work with what it can’t work with), because definition of utility is part of the decision problem, which in turn is part of the agent (or even whole of the agent).
When you’re playing a lottery, you’re deciding based on utility of the lottery, not on utility of inaccessible (and in this sense, meaningless to the agent) “actual outcome”. Utility of the unknown outcome is not what plays the role of utility in agent’s decision problem, hence we have a case of equivocation.
No, in PD each agent knows where it is and what utility value it gets. In PD with identical players the problem might be similar if it’s postulated that the two agents get different utilities.
Identical agents can’t get different utilities in the internal sense of what’s referred by their decision problems (and any other sense is decision-theoretically irrelevant, since the agent can’t work with what it can’t work with), because definition of utility is part of the decision problem, which in turn is part of the agent (or even whole of the agent).
When you’re playing a lottery, you’re deciding based on utility of the lottery, not on utility of inaccessible (and in this sense, meaningless to the agent) “actual outcome”. Utility of the unknown outcome is not what plays the role of utility in agent’s decision problem, hence we have a case of equivocation.