I guess the rightmost term could be zero or negative, right? (If the difference between T and P is greater than or equal to the difference between P and S.) In that case, the payoffs would be such that there’s no credence you could have that the other player will play Hare that would justify playing Hare yourself (or justify it as non-defection, that is).
So my claim #1 is always true, but claim #2 depends on the payoff values.
In other words, Stag Hunt could be subdivided into two games: one where the payoffs never justify playing Hare (as non-defection), and one where they sometimes do, depending on your credence that the other player will play Stag.
I guess the rightmost term could be zero or negative, right? (If the difference between T and P is greater than or equal to the difference between P and S.) In that case, the payoffs would be such that there’s no credence you could have that the other player will play Hare that would justify playing Hare yourself (or justify it as non-defection, that is).
So my claim #1 is always true, but claim #2 depends on the payoff values.
In other words, Stag Hunt could be subdivided into two games: one where the payoffs never justify playing Hare (as non-defection), and one where they sometimes do, depending on your credence that the other player will play Stag.
Yes, this is correct. For example, the following is an example of the second game:
Gotcha, thanks for confirming!