I’d appreciate more precision on “If G is a prisoner’s dilemma”.
We can read off the payoff matrix. G is a Prisoner’s Dilemma if for each player, utility(I defect, they cooperate)>utility(we both cooperate)>utility(we both defect)>utility(I cooperate, they defect).
We can read off the payoff matrix. G is a Prisoner’s Dilemma if for each player, utility(I defect, they cooperate)>utility(we both cooperate)>utility(we both defect)>utility(I cooperate, they defect).
That seems clear. Perhaps in addition, u(c,d)+u(d,c) < 2*u(c,c), though I’m not sure if that makes a difference to your claims.
Again, no difference for CDT or TDT (or the version of ADT I’ll present), but sometimes it matters for UDT.