Then, (Cooperate, Cooperate) with a transfer between 2 and 14 from Bob to Alice dominates (Defect, Defect).
I would use terminology like “is Pareto efficient,” which refers to outcomes, rather than dominate, because dominate refers to strategies. Note also that dominance requires it be superior, not just not inferior, to all other outcomes; so Bob would have to commit to cooperating and transferring more than 2 units of utility for Alice to consider cooperating.
My two cents on usage: “Dominates” in that context is standard in economics, although I should have qualified it as “Pareto dominates”. We can distinguish between at least three levels of dominance: every agent strictly preferring one outcome over another, at least one agent strictly preferring it and all others weakly preferring it, and every agent weakly preferring it. I think common usage is to call the first “strict Pareto dominance”, the second “weak Pareto dominance”, and the third doesn’t comes up. Unqualified, “Pareto dominance” probably means “weak Pareto dominance”, but that’s by no means standard. Also, I interpret “between 2 and 14” as “in the open interval (2, 14)”.
Thanks for the input on possible confusions! Dominance does get heavily overloaded depending on what’s being ordered.
Also, I interpret “between 2 and 14” as “in the open interval (2, 14)”.
Ah, okay. I generally picture that interval as closed unless someone says “strictly between,” but I should have thought through my objection and said “wait, this disappears if the interval is open.”
I would use terminology like “is Pareto efficient,” which refers to outcomes, rather than dominate, because dominate refers to strategies. Note also that dominance requires it be superior, not just not inferior, to all other outcomes; so Bob would have to commit to cooperating and transferring more than 2 units of utility for Alice to consider cooperating.
My two cents on usage: “Dominates” in that context is standard in economics, although I should have qualified it as “Pareto dominates”. We can distinguish between at least three levels of dominance: every agent strictly preferring one outcome over another, at least one agent strictly preferring it and all others weakly preferring it, and every agent weakly preferring it. I think common usage is to call the first “strict Pareto dominance”, the second “weak Pareto dominance”, and the third doesn’t comes up. Unqualified, “Pareto dominance” probably means “weak Pareto dominance”, but that’s by no means standard. Also, I interpret “between 2 and 14” as “in the open interval (2, 14)”.
Thanks for the input on possible confusions! Dominance does get heavily overloaded depending on what’s being ordered.
Ah, okay. I generally picture that interval as closed unless someone says “strictly between,” but I should have thought through my objection and said “wait, this disappears if the interval is open.”