Hm. At first glance this feels like a “1” game to me, if they both use the “take the strictly dominant action” solution concept. The alignment changes if they make decisions differently, but under the standard rationality assumptions, it feels like a perfectly aligned game.
Tabooing “aligned” what property are you trying to map on a scale of “constant sum” to “common payoff”?
Good question. I don’t have a crisp answer (part of why this is an open question), but I’ll try a few responses:
To what degree does player 1′s actions further the interests of player 2 within this normal form game, and vice versa?
This version requires specific response functions.
To what degree do the interests of players 1 and 2 coincide within a normal form game?
This feels more like correlation of the payout functions, represented as vectors.
So, given this payoff matrix (where P1 picks a row and gets the first payout, P2 picks column and gets 2nd payout):
5 / 0 ; 5 / 100
0 / 100 ; 0 / 1
Would you say P1′s action furthers the interest of player 2?
Would P2′s action further the interest of player 1?
Where would you rank this game on the 0 − 1 scale?
Hm. At first glance this feels like a “1” game to me, if they both use the “take the strictly dominant action” solution concept. The alignment changes if they make decisions differently, but under the standard rationality assumptions, it feels like a perfectly aligned game.