Does agency matter? There are 21 x 21 x 4 possible payoff matrixes for a 2x2 game if we use Ordinal payoffs. For the vast majority of them (all but about 7 x 7 x 4 of them) , one or both players can make a decision without knowing or caring what the other player’s payoffs are, and get the best possible result. Of the remaining 182 arrangements, 55 have exactly one box where both players get their #1 payoff (and, therefore, will easily select that as the equilibrium).

All the interesting choices happen in the other 128ish arrangements, ^{6}⁄_{7} of which have the pattern of the preferred (1st and 1st, or 1st and 2nd) options being on a diagonal. The most interesting one (for the player picking the row, and getting the first payoff) is:

1 / (2, 3, or 4) ; 4 / (any)

2 / (any) ; 3 / (any)

The optimal strategy for any interesting layout will be a mixed strategy, with the % split dependent on the relative Cardinal payoffs (which are generally not calculatable since they include Reputation and other non-quantifiable effects).

Therefore, you would want to weight the quality of any particular result by the chance of that result being achieved (which also works for the degenerate cases where one box gets 100% of the results, or two perfectly equivalent boxes share that)

So, your proposed definition of knowledge is information that pays rent in the form of anticipated experiences?