I believe the upper right-hand corner of a shouldn’t be 1; even if both players are acting in each other’s best interest, they are not acting in their own best interest. And alignment is about having both at the same time. The configuration of Prisoner’s dilemma makes it impossible to make both players maximally satisfied at the same time, so I believe it cannot have maximal alignment for any strategy.

Anyhow, your concept of alignment might involve altruism only, which is fair enough. In that case, Vanessa Kosoy has a similar proposal to mine, but not working with sums, which probably does exactly what you are looking for.

Getting alignment in the upper right-hand corner in the Prisoner’s dilemma matrix to be 1 may be possible if we redefine u(A,B) to u(A,B)=maxu,vuT(A+B)v, the best attainable payoff sum. But then zero-sum games will have maximal instead of minimal alignment! (This is one reason why I defined u(A,B)=maxu,vuTAv+maxu,vuTBv.)

(Btw, the coefficient isn’t symmetric; it’s only symmetric for symmetric games. No alignment coefficient depending on the strategies can be symmetric, as the vectors can have different lengths.)

I believe the upper right-hand corner of a shouldn’t be 1; even if both players are acting in each other’s best interest, they are not acting in their

ownbest interest. And alignment is about having both at the same time. The configuration of Prisoner’s dilemma makes it impossible to make both players maximally satisfied at the same time, so I believe it cannot have maximal alignment for any strategy.Anyhow, your concept of alignment might involve altruism only, which is fair enough. In that case, Vanessa Kosoy has a similar proposal to mine, but not working with sums, which probably does exactly what you are looking for.

Getting alignment in the upper right-hand corner in the Prisoner’s dilemma matrix to be 1 may be possible if we redefine u(A,B) to u(A,B)=maxu,vuT(A+B)v, the best attainable payoff sum. But then zero-sum games will have maximal instead of minimal alignment! (This is one reason why I defined u(A,B)=maxu,vuTAv+maxu,vuTBv.)

(Btw, the coefficient isn’t symmetric; it’s only symmetric for symmetric games. No alignment coefficient depending on the strategies can be symmetric, as the vectors can have different lengths.)