Thanks for careful analysis, I must confess that my metric does not consider the stochastic strategies, and in general works better if players actions are taken consequently, not simultaneously (which is much different from the classic description).
The reasoning being that for maximal alignment each action of P1 there exist exactly one action of P2 (and vice versa) that is Nash equilibrium. In this case the game stops in stable state after single pair of actions. And maximally unaligned game will have no nash equilibrium at all, meaning the players actions-reactions will just move over the matrix in closed loop.
Overall, my solution as is seems not fitted for the classical formulation of the game :) but thanks for considering it!
Thanks for careful analysis, I must confess that my metric does not consider the stochastic strategies, and in general works better if players actions are taken consequently, not simultaneously (which is much different from the classic description).
The reasoning being that for maximal alignment each action of P1 there exist exactly one action of P2 (and vice versa) that is Nash equilibrium. In this case the game stops in stable state after single pair of actions. And maximally unaligned game will have no nash equilibrium at all, meaning the players actions-reactions will just move over the matrix in closed loop.
Overall, my solution as is seems not fitted for the classical formulation of the game :) but thanks for considering it!