When solving for a mixed equilibrium, the basic task is to find, for each player, the probabilities to assign to the player's pure strategies that O would leave the other player indifferent amongst their pure strategies O allow the players to coordinate on a cooperative pure strategy equilibrium O minimize the singular values for the game's payoff matrix when it is subjected to an eigendecomposition O maximize the alpha-weighted product of the player's payoffs across the table for the game yield that player's maximum possible pure strategy payoff