Game theory has many paradoxical models in which a player prefers having worse information, not a result of wishful thinking, escapism, or blissful ignorance, but of cold rationality. Coarse information can have a number of advantages.
(a) It may permit a player to engage in trade because other players do not fear his superior information.
(b) It may give a player a stronger strategic position because he usually has a strong position and is better off not knowing that in a particular realization of the game his position is weak.
Or, (c) as in the more traditional economics of uncertainty, poor information may permit players to insure each other.
Rational players never wish to have less information. Strategic options are provably non-negative in value in standard games.
Against opponents who model the player, the player may wish their opponents do not believe they have these options or information. For more powerful modelers as opponents, the best way for the opponents not to know is to actually not have those capabilities. But the value is through opponent manipulation, not direct advantage of fewer options or less knowledge.
It’s important to keep this in mind, in order to avoid over-valuing ignorance. It’s very rarely the best way to manipulate your opponents in the real world.
Rational players never wish to have less information. Strategic options are provably non-negative in value in standard games.
Against opponents who model the player, the player may wish their opponents do not believe they have these options or information. For more powerful modelers as opponents, the best way for the opponents not to know is to actually not have those capabilities. But the value is through opponent manipulation, not direct advantage of fewer options or less knowledge.
It’s important to keep this in mind, in order to avoid over-valuing ignorance. It’s very rarely the best way to manipulate your opponents in the real world.