You are a poor pleb working in a large organization.  Your career has reached a stage where you are asked to join one of two divisions, division A or division B.  You can’t avoid the choice even if you prefer the status quo – it would be bad for your career.  Each division is controlled by a boss.  Boss A is sneaky and self-serving. perhaps he is “rational” in the parlance of economics.  Even better, perhaps his strategy is quite transparent to you after a brief chat with him so you can predict his every move.  He is the Devil you know. Boss B might be rational or might be somewhat altruistic and have your best interests at heart.  He is the Devil you don’t know.  Neither boss is going anywhere soon and you have no realistic chance of further advancement.  You will be interacting frequently with the boss of the division you choose.

Which division should you join?

You face a trade-off it seems.  If you join division A, it is easier for you to play a best-response to boss A’s strategy – you can pretty much work out what it is.  If you join division B, it is harder but the fact that you don’t know can help your strategic interaction.

For example, suppose you are playing a game where “cooperation” is not an equilibrium if it is common knowledge that both players are rational – the classical story is the Prisoner’s Dilemma.  Then, the incomplete information might help you to cooperate.  If you do not cooperate, you reveal you are rational and the game collapses into joint defection.  If you cooperate, you might be able to sustain cooperation well into the future (this is the famous work of Kreps, Milgrom, Roberts and Wilson).

On the other hand, if you are playing a pure coordination game, this logic is less useful.  All you care about is the action the other player is going to take and you want to play a best response to it.  So, the division you should join depends on the structure of the later boss-pleb game.

Perhaps it is possible to frame this question in such a way that the existing reputation and game theory literature tells us if and when incomplete information should be welcomed by the pleb so you should play with the Devil you don’t know and when it is bad, so you should play with the Devil you know?