In a Bayesian game, is the actions set for a player fixed? Or does her actions set depend on her type?
In other words, can I model as a Bayesian game the following situation.
I have two players: master and worker. The worker is honest or malicious.
- If the worker is honest, she can only work honestly (she has only one action).
- If the worker is malicious, she can work honestly or maliciously (she has two actions).
Yes, you can assume different action sets for different types of a player.
To simplify notation, it is a common assumption in the literature to assume that all types of a player have the same set of actions.
If you like this approach for your example, assume that both types can work honestly or maliciously but the honest type has a payoff of $- \infty$ (or some other very low value) if he works maliciously, so that he would never opt for this action. In other words, assume that working honestly strictly dominates working maliciously for the honest type.