Suppose you have two players playing a simultaneous game. Player $A$ chooses a move from one of the sets in $S_A = \{s_A^1,\ldots,s_A^n\}$ and player $B$ simultaneously chooses a move from one of the sets in $S_B = \{s_B^1,\ldots,s_B^m\}$. The payoffs for each pair of actions is known to both players. Furthermore, each player can choose from only one set of actions.
Player $A$
- Knows to which set of actions he is restricted
- Knows that player $B$ is restricted to one set of actions
- Does not know to which set of actions player $B$ is restricted
and vice versa.
My question: is it possible to solve this game without assuming some probability function over the sets of actions? Can you give me some articles/info on how to do that?