I have a question about game theory terminology. I am working on a model in which players are heterogeneous in two dimensions, and there are four types of players. For example one type of players receive some reward and have some cost of playing, while the other type differs in this reward and cost.
I am interested in the equilibria of the game in which the strategies of users who face the same reward and costs (i.e. same type) are the same.
I think symmetric equilibrium in this case is misleading since not all players are expected to have the same strategies, but it is something more like a separating equilibrium across types. However, there is perfect information so I'm unsure whether separating/pooling equilibria concepts can also be applied here.
Any thoughts/references would be helpful!