I am analyzing a model in the signaling game, There are three stages of a game. there are two participants in the game, a supplier and a buyer. The supplier has private information about its capacity level. In the first stage, the supplier sets a wholesale price. In the second stage, the buyer gets the wholesale price as a signal and decides on its order quantity and finally, in stage 3 both agents decide on selling quantity to the market. If the supplier has high capacity, it may have incentive to pretend to be of the low capacity. The problem that I have is, I get the range of pooling equilibrium, Is there any equilibrium refinement that allows me to choose the best pooling equilibrium?
There are many refinements of pooling equilibria. For starters, you want to make sure all your equilibria are Perfect Bayesian Equilibria. After that, you can also require any equilibrium to survive the intuitive criterion or other forms of forward induction. Lastly, you could also require things like efficiency or symmetry.
The choice of refinements is not always straight-forward, it depends on what you mean by "best" and how well the assumptions implied by each refinement match the story of in your model.