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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?

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    $\begingroup$ Just to be clear, you want the "best" one? $\endgroup$ – Giskard Apr 28 at 18:02
  • $\begingroup$ Yes! I want the most logically appealing one $\endgroup$ – user3425989 Apr 29 at 16:05
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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.

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  • $\begingroup$ Thanks, Regio, You have been really helpful. Can IC be applied to Pooling only? $\endgroup$ – user3425989 Apr 29 at 16:05
  • $\begingroup$ IC can also be applied to refine semi-separating equilibria, so long as there is a signal that is not used by any type. Note that, all separating equilibria satisfy the IC. $\endgroup$ – Regio Apr 29 at 17:28
  • $\begingroup$ Perfect very helpful! do you know any papers which used LMSE and intuitive criterion together? not as a substitue $\endgroup$ – user3425989 Apr 29 at 17:31
  • $\begingroup$ Not sure I know what you mean by LMSE, sorry. $\endgroup$ – Regio Apr 29 at 17:34
  • $\begingroup$ Also, @user3425989 would you mind marking the answer as accepted if you think it answered your original question? Happy to discuss LMSE as well once you provide more details about the acronym. $\endgroup$ – Regio May 4 at 3:38

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