I am solving a three-stage game in which first the sender sends the signal, then the receiver acts based on the signal and finally, the sender moves again. The sender has two types high and low and the high type would like to pretend to be the low type. The last stage action of high or low type is already defined and is different for the agents. I am struggling with the pooling equilibrium. Since the last stage actions of the senders are different, the optimal pooling signal of them is different as well. How should I come up with the pooling equilibrium? Thank you very much

  • $\begingroup$ Since the pooling signal cannot be different, perhaps you have made a mistake. $\endgroup$
    – Giskard
    Nov 1 '18 at 11:30
  • $\begingroup$ The calculation is correct. On the second stage, the buyer solves the expected payoff and in the first stage, anticipating that, the sender acts accordingly. $\endgroup$ Nov 1 '18 at 11:55
  • 1
    $\begingroup$ Perhaps one of your assumptions is mistaken. Again, pooling equilibrium means that the signals are identical. $\endgroup$
    – Giskard
    Nov 1 '18 at 12:48

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