Separating Equilibrium

We now begin solving for signaling games, beginning with the easiest case: separating equilibrium.

Takeaway Points

  1. Review: Types separate when they each choose distinct strategies. Thus, after observing the move, the opponent becomes informed exactly what type it is facing.
  2. Finding separating equilibria is a four step process:
    1. Identify a set of separating strategies.
    2. Solve for the other player’s best response to those strategies.
    3. Check whether the first player can profitably deviate.
    4. Repeat Step #1 until you have exhausted all sets of separating strategies.
  3. Intuitively, a separating equilibrium asks a simple question. Suppose my type could pretend to be another type by switching to the other strategy, and I will completely trick my opponent in the process. Is it still optimal for me to play my proposed equilibrium strategy? If the answer is no, then the proposed strategies are not an equilibrium. I would prefer to bluff instead.
  4. When writing down the perfect Bayesian equilibrium, separating strategies lead to trivial beliefs. On the equilibrium path, all beliefs will place probability 1 on whatever type chooses the associated strategy.

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