Separating and Pooling Equilibria

Game Theory · Axiom Academy

LESSON Separating and Pooling Equilibria Unit 5: Games with Incomplete Information In a separating equilibrium, each type "separates" itself from other types through its choice of action. This allows uninformed players to perfectly infer the informed player's type from observing their action. Classic Example: In the job market signaling model, high-ability workers invest in education while low-ability workers do not. The employer can perfectly distinguish worker types by observing their education level. In a pooling equilibrium, all types choose the same action, so observing this action provides no new information to other players. The uninformed player's beliefs remain at their prior probabilities. Classic Example: In some market settings, both high-quality and low-quality firms might offer the same warranty, making it impossible for consumers to distinguish quality from the warranty alone. 3. Semi-Separating (Partially Pooling) Equilibria Semi-separating equilibria fall between the extremes of full separation and complete pooling. Some types may separate while others pool, or types may use mixed strategies that partially reveal information. Typical Structure: One type always chooses action A, while another type randomizes between A and B. Observing action B reveals the type with certainty, but observing A leaves residual uncertainty. 4. When Each Equilibrium Type Exists

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