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2 Two-by-two signaling game Suppose that Alan can be either of type 1 or type 2. These types occur with probability 1/2. After learning his type, Alan chooses L or R. Betty observes Alan's decision, but not Alan's type. Then she selects Z or S. The payoffs after each combination of types and actions are described by the following tables Betty 2 S L 1,1 2,0 R 2,2 0,0 Betty Z S L 0,0 0,1 R 1,0 1,1 Alan (type 1) Alan (type 2) 1. Sketch the game tree. Give an example of pooling strategy for Alan. Give an example of a separating strategy for Alan. Explain what kind of object is a perfect Bayesian equilibrium (don't find it yet!). 1 2. Is there a PBE in which Alan uses a separating (pure) strategy? 3. Is there a PBE in which Alan uses a pooling (pure) strategy? 2 Two-by-two signaling game Suppose that Alan can be either of type 1 or type 2. These types occur with probability 1/2. After learning his type, Alan chooses L or R. Betty observes Alan's decision, but not Alan's type. Then she selects Z or S. The payoffs after each combination of types and actions are described by the following tables Betty 2 S L 1,1 2,0 R 2,2 0,0 Betty Z S L 0,0 0,1 R 1,0 1,1 Alan (type 1) Alan (type 2) 1. Sketch the game tree. Give an example of pooling strategy for Alan. Give an example of a separating strategy for Alan. Explain what kind of object is a perfect Bayesian equilibrium (don't find it yet!). 1 2. Is there a PBE in which Alan uses a separating (pure) strategy? 3. Is there a PBE in which Alan uses a pooling (pure) strategy