Question

Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he cannot condition on player 1's action. Draw this as an extensive form game. How many sub games are there now? 4. Represent this game as a Normal form game and find all Nash Eq (both pure and mixed strategy)

Answer 1

SG2 Lo 2 131 (1 (,3) (o3) b) Sub-Games. SPNE Solwing via Bachwcvao Anduchon

pa) P) No Mixed st Ne exfsts 3) Sthmultameous Move Game - extensive forn → P1 1 Sulb Gaume (entise Game) 1a) 2 (38( (aa) (013) L R P2) 8 (13) (o3)

4) with simultaneous game, player 2 has only two actions L & R

Since P2 is indifferent between two nodes, so no distinction between strategies L 1 & L2, R1 & R2

Since both players have dominant strategies, so no mixed strategy NE exists