Question

Technology Adoption: During the adoption of a new technology a CEO (player 1) can design a new task for a division manager. The new task can be either high level (H) or low level (L). The manager simultaneously chooses to invest in good training (G) or bad training (B). The payoffs from this interaction are given by the following matrix: Player 2 GB 5,4 -5,2 H Player 1 L 2, -2 0,0 a. Present the game in extensive form (a game tree) and solve for all the Nash equilibria and subgame-perfect equilibria. b. Now assume that before the game is played the CEO can choose not to adopt this new technology, in which case the payoffs are (1, 1), or to adopt it, in which case the game is played. Present the entire game in extensive form. How many proper subgames does it have? c. Solve for all the Nash equilibria and subgame-perfect equilibria of the game described in (b).

Answer 1

Extensive form Page No. Date : 1 1 1 ما 2 24 (514) (-5,2) (2,-2) 10o) 2 a B и t (5, 4) (-5,2) (2,-2) (oro) NE (HG) and (L,B) by backward. Induction, SPE is (4 GB) CEOCH 5 ) NA A (11) и (2) (2) B ريا (5.42 (-5,2) (2-2) (0,0) © There are two proper subgames; the whole game and the game after history A ie Adopt. Also techndegy, adopted NE is (A, (1,G)) or (A, (L,B) (A, (H, GB)) NA is no SPE is