Question

Problem 3 - Battle of the sexes with a first mover Consider once again Tony and Maria and their movie night coordination game. Tony and Maria have different preferences for movies. Tony prefers Action movies over Comedies. Maria prefers Comedies to Action movies. They prefer to watch movies together rather than separately. The payoff matrix is as follows. Table 1: Tony and Maria payoffs Tony Action Comedy Action 2,5 -1,-1 Maria Comedy 1.1 5,2 1. Determine all the pure strategy Nash equilibria of the simultaneous move game. For this purpose, you can analyse the game using its normal form as we did in lecture. 2. Now, relative to the simultaneous move game we considered in lecture, change the game so that Maria moves first. Tony sees her move and then he makes his choice. Thus, it is a sequential move game where Maria moves first. The payoffs remain the same. (a) Write up the extensive form game (game tree). (b) Using backward induction, determine the unique subgame perfect equilibrium of the game.

Answer 1

1) Payoff matrix

	Action	Comedy
Action	(2*,5•)	(-1,-1)
Comedy	(1,1)	(5*,2•)

Pure strategy NE : (Maria & Tony prefers actions)

& ( Maria & Tony prefers Comedy)

2) sequential game

A)

A+ → Action Comedy Maria was Tony on Tony (215) (Ho) (1.1) (5,2 6.) Soluſho backw cods А / Ус 08,5) 1521 SPNE: <C, AC7 Ang d Maria

B) SPNE :

Maria chooses comedy, Tony choose comedy if Maria choose comedy,

Tony selects action, if Maria selects action