Consider the Battle of the Sexes game: Jim Boxing (q) Opera (1-q) Sophia Boxing (p) 2,...

Consider the Battle of the Sexes game:

		Jim
		Boxing (q)	Opera (1-q)
Sophia	Boxing (p)	2, 1	0, 0
Sophia	Opera (1-p)	0, 0	1, 2

1. (1.5 point) Give the pure-strategy Nash equilibrium or equilibria, if any.

2. (6 points) Compute the mixed-strategy Nash equilibrium with p being the probability of boxing for Sophia q being the probability of boxing for Jim. As part of your answer, show how you calculate the best responses for each player by calculating the expected value of each strategy:

- Sophia:
  - EV(Boxing)=
  - EV(Opera)=
  - EV(Boxing)>EV(Opera) if
  - EV(Opera)>EV(Boxing) if
- Jim:
  - EV(Boxing)=
  - EV(Opera)=
  - EV(Boxing)>EV(Opera) if
  - EV(Opera)>EV(Boxing) if

3. (2 points) Draw the best-response functions diagram on a (p, q) graph. Clearly label the best response of Jim by BRJ and the best response of Sophia by BRS.

4. (1.5 points) Show where these best response intersect and indicate at each intersection whether it defines a pure or mixed strategy equilibrium.

Expert Solution

Rahul Sunny answered 8 months ago

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