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.

Solutions

Expert Solution

Rahul Sunny answered 1 month ago

Next > < Previous

Related Solutions

Question: The Battle of the Sexes is a coordination game. Describe an instance in health care...

Question: The Battle of the Sexes is a coordination game. Describe an instance in health care that arises as a coordination game. It’s ok to simplify matters here and you don’t have to mathematically derive the final decisions. Just describe the situation, the players, and what might happen. Example (does not include discussion of what might happen): There are two physicians caring for a patient with a chronic disease (e.g. diabetes). Both physicians have an obligation to do what is...

the prisoner’s dilemma, coordination and assurance games, the battle of the sexes and the chicken game....

the prisoner’s dilemma, coordination and assurance games, the battle of the sexes and the chicken game. Describe and briefly discuss an application of one of these games. The application can relate to situations from your own direct experience or describe an example from economics, politics, or some other field.

consider battle of networks game with 3 networks instead of 2. the payoff matrices represent market...

consider battle of networks game with 3 networks instead of 2. the payoff matrices represent market share (%) for each network depending on whether they show sit come or sports events. solve pure strategy. N3-Sitcom N1/N2 Sitcom Sports Sitcom 50,40,10 42,38,20 Sports 35,35,30 40,50,10 N3-Sports N1/N2 Sitcom Sports Sitcom 45,35,20 40,36,24 Sports 40,40,20 30,40,30

Consider the following game, where p is the first player's probability of playing Up and q...

Consider the following game, where p is the first player's probability of playing Up and q is the second player's strategy of playing Left. Left (q) Right (1-q) Up (p) (2,6) (0,0) Down (1-p) (0,0) (6,2) What are the pure-strategy Nash equilibria? Group of answer choices (p,q)=(1,1) (p,q)=(1,0) (p,q)=(0,1) (p,q)=(0,0) Compute the probabilities for the mixed-strategy Nash equilibrium. Show your work step by step

P 2-10: Verdi Opera or Madonna? You won a free ticket to see Verdi's Aida opera....

P 2-10: Verdi Opera or Madonna? You won a free ticket to see Verdi's Aida opera. The ticket has no resale value, but since you enjoy Verdi operas, you would be willing to pay $30 for the ticket had you not received it for free. Madonna is performing on the same night. There is absolutely nothing else you can do that night other than either attending the Verdi opera or the Madonna concert. Tickets to the Madonna concert cost $160....

1. Determine if the following deduction rule is valid: p∨q ¬p _______ ∴ q 2. Determine...

1. Determine if the following deduction rule is valid: p∨q ¬p _______ ∴ q 2. Determine if the following is a valid deduction rule: (p∧q)→r ¬ p ∨ ¬ q ________ ∴ ¬r 3. Suppose p and q are (possibly molecular) propositional statements. Prove that p and q are logically equivalent if any only if p↔q is a tautology.

1. Consider the following demand for Ross Home Accents’ handmade candles: Q P 1 38 2...

1. Consider the following demand for Ross Home Accents’ handmade candles: Q P 1 38 2 36 3 34 4 32 5 30 6 28 7 26 8 24 9 22 10 20 Suppose the marginal cost of producing each candle is $10. (a) Obtain the profit-maximizing single price for Ross Home Accents’ candles and its profit. (b) From the table above, calculate the consumer surplus obtained by consumers of Ross’ candles. Explain why this consumer surplus constitutes a loss...

1. Show that the argument (a) p → q q → p therefore p...

1. Show that the argument (a) p → q q → p therefore p V q is invalid using the truth table. ( 6 marks ) (b) p → q P therefore p is invalid using the truth table. ( 6 marks ) (c) p → q q → r therefore p → r is invalid using the truth table. ( 8 marks )

#1) Consider a market with demand curve given by P = 90 - Q . The...

#1) Consider a market with demand curve given by P = 90 - Q . The total cost of production for one firm is given by TC(q) = (q2/2)+10 . The marginal cost of production is MC = q . a) If the market is perfectly competitive, find the supply curve for one firm. Explain. b) If the market price was $10, how many perfectly competitive firms are in the industry if they are identical? Explain. c) Find an expression...

Consider the following demand for Ross Home Accents’ handmade candles: Q P 1 38 2 36...

Consider the following demand for Ross Home Accents’ handmade candles: Q P 1 38 2 36 3 34 4 32 5 30 6 28 7 26 8 24 9 22 10 20 Suppose the marginal cost of producing each candles is $10. (a) Obtain the profit maximizing single price for Ross Home Accents’ candles and its profit. (b) From the table above, calculate the consumer surplus obtained by consumers of Ross’ candles. Explain why this consumer surplus constitutes a loss...

Subjects