ECP 3703 - Two siblings, Sarah and Tom are playing

Use the following scenario for questions 1-7

Two siblings, Sarah and Tom are playing a simultaneous hit and tell game. Sarah’s two options are to either hit Tom or not, while Tom’s two options are to either tattle on Sarah or not. Listed below are the four possible outcomes of the game:

If Sarah hits Tom and he tattles on her, they both experience a loss of 10.

If Sarah hits Tom and he doesn’t tattle on her, he experiences a loss of 5, while Sarah gains 5.

If Tom tattles untruthfully then he experiences a gain of 5, while Sarah loses 5.

If they both get along (no hitting, no tattling) then no one gets anything (gains equal to 0).

1. If Sarah decides to hit Tom, what would Tom’s best response be?

2. If Tom tattles, what would Sarah’s best response be?

3. If Sarah decides not to hit Tom, what would Tom’s best response be?

4. If Tom does not tattle, what would Sarah’s best response be?

5. What would be the Nash equilibrium of this simultaneous game?

6. If Tom wants to not be hit, what strategy could he follow?

7. If Tom threatens to tell, what would Sarah’s best response be?

Use the following scenario for questions 8-9

Alvin C. Monk and Barnaby Jones are both ice-cream vendors. They have only just recently met each other, and both are strong competitors always looking for an advantage over the other guy.

Currently, Alvin and Barnaby are engaged in a simultaneous pricing game. Listed below are the four (4) possible outcomes of this game:

If only one of them prices low, he gets the vast majority of the customers, a payoff of $1000, while the one who doesn’t price low gets $0.

If they both price high, they each get a payoff of $600.

If they both price low, they each get a payoff of $500.

8. What is the Nash equilibrium of this game?

9. [BONUS] Suppose that this game is repeated indefinitely and the vendors both adopt a “trigger strategy,” such that if a vendor prices low in a given iteration of the game, the other vendor will respond to this action by pricing low in all subsequent games! Under these conditions, what would be the (eventual) Nash equilibrium?

For questions 10-15, consider the following scenario:

(To solve this problem, instead of a “game matrix,” you’ll want to sketch out two “decision trees,” one of which depicts the customer as the “first mover,” and the other depicting the shopkeeper as the “first mover.”)

Consider a sequential game between a shopkeeper and a haggling customer. Assume that the item being negotiated over is a rare, antique MacGuffin that’s virtually impossible to find elsewhere.

The party who moves first chooses either a high price ($50) or low price ($20), and the second mover either agrees to the price or walks away from the deal, whereupon neither party gets anything.

Assume that the customer values the MacGuffin at $60. (Ignore any other costs.)

(Note that if a deal can be reached, the payoff to the shopkeeper is, obviously, the selling price, while the payoff to the customer is the consumer surplus received.)

10. If the customer moves first with a low price quote, what is the best response of the shopkeeper?

11. Looking ahead to how the shopkeeper is likely to respond, what price should the customer quote?

12. If the shopkeeper goes first and quotes a high price, what is the best response of the customer?

13. Looking ahead at how the customer is likely to respond, what price should the shopkeeper charge?

14. This sequential game illustrates a…

a.

Offer the high price

b.

Offer the low price

c.

Walk away from the deal

Use the following scenario for questions 16-18:

Consider a non-strategic game between a firm and its union.

The total agreement value of the union members returning to work is $5 million.

If no agreement is reached, the firm can hire nonunion workers, “scabs,” who would earn the firm $1 million.

However, the union members can find temporary employment elsewhere, where they would earn wages equal to $2 million.

16. If the firm reaches agreement with the union…

17. The union would have a better bargaining position in the negotiations if…

18. The firm would have a better bargaining position if…