Temple University
Department of Economics

Games
Nash Equilibrium

Name

A. Oil Wells There are two oil companies, Beverly Oil Company (BOC) and Clampett Exploration (ClEx), that have adjacent land leases over an oil reservoir of known size. They must choose whether to drill and the size of well to drill if they choose that option.  It costs less to drill a narrow well, but the oil is extracted over a greater length of time.  If one firm drills a narrow well and the other a wide well then the second firm will be able to pump the greater share of the oil in the reservoir.  The payoff matrix for the game is

 ClEx Don't drill Narrow Wide BOC Don't drill 0, 0 0, 44 0, 31 Narrow 44, 0 14, 14 -1, 16 Wide 31, 0 16, -1 1, 1

1. Does Clampett Exploration have a dominant pure strategy? Yes   No

2. Does Beverly Oil have a dominant pure strategy? Yes   No

3. Does Clampett have a dominated strategy?  Yes   No
If so, what is the strategy that is dominated
and which strategy dominates it?

4. After eliminating any dominated strategies, is there a pure strategy solution to the game? Yes  No

5. What is the strategy profile for the solution to the game?
BOC ,  Clampett

Suppose that the payoff matrix is changed somewhat.  When they both drill a wide well Clampett has a slight advantage for some geologic or technical reason so the payoffs are changed to the following:

 Clampett Narrow Wide BOC Narrow 14, 14 2, 16 Wide 16, 2 1, 3

6. In this new version of the game is there a dominant strategy equilibrium?  Yes   No

7. In this new version of the game, what is Clampett's best response to a play of Narrow by BOC?

8. When Clampett conjectures that BOC will play Wide, what strategy should Clampett play?

9. When BOC conjectures that Clampett will play Narrow, what strategy should BOC play?

10. What is BOC's best response to a play of Wide by Clampett?

11. What is the solution to the game?
BOC:   Clampett:

Let's change the payoffs again.  No one has a technical advantage so the payoffs become:

 Clampett Narrow Wide BOC Narrow 14, 14 2, 16 Wide 16, 2 1, 1

12. BOC conjectures that Clampett will play Wide.  What strategy should BOC play?

13. Clampett conjectures that BOC will play Wide.  What strategy should Clampett play?

14. How many Nash equilibria are there in this version of the game?

15. What is/are the Nash equilibria?

 Equilibrium # BOC Clampett 1 and 2 and 3 and 4 and

B. Rhett and Scarlett hope to have a date.  Rhett would prefer to spend the evening in a low-life saloon.  Scarlett prefers the more genteel company to be found in a posh dinner club.  They would both prefer to spend the evening together rather than go their separate ways.  The payoff matrix is as follows:

 Rhett Saloon Dinner club Scarlett Saloon 5, 10 -30, -20 Dinner club -2, -5 12, 2

16. What are the strategic profiles for the Nash equilibria in this game?

 Equilibrium # Scarlett Rhett 1 and 2 and

17. Do you believe that there is a focal point in this coordination game that will help them decide where to go? A focal point might be based on any one of several criteria: Payoff dominance, chivalry, altruism, etc. Be prepared to answer this one in class.