Department of Economics
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
1. Does Clampett Exploration have a dominant pure strategy? Yes
2. Does Beverly Oil have a dominant pure strategy?
3. Does Clampett have a dominated strategy?
If so, what is the strategy that is
and which strategy dominates it?
4. After eliminating any dominated strategies, is there a pure strategy
solution to the game? Yes
5. What is the strategy profile for the solution to the game?
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:
6. In this new version of the game is there a dominant strategy
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
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?
Let's change the payoffs again. No one has a technical advantage so
the payoffs become:
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?
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:
16. What are the strategic profiles for the Nash equilibria in this game?
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