<p>I presume your &quot;Thomson, Webster&quot; should really be Thomas J. Webster (2009), <em>Introduction to Game Theory in Business and Economics</em>, Routledge.</p>
<p>The explanation the author gives is simply wrong. The asymmetric strategy profiles clearly are Nash equilibria.</p>
<p>(This seems to be a very bad textbook. E.g. on page 46 it defines</p>
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<p>which of course is also wrong.)</p>

CC BY-SA 4.0
2022-09-19T09:41:36.713Z
Wow, this SDS definition is incredible :O
Giskard
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2022-09-19T09:18:49.280Z
2022-09-19T09:28:51.713Z
2022-09-19T09:28:51.713Z
VARulle
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<p>Bold indicates best responses and we can see that both responses in (Wide, Narrow) cell and (Narrow,Wide) cell are best responses, then how come those are not Nash Equilibria as per the book?</p>

CC BY-SA 4.0
2022-09-18T10:17:03.293Z
As a half answer, you are supposed to eliminate the weakly dominated strategy. Going "Narrow" is weakly dominated by going "Wide" for each player, so the only Nash is {Wide, Wide}. For example, if Glomar goes "Narrow", the best response of PETROX is "Wide". If Glomar goes "Wide", PETROX is indifferent between "Wide" and "Narrow". PETROX will thus always choose "Wide".
Eli J
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2022-09-18T11:27:19.070Z
@EliJ Game Theory 101 by William Spaniel says that IEWDS may eliminate some NE like in your case. Why does the Best Responses method not work?
learner
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2022-09-19T09:06:23.863Z
What is "Thomson, Webster"?
VARulle
<game-theory>
Oil Drilling Game from Thomas J. Webster : How are (Wide, Narrow) and (Narrow, Wide) not Nash Equilibria?
learner
# Oil Drilling Game from Thomas J. Webster : How are (Wide, Narrow) and (Narrow, Wide) not Nash Equilibria?

(Asked by: username_0 on 2022-09-18)

[![enter image description here](https://i.sstatic.net/b5RBq.png)](https://i.sstatic.net/b5RBq.png)

[![enter image description here](https://i.sstatic.net/o4VTn.jpg)](https://i.sstatic.net/o4VTn.jpg)

Bold indicates best responses and we can see that both responses in (Wide, Narrow) cell and (Narrow,Wide) cell are best responses, then how come those are not Nash Equilibria as per the book?

**Tags:** game-theory

> **Comments:**
> **username_1**: As a half answer, you are supposed to eliminate the weakly dominated strategy. Going "Narrow" is weakly dominated by going "Wide" for each player, so the only Nash is {Wide, Wide}. For example, if Glomar goes "Narrow", the best response of PETROX is "Wide". If Glomar goes "Wide", PETROX is indifferent between "Wide" and "Narrow". PETROX will thus always choose "Wide".  
> **username_0**: @EliJ Game Theory 101 by William Spaniel says that IEWDS may eliminate some NE like in your case. Why does the Best Responses method not work?  
> **username_2**: What is "Thomson, Webster"?  

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## 1 answers

### Answer by username_2 on 2022-09-19. Score: 2 | Accepted answer

I presume your "Thomson, Webster" should really be Thomas J. Webster (2009), *Introduction to Game Theory in Business and Economics*, Routledge.

The explanation the author gives is simply wrong. The asymmetric strategy profiles clearly are Nash equilibria.

(This seems to be a very bad textbook. E.g. on page 46 it defines

[![enter image description here](https://i.sstatic.net/yF17p.png)](https://i.sstatic.net/yF17p.png)

which of course is also wrong.)

> **Comments:**
> **username_3**: Wow, this SDS definition is incredible :O  

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