<p>Almost all textbooks on game theory include a part on cooperative game theory and therefore also treat Nash bargaining. A random sample (<span class="math-container">$n=3$</span>) from my shelf produced <a href="https://global.oup.com/ushe/product/an-introduction-to-game-theory-9780195128956?cc=at&amp;lang=en&amp;" rel="nofollow noreferrer">this one</a>, <a href="https://www.worldscientific.com/worldscibooks/10.1142/9322" rel="nofollow noreferrer">this one</a>, and <a href="https://www.cambridge.org/core/books/game-theory/B0C072F66E027614E46A5CAB26394C7D" rel="nofollow noreferrer">this one</a>.</p>

CC BY-SA 4.0
2021-07-14T10:41:48.387Z
2021-07-14T10:41:48.387Z
VARulle
<p>I'm looking for some reference that treats the solution that Nash gave to the bargaining problem in which two parties must share the surplus derived from engaging in a cooperative relationship. Following <a href="https://en.wikipedia.org/wiki/Cooperative_bargaining#Bargaining_solutions" rel="nofollow noreferrer">Wikipedia</a>, the solution proposed by Nash meets: 1. Invariant to affine transformations or Invariant to equivalent utility representations.
2. Pareto optimality.
3. Independence of irrelevant alternatives.
4. Symmetry.</p>
<p>Resulting from that Nash says that optimally both parties must maximize the so called Nash product: <span class="math-container">$(u(x)-u(d))(v(y)-v(d))$</span> by choosing <span class="math-container">$(x,y)$</span>. I'd like to understand a bit more those concepts (as well as &quot;resource monotonicity&quot;) not need to be in a very depth manner, so an intermediate textbook treatment of this would suffice for my purposes. Then I'd be grateful if you may provide me some reference. (I have basic knowledge in non-cooperative game theory, and basic mathematical economics tools).</p>
<p>Thanks.</p>

CC BY-SA 4.0
2021-07-03T06:58:49.507Z
Have you looked at Nash's [original paper](https://www.eecs.harvard.edu/cs286r/courses/spring02/papers/nash50a.pdf)? It is quite readable.
Michael Greinecker
<game-theory><reference-request><bargaining>
Nash bargaining solution textbook treatment
manifold
# Nash bargaining solution textbook treatment

(Asked by: username_0 on 2021-07-03)

I'm looking for some reference that treats the solution that Nash gave to the bargaining problem in which two parties must share the surplus derived from engaging in a cooperative relationship. Following [Wikipedia](https://en.wikipedia.org/wiki/Cooperative_bargaining#Bargaining_solutions), the solution proposed by Nash meets: 1. Invariant to affine transformations or Invariant to equivalent utility representations.
2. Pareto optimality.
3. Independence of irrelevant alternatives.
4. Symmetry.

Resulting from that Nash says that optimally both parties must maximize the so called Nash product: $(u(x)-u(d))(v(y)-v(d))$ by choosing $(x,y)$. I'd like to understand a bit more those concepts (as well as "resource monotonicity") not need to be in a very depth manner, so an intermediate textbook treatment of this would suffice for my purposes. Then I'd be grateful if you may provide me some reference. (I have basic knowledge in non-cooperative game theory, and basic mathematical economics tools).

Thanks.

**Tags:** game-theory, reference-request, bargaining

> **Comments:**
> **username_1**: Have you looked at Nash's [original paper](https://www.eecs.harvard.edu/cs286r/courses/spring02/papers/nash50a.pdf)? It is quite readable.  

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## 1 answers

### Answer by username_2 on 2021-07-14. Score: 4 | Accepted answer

Almost all textbooks on game theory include a part on cooperative game theory and therefore also treat Nash bargaining. A random sample ($n=3$) from my shelf produced [this one](https://global.oup.com/ushe/product/an-introduction-to-game-theory-9780195128956?cc=at&lang=en&), [this one](https://www.worldscientific.com/worldscibooks/10.1142/9322), and [this one](https://www.cambridge.org/core/books/game-theory/B0C072F66E027614E46A5CAB26394C7D).


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