Talk:Nash bargaining game

Merge from Nash bargaining solution

Any objections? --best, kevin [kzollman][talk] 00:02, 20 March 2006 (UTC)

None from me, I think I created it because it was a redlink somewhere and I dug up the references while trying to find a decent source for this in the course of reading through Roughgarden's recent Science paper... It should still go down in the game theory project as a topic in (pretty desperate) need of a good write-up. Cheers, Pete.Hurd 00:44, 20 March 2006 (UTC)

Indeed! Its been on my list of things to do for a long time... I'll merge the two now. Thanks Pete! --best, kevin [kzollman][talk] 00:48, 20 March 2006 (UTC)

Has this article been merged yet? I ask as - as it stands - it is badly confused: Nash's bargaining solution is an example of cooperative game theory. Thus, as game forms are a feature of non-cooperative games, and Nash equilibrium their usual solution concept, it is incorrect to attempt to introduce Nash's bargaining solution in these terms. The Nash project attempts to connect cooperative and non-cooperative game theory, asking what non-cooperative games yield, as their (Nash) equilibria, the solutions of cooperative games. This has been done in the case of Nash's bargaining solution - q.v. Rubinstein's alternating offers game. Further, disagreement need not yield zero payoffs, merely the disagreement point. The basic confusion of this article therefore leaves it worse than the game theory section of the bargaining article. (As a minor point, I'm not sure why Paul Walker is credited at the outset with telling us about the link found by Harsanyi in 1956: Harsanyi's discovery is relevant to a discussion of the bargaining solution; Walker's mention of it on his website is not.) Colin Rowat (talk) 22:59, 4 March 2010 (UTC)

nash's 1950 paper

I took a look at Nash's famous 1950 paper, and it doesn't seem to express bargaining in terms of the game used here. In fact there isn't really any notion of the process of bargaining, just a discussion of what the outcomes might be. Is there some other paper in which Nash described the game form shown here?

The most important game associated with the Nash bargaining solution is probably Ariel Rubinstein's, described in 1982 in "Perfect Equilibrium in a Bargaining Model".

Check out Nash (1953)"The Two Person Co-Operative Game" Econometrica p. 128-40. It has the full discussion of the relevant material. El_Jogg 18:59, 23 April 2007 (UTC)

Absolute values? / Article emphasis

Two points:

First, the Nash product in the article is currently |u(x) - u(d)||v(y) - v(d)|, which suggests that negative "excesses" are just as valuable as positive ones. Perhaps the notation could be changed to, for example, max(u(x)-u(d),0) or (u(x) - u(d))^+ (the latter is used commonly in engineering literature, at least). This would resolve the ambiguity.

Second, surely the Nash bargaining solution itself is more important than its application to this particular game. NBS is studied extensively in its own right, unconnected to any single game. The game also doesn't appear (as is alleged in the introduction) in the 1950 "The Bargaining Problem". Perhaps the article should be reorganized to present the NBS as the central focus, showing the bargaining game as an application that has gotten recent attention by Skyrms and others. Thoughts?

Mateoee (talk) 20:03, 6 March 2008 (UTC)

"The Bargaining Problem"

In the absence of any feedback, I removed the statement suggesting that the Nash Bargaining Game appears in Nash's 1950 "The Bargaining Problem". I also skimmed through his 1953 Econometrica paper, as was suggested by another user, and I didn't find a specific description of the game, either. Mateoee (talk) 22:43, 3 April 2008 (UTC)