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"Nash Equilibrium"

8 messages · ivo welch, Spencer Graves, Ravi Varadhan +2 more

#
Dear R experts:

I searched cran (and r-help) for "nash equilibrium" and "game" but
nothing stuck out.  has someone written a numerical nash optimizer for
two players?

player a has choices x1,x2,x3,... and cares about (maximizes)
pa(x1,x2,x3,...,y1,y2,y3)
player b has choices y1,y2,y3,..., and cares about (maximizes)
pb(x1,x2,x3,...,y1,y2,y3)

I can tune it to my problem, but if someone has already invented this,
please point me to it, so that I do not have to reinvent the wheel.

regards,

/iaw

----
Ivo Welch (ivo.welch at brown.edu, ivo.welch at gmail.com)
#
I think Christophe Dutang is writing a package for generalized Nash
Equilibria models called "GNE".

I am cc'ing him here.  

I don't know if there are other packages out there.  Christophe would know.

Ravi.

-------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine Johns
Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of ivo welch
Sent: Friday, December 03, 2010 5:40 PM
To: r-help
Subject: [R] "Nash Equilibrium"

Dear R experts:

I searched cran (and r-help) for "nash equilibrium" and "game" but
nothing stuck out.  has someone written a numerical nash optimizer for
two players?

player a has choices x1,x2,x3,... and cares about (maximizes)
pa(x1,x2,x3,...,y1,y2,y3)
player b has choices y1,y2,y3,..., and cares about (maximizes)
pb(x1,x2,x3,...,y1,y2,y3)

I can tune it to my problem, but if someone has already invented this,
please point me to it, so that I do not have to reinvent the wheel.

regards,

/iaw

----
Ivo Welch (ivo.welch at brown.edu, ivo.welch at gmail.com)

______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
#
Might something like "Nash-Sutcliffe Efficiency" be relevant?


I found this as follows:


library(sos)
(n <- ???nash)
# found 22 links in 11 packages


       Hope this helps.
       Spencer
On 12/3/2010 3:25 PM, Ravi Varadhan wrote:

  
    
#
No, Spencer.  Nash-Sutcliff efficiency is due to John E. Nash. It is
unrelated to game theory.

The well-known Nash equilibrium in game theory is due to John Forbes Nash,
Jr.

Ravi.

-------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine Johns
Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


-----Original Message-----
From: Spencer Graves [mailto:spencer.graves at structuremonitoring.com] 
Sent: Friday, December 03, 2010 6:52 PM
To: Ravi Varadhan
Cc: 'ivo welch'; 'r-help'; dutangc at gmail.com
Subject: Re: [R] "Nash Equilibrium"

Might something like "Nash-Sutcliffe Efficiency" be relevant?


I found this as follows:


library(sos)
(n <- ???nash)
# found 22 links in 11 packages


       Hope this helps.
       Spencer
On 12/3/2010 3:25 PM, Ravi Varadhan wrote:
know.
On
http://www.R-project.org/posting-guide.html
http://www.R-project.org/posting-guide.html

  
    
#
Hello all,

Months ago, when I wanted to compute Nash equilibria (both standard and generalized), I only found one package that implements the discrete, i.e. when the player payoff is represented by a matrix. So I decided to implement the computation when the payoff is a continuous payoff, generally on a compact set.

The project NE computation is available on R-forge (https://r-forge.r-project.org/R/?group_id=860), there is one package called GNE computing generalized Nash Equilibria.

Two days ago, I commit a first stable and documented version. Please download the binary from the "R packages" tab. The package depends on the alabama package, which depends also on numDeriv. So you need to download these two packages as well. 

Once loaded, ?GNE is an overview of the package. I put 3 examples of GNE in the man page taken from von Heusinger & Kanzow (2009). 

Christophe  

PS: send me an email if you have problems with the functions.

Le 4 d?c. 2010 ? 00:25, Ravi Varadhan a ?crit :
--
Christophe Dutang
Ph.D. student at ISFA, Lyon, France
website: http://dutangc.free.fr
#
Hi Christophe,

Aren't you also using fixed-point acceleration schemes (from the SQUAREM package) for solving the Nash equilibria?  

How does fixed-point acceleration approach compare to the optimization approach in terms of speed and robustness (i.e. convergence from bad starting values)?

Ravi.
____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: Christophe Dutang <dutangc at gmail.com>
Date: Saturday, December 4, 2010 5:09 am
Subject: Re: [R] "Nash Equilibrium"
To: Ravi Varadhan <rvaradhan at jhmi.edu>, ivo welch <ivowel at gmail.com>
Cc: r-help <r-help at stat.math.ethz.ch>
#
Finally, I decided not to depends on SQUAREM, which I used for testing. Nevertherless extrapolation methods for fixed point iteration are at least twice faster than the crude fixed-point iteration or other relaxation methods. Later I would like to do a real benchmark of all methods, not just fixed-point iterations.

Christophe

Le 4 d?c. 2010 ? 15:49, Ravi Varadhan a ?crit :
--
Christophe Dutang
Ph.D. student at ISFA, Lyon, France
website: http://dutangc.free.fr
#
On Sat, Dec 4, 2010 at 10:09 AM, Christophe Dutang <dutangc at gmail.com> wrote:
Could you please tell us which R package solves matrix games?

Paul