[R] "Nash Equilibrium"

[Christophe Dutang]

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 déc. 2010 à 15:49, Ravi Varadhan a écrit :

> 
> 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>
> 
> 
>> 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 (, 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 déc. 2010 à 00:25, Ravi Varadhan a écrit :
>> 
>>> 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 [ 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)
>>> 
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> 
>>> PLEASE do read the posting guide 
>>> and provide commented, minimal, self-contained, reproducible code.
>>> 
>> 
>> --
>> Christophe Dutang
>> Ph.D. student at ISFA, Lyon, France
>> website: 
>> 
>> 
>> 
>> 
>> 
>> 

--
Christophe Dutang
Ph.D. student at ISFA, Lyon, France
website: http://dutangc.free.fr