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MathGroup Archive 2008

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mathematica and CGT

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92741] mathematica and CGT
  • From: Francisco Gutierrez <fgutiers2002 at yahoo.com>
  • Date: Sun, 12 Oct 2008 04:31:05 -0400 (EDT)
  • Reply-to: fgutiers2002 at yahoo.com

Dear Friends:
This is a question indirectly (but importantly for me) related to Mathematica. I am trying to make Mathemtica code to represent cooperative game theory concepts (of course, expecting it to work only for very simple games, because making algorithms for practically all these concepts is an NP-Hard problem).
 
Of course, one would want to check the code with simple numerical examples. I come across the following one in the book by Milan Mares (Fuzzy cooperative games, p. 21).
 
The example is the following: Game (N,v), N={1,2,3}, v(empty set)=0
v(1)=0
v(2)=v(3)=v(12)=v(13)=v(23)=2
v(N)=4
 
The problem: find the core of this game.
Now, Mares claims that this core has many components: (0,2,2), (1,2,1), (2,2,0) and (2,0,2).
My Mathematica code finds only one core element (0,2,2), as both players 2 and 3 can guarantee for themselves at least 2 without joining any coalition.
I think this is the correct answer, but I may by fatally wrong...
Can anybody out there help me?
Thanks,
Francisco


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