Mfcttrf

I am trying to remove the bottom two rows (C and D) completely so as to create a 2*4 payoff matrix. In addition to this, I would also like to move "Player 2" up slightly once they have been removed (roughly between A and B). I am having trouble figuring out how to do so and was wondering if anyone could help?

What I'd like it to look like more or less (with "Player 2" re-positioned to the middle of A and B):

documentclass[12pt]article
usepackagetikz
usetikzlibrarycalc
usetikzlibrarymatrix
usetikzlibrarypositioning
usepackagenatbib
begindocument
begincenterbegintikzpicture
defmyrowhead"T","F","G","T"
defmycolhead"A","B","C","D"

matrix[matrix of math nodes,draw,
every odd row/.style=align=right,every evenrow/.style=align=left,
nodes=text width=1.5cm,row sep=0.2cm,column sep=0.2cm]
 (m) 2&3&6&5\12&2&9&9\-1&0&0&2\0&0&0&3\2&3&6&1\4&2&-1&8\4&2&4&8\4&2&-1&7\;
foreachx[count=xi from 2,evaluate=xx=int(2*x);xxi=int(xx+1)] in 1,2,3-m.north) -- ($(m-1-x)!0.5!(m-1-xi)$
foreachx in0,1,2,3
 node[text depth=0.25ex,above=2mm] at ($(m.north west)!(2*x+1)/8!(m.north east)$)
 pgfmathparsemyrowhead[x]pgfmathresult;
 node[left=2mm] at ($(m.north west)!(2*x+1)/8!(m.south west)$)
 pgfmathparsemycolhead[x]pgfmathresult;


node[above=18pt of m.north] (firm b) Player 1;
node[left=1.6cm of m.west,align=center,anchor=center] Player 2;
endtikzpicture
endcenter
enddocument

I have tried to keep the same code skeleton you provided. The only thing that I might have changed is the two empty entires in defmycolhead"A","B","","".

documentclass[12pt]article
usepackagetikz
usetikzlibrarycalc
usetikzlibrarymatrix
usetikzlibrarypositioning
usepackagenatbib
begindocument
begincenterbegintikzpicture
defmyrowhead"T","F","G","T"
defmycolhead"A","B","",""
matrix[matrix of math nodes, 
 draw, every odd row/.style=align=right,
 every evenrow/.style=align=left, 
 nodes=text width=1.5cm,
 row sep=0.2cm,column sep=0.2cm]
 (m)
 2&3&6&5\
 12&2&9&9\
 -1&0&0&2\
 0&0&0&3\
 ;
foreachx[count=xi from 2,evaluate=xx=int(2*x);xxi=int(xx+1)] in 1-m.north) -- ($(m-1-x)!0.5!(m-1-xi)$
foreachx in0,1,2,3
 node[text depth=0.25ex,above=2mm] at ($(m.north west)!(2*x+1)/8!(m.north east)$)
 pgfmathparsemyrowhead[x]pgfmathresult;
 node[left=2mm] at ($(m.north west)!(2*x+1)/4!(m.south west)$)
 pgfmathparsemycolhead[x]pgfmathresult;

node[above=18pt of m.north] (firm b) Player 1;
node[left=1.6cm of m.west,align=center,anchor=center] Player 2;
endtikzpicture
endcenter
enddocument

This answer comes with a style payoff matrix which does all the work for you. All you need to do is to say

matrix [payoff matrix]& T & F & G & T\
 A & pft212 & pft32 & pft69 & pft59 \
 B & pft-10 & pft00 & pft00 & pft23 \
;

where pft takes two arguments, the entry at the top right and bottom left of the cell. The names of the players are stored in pgf keys so that you can change them easily.

documentclass[tikz,border=3.14mm]standalone
usetikzlibrarymatrix
tikzsetpayoff matrix/.style=matrix of nodes,column sep=-pgflinewidth,row sep=-pgflinewidth,
 nodes=/utils/exec=ifnumthepgfmatrixcurrentrow>1
 ifnumthepgfmatrixcurrentcolumn>1
 tikzset
 text height=1.2em,text width=4em,draw
 fi
 fi,
 align=center,anchor=center,
 column 1/.style=text width=1em,
 row 1/.style=text depth=0.3em,
 execute at end matrix=tikzmatrixname.west)pgfkeysvalueof/tikz/payoff
 matrix/player 2;,
 payoff matrix/.cd,player 1/.initial=Player 1,player 2/.initial=Player 2
begindocument
begintikzpicture
newcommandpft[2]hfill$#1$ \ $#2$hfillmbox
matrix [payoff matrix]& T & F & G & T\
A & pft212 & pft32 & pft69 & pft59 \
B & pft-10 & pft00 & pft00 & pft23 \
;
endtikzpicture
enddocument

Just to show you don't need a TikZ matrix to draw your table, some nested tabulars are enough.

For convenience, I used a macro for the couple of payoffs, as in marmot's answer.

documentclass[12pt]article
usepackagearray
newcommandpft[2]begintabularc@hspace1.5emc 
 rule0pt3ex & #1 \[1ex]
 #2 & \[1ex]
endtabular
newcolumntypeC[1]>centeringarraybackslashp#1
newcommandmyh[2]multicolumn1C#1#2

begindocument

begincenter
 begintabularcC1.5em
 & myh1.5em & multicolumn4cPlayer 1 \[1ex]
 & myh1.5em & myh4emT & myh4emF & myh4emG & myh4emT \[1ex]
 Player 2 & multicolumn5c%
 begintabular@C1.5em
 cline2-5
 A & pft212 & pft32 & pft69 & pft59 \
 cline2-5
 B & pft-10 & pft00 & pft00 & pft23 \
 cline2-5
 endtabular
 endtabular 
endcenter
enddocument