A Location Game On Disjoint Circles

Strategy T*

if r = 1 then

|_ place one point in some circle

else if r ≥ 2 then

(a)

if at r - 1 G played in a free circle then

place one point in that circle taking a key position (defined by
the position of the green point and dN/Ke

if (K — L(r)) dN/Ke = φ(r) then

take all key positions in the occupied circles and then
divide the free circles equally by taking key positions on
them with all remaining points

(b)

else if at r — 1 G played in the circle with at least one red point

and vacant key position, not taking a key position then

place one point in that circle taking a key position (defined by
the position of the red point and dN/Ke

(c)

else if there is a circle with red points only and vacant key

positions then

place one point in that circle taking a key position (defined by
the position of the red points and dN/Ke

(d)

else

place one point in a free circle

if (K — L(r))dN/Ke = N — r or (K — L(r))bN/Kc = N — r

then

divide the free circles equally by taking key positions on
them with all remaining points