How to use ParametricPlot Wih Conditions (or similar)

Question

I´m analizyng the game "Battle of the Buddies" similar to "Prisioner´s Dilenma"

All works fine, BUT... I want to draw in red the point whose coordinates are less than the coords of a strategy.

Manipulate[

 ParametricPlot[{5* x*y - x - y + 1, 6*x*y - 5 x - 5 y + 5}, {x, 0, 
   1}, {y, 0, 1}, PerformanceGoal -> "Quality",

  Epilog -> {Red, PointSize -> .036, 
    Point[{5* p*q - p - q + 1, 6*p*q - 5 p - 5 q + 5}]}],
 (*ParametricPlot[{5* \
x*y-x-y+1,6*x*y-5x-5y+5},{x,0,1},{y,0,1},PerformanceGoal->"Quality",*)
\


 Style["Representación de los pagos Norm(abscisas) y Cliff(ordenadas) \
en Battle of the Buddies", 11, Bold],
 Delimiter,

 Style["Norm usa la estrategia mixta(p,1-p), con el valor de p \
indicado a continuación", 10, Darker@Blue],
 {{p, 0}, 0, 1, Appearance -> "Open"},
 Delimiter,

 Style["Cliff usa la estrategia mixta (q,1-q), con el valor de q \
indicado a continuación", 10, Darker@Orange],
 {{q, 0}, 0, 1, Appearance -> "Open"},
 Delimiter,

 Style["Valores MAXIMIN", 11, Bold, Darker@Black],
 Style["Valor Maximin para Norm: 5/6", 10, Darker@Gray],
 Style["Valor Maximin para Cliff: 5/6", 10, Darker@Gray],

 Delimiter,
 Style["Estrategias de Equilibrio", 11, Bold, Darker@Black],
 Delimiter,
 Style["Creado por Mika Ike ([email protected])", 10, 
  Darker@Black],

 ControlPlacement -> Left, SaveDefinitions -> True

 ]

I can view this

BUT I want to view this.... and I can´t coding that. (Highlighting the set in red)

Answer 1

Just for illustrative purposes. You can modify and limit range in parameter space as required.

Manipulate[
 {p, q} = m;
 p1 = ParametricPlot[fun[x, y], {x, 0, 1}, {y, 0, 1}, 
   Epilog -> {{Red, PointSize[0.02], Point[fun[p, q]]}, 
     Text[fun[p, q], {3, 5}]}, PerformanceGoal -> "Quality", 
   ImageSize -> {300, 300}];
 p2 = ParametricPlot[fun[x, y], {x, p, 1}, {y, 0, q}, 
   PlotStyle -> Red, Mesh -> False, PerformanceGoal -> "Quality", 
   ImageSize -> {300, 300}];
 Show[p1, p2],
 {m, {0.1, 0.1}, {0.99, 0.99}}, 
 Initialization :> (fun[x_, y_] := {5*x*y - x - y + 1, 
     6*x*y - 5 x - 5 y + 5})]

EDIT

In light of Mika Ike requestL

Manipulate[{p, q} = m;
 p1 = ParametricPlot[fun[x, y], {x, 0, 1}, {y, 0, 1}, 
   Epilog -> {{Red, PointSize[0.02], Point[fun[p, q]]}, 
     Text[fun[p, q], {3, 5}]}, PerformanceGoal -> "Quality", 
   ImageSize -> {300, 300}];
 p2 = ParametricPlot[fun[x, y], {x, 0, 1}, {y, 0, 1}, 
   PlotStyle -> Red, 
   RegionFunction -> 
    Function[{x, y, u, v}, 
     0 < x < fun[p, q][[1]] && 0 < y < fun[p, q][[2]]], Mesh -> False,
    PerformanceGoal -> "Quality", ImageSize -> {300, 300}];
 Show[p1, p2], {m, {0.1, 0.1}, {0.99, 0.99}}, 
 Initialization :> (fun[x_, y_] := {5*x*y - x - y + 1, 
     6*x*y - 5 x - 5 y + 5})]

yields: