In[ ]payoffStravinsky = {{3, 0}, {0, 5}};

(*Define the payoff matrices*)payoffBach = {{5, 0}, {0, 3}};
payoffStravinsky = {{3, 0}, {0, 5}};

(*Display the payoff matrices*)
MatrixForm /@ {payoffBach, payoffStravinsky}

(*Calculate and display the Nash equilibria*)
nashEquilibrium[matrix_] := 
  Module[{rowMax, colMax, equilibria}, rowMax = Max /@ matrix;
   colMax = Max /@ Transpose[matrix];
   equilibria = 
    Select[Flatten[
      Table[{i, j}, {i, 1, Length[rowMax]}, {j, 1, Length[colMax]}], 
      1], matrix[[Sequence @@ #]] == rowMax[[#[[1]]]] && 
       matrix[[Sequence @@ #]] == colMax[[#[[2]]]] &];
   If[Length[equilibria] == 0, "No Nash Equilibrium", equilibria]];

nashBach = nashEquilibrium[payoffBach];
nashStravinsky = nashEquilibrium[payoffStravinsky];

(*Define the equilibrium analysis function*)
equilibriumAnalysis[player_, nash_] := 
 If[nash == "No Nash Equilibrium", "No Nash Equilibrium", 
  "Equilibrium analysis for " <> player <> " Game: " <> 
   If[Length[nash] == 1, 
    "Pure Nash Equilibrium at " <> ToString[nash[[1]]], 
    "Mixed Nash Equilibrium"]]

(*Display the equilibrium analysis*)
equilibriumAnalysis["Bach", nashBach]
equilibriumAnalysis["Stravinsky", nashStravinsky]


**Payoff Matrices Output **
{\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"5", "0"},
{"0", "3"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$, 
MatrixForm[BoxForm`e$]]]\), \!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"3", "0"},
{"0", "5"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$, 
MatrixForm[BoxForm`e$]]]\)}

(*Bach Equilibrium Analysis Output*)

If[{{1, 1}, {2, 2}} == "No Nash Equilibrium", "No Nash Equilibrium", 
 "Equilibrium analysis for " <> "Bach" <> " Game: " <> 
  If[Length[{{1, 1}, {2, 2}}] == 1, 
   "Pure Nash Equilibrium at " <> ToString[{{1, 1}, {2, 2}}[[1]]], 
   "Mixed Nash Equilibrium"]]
   
(*Stavinsky Equilibrium Analysis Output*)

If[{{1, 1}, {2, 2}} == "No Nash Equilibrium", "No Nash Equilibrium", 
 "Equilibrium analysis for " <> "Stravinsky" <> " Game: " <> 
  If[Length[{{1, 1}, {2, 2}}] == 1, 
   "Pure Nash Equilibrium at " <> ToString[{{1, 1}, {2, 2}}[[1]]], 
   "Mixed Nash Equilibrium"]]   

	
###3D payoff matrices##
	
(*Define the payoff matrices*)payoffBach = {{5, 0}, {0, 3}};
payoffStravinsky = {{3, 0}, {0, 5}};

(*Define the utility functions*)
utilityPlayer1[x_, y_, matrix_] := matrix[[1, 1]] x + matrix[[1, 2]] y;
utilityPlayer2[x_, y_, matrix_] := matrix[[2, 1]] x + matrix[[2, 2]] y;

(*Plot the payoff functions*)
Plot3D[{utilityPlayer1[x, y, payoffBach], 
  utilityPlayer2[x, y, payoffBach]}, {x, 0, 1}, {y, 0, 1}, 
 PlotRange -> All, 
 AxesLabel -> {"Player 1 Choice", "Player 2 Choice", "Payoff"}, 
 PlotLabel -> "Payoff Functions for Bach Game"]

Plot3D[{utilityPlayer1[x, y, payoffStravinsky], 
  utilityPlayer2[x, y, payoffStravinsky]}, {x, 0, 1}, {y, 0, 1}, 
 PlotRange -> All, 
 AxesLabel -> {"Player 1 Choice", "Player 2 Choice", "Payoff"}, 
 PlotLabel -> "Payoff Functions for Stravinsky Game"]