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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 657231, 13946]*) (*NotebookOutlinePosition[ 658257, 13978]*) (* CellTagsIndexPosition[ 658213, 13974]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Modeling extra-pair parentage using a cooperative game Erol Ak\[CCedilla]ay\ \>", "Subtitle"], Cell[CellGroupData[{ Cell[TextData[{ "This ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook supplements the paper \"Extra-pair parentage:A new theory based \ on transactions in a cooperative game\" by Erol Ak\[CCedilla]ay and Joan \ Roughgarden and contains the code used for the calculations and graphs in the \ paper." }], "Subsubsection"], Cell[BoxData[{ \(x = x; Remove["\"];\), "\[IndentingNewLine]", \(Off[General::spell1]; \ Off[General::spell];\), "\[IndentingNewLine]", \(\($TextStyle = {FontFamily -> "\", \ FontSize -> 12};\)\), "\[IndentingNewLine]", \(<< Graphics`\), "\[IndentingNewLine]", \(<< Statistics`LinearRegression`\), "\[IndentingNewLine]", \(\(SetOptions[Graphics, \ Axes -> False, \ Frame -> True];\)\)}], "Input",\ CellLabel->"In[1]:="] }, Closed]], Cell[CellGroupData[{ Cell["Calculating the Core", "Section"], Cell[CellGroupData[{ Cell["\<\ First, we calculate the arrangement(s) that maximize the total output from \ the pairing matrix.\ \>", "Subsubsection"], Cell[BoxData[ \(\(\( (*This\ calculates\ the\ maximum\ output\ of\ any\ n\ by\ n\ \ matrix\ and\ gives\ all\ the\ orderings\ that\ maximize\ the\ output\ *) \)\(\ \[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\(maxOutput[game_] := Module[{alt, perm, pos, n, nmax, alternatives, altord, maxoutput}, \[IndentingNewLine]n = Length[game]; \[IndentingNewLine]perm = Permutations[Table[i, {i, 1, n}]]; \[IndentingNewLine]alt = Table[Sum[game[\([i, perm[\([j, i]\)]]\)], {i, 1, n}], {j, 1, Length[perm]}]; \[IndentingNewLine]maxoutput = Max[alt]; \[IndentingNewLine]nmax = Count[alt, \ x_?\((# \[Equal] Max[alt] &)\)]; \[IndentingNewLine]alternatives = Position[alt, \ x_?\((# \[Equal] Max[alt] &)\)]; \[IndentingNewLine]altord = Table[\(perm[\([alternatives[\([i]\)]]\)]\)[\([1]\)], {i, 1, Length[alternatives]}]; \[IndentingNewLine]Flatten[{maxoutput, nmax, altord}, 1]\[IndentingNewLine]]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\ \) \( (*The\ output\ is\ of\ the\ format\ {maximum\ output, \ #\ of\ \ different\ arrangements\ that\ attain\ the\ maximum\ output, \ list\ of\ different\ arrangement, \ each\ of\ the\ format\ {M1' s\ mate, M2' s\ mate, \ ... }\ }*) \)\)\)\)], "Input", CellLabel->"In[7]:="] }, Closed]], Cell[CellGroupData[{ Cell["Below is an example.", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(game = {{17, 4, 5, 5}, {16, 3, 3, 4}, {4, 3, 4, 23}, {4, 2, 2, 22}}; game // MatrixForm\)], "Input", CellLabel->"In[8]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"17", "4", "5", "5"}, {"16", "3", "3", "4"}, {"4", "3", "4", "23"}, {"4", "2", "2", "22"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[8]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(maxout = maxOutput[game]\)], "Input", CellLabel->"In[9]:="], Cell[BoxData[ \({46, 4, {1, 2, 3, 4}, {2, 1, 3, 4}, {3, 1, 2, 4}, {3, 1, 4, 2}}\)], "Output",\ CellLabel->"Out[9]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ The function \" sidepayment[game] \" calculates the side-payments needed and \ prints them neatly.\ \>", "Subsubsection"], Cell[BoxData[ \(\(\(sidepayment[ game_]\)\(:=\)\(Module[{maxout, alternatives, n, arr, malepayoffs, femalepayoffs, satisfaction, \ sidepaymatrix, desired, rsfe, sr, sidep, sidearr, totmales, totfemales, minsidepmale, minsidepfemale}, \[IndentingNewLine]n = Length[game]; \[IndentingNewLine]\[IndentingNewLine] (*We\ start\ \ by\ identifying\ the\ maximum\ output\ \ arrangements*) \[IndentingNewLine]maxout = maxOutput[ game]; \[IndentingNewLine]\[IndentingNewLine] (*The\ following\ \ computes\ whether\ and\ how\ much\ sidepayment\ is\ needed\ to\ whom\ to\ \ stabilize\ each\ of\ the\ mating\ arrangements\ that\ maximize\ the\ output\ *) \[IndentingNewLine]\[IndentingNewLine]sidep = \ \(Reap[\[IndentingNewLine]\(Do[\[IndentingNewLine]\[IndentingNewLine]malearr \ = maxout[\([i + 2]\)]; \ (*which\ female\ each\ male\ is\ mating\ *) \[IndentingNewLine]femalearr = Table[\(Position[malearr, x_?\((# \[Equal] j &)\)]\)[\([1, 1]\)], {j, 1, n}]; \ (*which\ male\ each\ female\ is\ mating\ *) \[IndentingNewLine]malepayoffs = Table[game[\([j, malearr[\([j]\)]]\)], {j, 1, n}]; \ (*the\ payoff\ to\ each\ male\ *) \[IndentingNewLine]femalepayoffs = Table[game[\([femalearr[\([j]\)], j]\)], {j, 1, n}]; \ (*the\ payoff\ to\ each\ female\ *) \[IndentingNewLine]\[IndentingNewLine] (*the\ following\ creates\ a\ \ matrix\ that\ has\ 1\ in\ a\ position\ if\ the\ corresponding\ pairing\ in\ \ the\ original\ game\ matrix\ is\ preferred\ by\ both\ the\ male\ and\ the\ \ female\ to\ their\ pairing\ under\ the\ maximum\ output\ mating\ arrangement\ \ *) \[IndentingNewLine]\[IndentingNewLine]satisfaction = Table[If[ game[\([k, j]\)] > malepayoffs[\([k]\)] && game[\([k, j]\)] > femalepayoffs[\([j]\)], \ 1, 0], {k, 1, n}, {j, 1, n}]; \ \[IndentingNewLine]\[IndentingNewLine] (*Now, \ \ the\ individuals\ who\ have\ a\ 1\ for\ any\ of\ their\ potential\ pairings\ \ need\ to\ be\ compansated\ in\ order\ to\ agree\ on\ the\ maximum\ output\ \ arrangement*) \[IndentingNewLine]\[IndentingNewLine]sidepaymatrix = Table[{"\<|\>"}, {k, 1, n}, {j, 1, n}]; \[IndentingNewLine]\[IndentingNewLine] (*The\ \ following\ provides\ information\ about\ which\ male\ should\ be\ getting\ \ how\ much\ sidepayment\ to\ prevent\ each\ particular\ pair\ from\ forming . \ \ The\ information\ is\ stored\ in\ a\ n\ by\ n\ matrix*) \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]desired = Flatten[ Position[satisfaction[\([m]\)], \ x_?\((# \[Equal] 1 &)\)]]; \[IndentingNewLine]\ \[IndentingNewLine]Do[\ \[IndentingNewLine]sr = game[\([m, desired[\([l]\)]]\)] - malepayoffs[\([m]\)]; \ \[IndentingNewLine]sidepaymatrix = Insert[sidepaymatrix, \ x > sr, {m, desired[\([l]\)], 1}], \ {l, 1, Length[desired]}\ ];\[IndentingNewLine], {m, 1, n}]; \[IndentingNewLine]\[IndentingNewLine]Do[\ \[IndentingNewLine]\[IndentingNewLine]desired = Flatten[ Position[satisfaction[\([All, \ f]\)], \ x_?\((# \[Equal] 1 &)\)]]; \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]sr = game[\([desired[\([l]\)], f]\)] - femalepayoffs[\([f]\)]; \ \[IndentingNewLine]sidepaymatrix = Insert[sidepaymatrix, y > sr, {desired[\([l]\)], f\ , \(-1\)}], \ {l, 1, Length[ desired]}\ \ \[IndentingNewLine]];\[IndentingNewLine], {f, 1, n}]; \[IndentingNewLine]\[IndentingNewLine]Sow[ sidepaymatrix]\[IndentingNewLine], {i, 1, maxout[\([2]\)]}];\)\[IndentingNewLine]]\)[\([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine] (*sidep\ is\ a\ \ list\ of\ matrices, \ where\ each\ matrix\ corresponds\ to\ one\ of\ the\ alternative\ \ maximum\ output\ arrangements . \ The\ entries\ in\ the\ matrix, \ where\ they\ exist, \ give\ how\ much\ the\ male\ and\ female\ need\ to\ be\ paid\ in\ \ order\ to\ forsake\ that\ particular\ pairing\ in\ favor\ of\ this\ specific\ \ maximum\ output\ arrangement . \ The\ entries\ are\ in\ the\ format\ {x > minimum\ sidepayment\ to\ the\ male | y > minimum\ sidepayment\ to\ the\ female}\ \ *) \[IndentingNewLine]\[IndentingNewLine] (*the\ following\ commands\ \ calculate\ the\ total\ amount\ of\ sidepayment\ required\ for\ each\ mating\ \ arrangement\ and\ take\ the\ three\ that\ require\ the\ least\ *) \[IndentingNewLine]\[IndentingNewLine]totsidep = \ \(Reap[\[IndentingNewLine]\[IndentingNewLine]Do[\[IndentingNewLine]sidearr = sidep[\([i]\)]; \[IndentingNewLine]totmales = Sum[Max[ Table[If[Length[sidearr[\([k, l]\)]] \[Equal] 3, Part[sidearr[\([k, l, 1]\)], 2], 0], {l, 1, n}]], {k, 1, n}]; \[IndentingNewLine]totfemales = Sum[Max[ Table[If[Length[sidearr[\([k, l]\)]] \[Equal] 3, Part[sidearr[\([k, l, 3]\)], 2], 0], {k, 1, n}]], {l, 1, n}]; \[IndentingNewLine]Sow[{totmales, totfemales}], \[IndentingNewLine]{i, 1, maxout[\([2]\)]}\[IndentingNewLine]]\[IndentingNewLine]\ \[IndentingNewLine]]\)[\([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine]minsidepmale = Ordering[totsidep[\([All, 1]\)], Min[1, maxout[\([2]\)]]]; \[IndentingNewLine]minsidepfemale = Ordering[totsidep[\([All, 2]\)], Min[1, maxout[\([2]\)]]]; \[IndentingNewLine]resultmale = Table[{maxout[\([minsidepmale[\([i]\)] + 2]\)], sidep[\([minsidepmale[\([i]\)]]\)], totsidep[\([minsidepmale[\([i]\)], 1]\)]}, {i, 1, Min[1, maxout[\([2]\)]]}]; \[IndentingNewLine]resultfemale = Table[{maxout[\([minsidepfemale[\([i]\)] + 2]\)], sidep[\([minsidepfemale[\([i]\)]]\)], \ totsidep[\([minsidepfemale[\([i]\)], 2]\)]}, {i, 1, Min[1, maxout[\([2]\)]]}]; \[IndentingNewLine]\ \[IndentingNewLine] (*The\ following\ generates\ the\ output\ of\ this\ \ function\ *) \[IndentingNewLine]\[IndentingNewLine]Print["\"]; \[IndentingNewLine]Table[{Print[\ \ "\", \ maxout[\([1]\)]]\ , \[IndentingNewLine]Print["\", \ resultmale[\([i, 1]\)]]; \[IndentingNewLine]Print[ ColumnForm[{"\", \ resultmale[\([i, 2]\)] // MatrixForm\ , "\<\>"}]], Print["\", Round[resultmale[\([i, 3]\)]/ maxout[\([1]\)]*100]\ , "\< percent EPP\>"], Print["\<____________________________\>"]}, \ {i, 1, Length[resultmale]}]; \[IndentingNewLine]Print["\<\>"]; \ \[IndentingNewLine]Print["\"]; \[IndentingNewLine]Table[{Print["\", \ resultfemale[\([i, 1]\)]]\ , Print[ColumnForm[{"\", \ resultfemale[\([i, 2]\)] // MatrixForm\ , "\<\>"}]], Print["\", Round[resultfemale[\([i, 3]\)]/ maxout[\([1]\)]*100]\ , "\< percent EPM\>"], Print["\<____________________________\>"]}, \ {i, 1, Length[resultfemale]}]; \[IndentingNewLine]totsidep;\ \[IndentingNewLine]\[IndentingNewLine]]\)\( (*End\ of\ Module[]*) \)\)\)], \ "Input", CellLabel->"In[26]:="] }, Closed]], Cell[CellGroupData[{ Cell["Some examples", "Subsubsection"], Cell["A two by two game", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(game = {{8, 4}, {9, 7}}; game // MatrixForm\)], "Input", CellLabel->"In[11]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"8", "4"}, {"9", "7"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[11]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(maxOutput[game]\)], "Input", CellLabel->"In[12]:="], Cell[BoxData[ \({15, 1, {1, 2}}\)], "Output", CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sidepayment[game]\)], "Input", CellLabel->"In[13]:="], Cell[BoxData[ \("For the least sidepayments on the males' part"\)], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[\("Total fledgling production: "\[InvisibleSpace]15\), SequenceForm[ "Total fledgling production: ", 15], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[\("Mating arrangement is: "\[InvisibleSpace]{1, 2}\), SequenceForm[ "Mating arrangement is: ", {1, 2}], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[GridBox[{ {"\<\"Resulting sidepayments are: \"\>"}, { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\({"|"}\), \({"|"}\)}, {\({x > 2, "|", y > 1}\), \({"|"}\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]}, {"\<\"\"\>"} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {"Resulting sidepayments are: ", MatrixForm[ {{{"|"}, {"|"}}, {{ Greater[ x, 2], "|", Greater[ y, 1]}, {"|"}}}], ""}], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[\("which amount to: "\[InvisibleSpace]13\ \[InvisibleSpace]" percent EPP"\), SequenceForm[ "which amount to: ", 13, " percent EPP"], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ \("____________________________"\)], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ \(\*"\<\"\"\>"\)], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ \("For the least sidepayments on the females' part"\)], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[\("Mating arrangement is: "\[InvisibleSpace]{1, 2}\), SequenceForm[ "Mating arrangement is: ", {1, 2}], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[GridBox[{ {"\<\"Resulting sidepayments are: \"\>"}, { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\({"|"}\), \({"|"}\)}, {\({x > 2, "|", y > 1}\), \({"|"}\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]}, {"\<\"\"\>"} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {"Resulting sidepayments are: ", MatrixForm[ {{{"|"}, {"|"}}, {{ Greater[ x, 2], "|", Greater[ y, 1]}, {"|"}}}], ""}], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ InterpretationBox[\("which amount to: \ "\[InvisibleSpace]7\[InvisibleSpace]" percent EPM"\), SequenceForm[ "which amount to: ", 7, " percent EPM"], Editable->False]], "Print", CellLabel->"From In[13]:="], Cell[BoxData[ \("____________________________"\)], "Print", CellLabel->"From In[13]:="] }, Open ]], Cell["A three by three game", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(game3 = {{8, 2, 4}, {3, 5, 7}, {1, 4, 5.5}}; game3 // MatrixForm\)], "Input", CellLabel->"In[14]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"8", "2", "4"}, {"3", "5", "7"}, {"1", "4", "5.5`"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[14]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sidepayment[game3]\)], "Input", CellLabel->"In[15]:="], Cell[BoxData[ \("For the least sidepayments on the males' part"\)], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[\("Total fledgling production: "\[InvisibleSpace]19\), SequenceForm[ "Total fledgling production: ", 19], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[\("Mating arrangement is: "\[InvisibleSpace]{1, 3, 2}\), SequenceForm[ "Mating arrangement is: ", {1, 3, 2}], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[GridBox[{ {"\<\"Resulting sidepayments are: \"\>"}, { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}]} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]}, {"\<\"\"\>"} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {"Resulting sidepayments are: ", MatrixForm[ {{{"|"}, {"|"}, {"|"}}, {{"|"}, {"|"}, {"|"}}, {{"|"}, { "|"}, {"|"}}}], ""}], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[\("which amount to: \ "\[InvisibleSpace]0\[InvisibleSpace]" percent EPP"\), SequenceForm[ "which amount to: ", 0, " percent EPP"], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ \("____________________________"\)], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ \(\*"\<\"\"\>"\)], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ \("For the least sidepayments on the females' part"\)], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[\("Mating arrangement is: "\[InvisibleSpace]{1, 3, 2}\), SequenceForm[ "Mating arrangement is: ", {1, 3, 2}], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[GridBox[{ {"\<\"Resulting sidepayments are: \"\>"}, { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}]}, { RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}], RowBox[{"(", "\[NoBreak]", TagBox[GridBox[{ {"\<\"|\"\>"} }, RowSpacings->1, ColumnAlignments->{Left}], Column], "\[NoBreak]", ")"}]} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]}, {"\<\"\"\>"} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {"Resulting sidepayments are: ", MatrixForm[ {{{"|"}, {"|"}, {"|"}}, {{"|"}, {"|"}, {"|"}}, {{"|"}, { "|"}, {"|"}}}], ""}], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ InterpretationBox[\("which amount to: \ "\[InvisibleSpace]0\[InvisibleSpace]" percent EPM"\), SequenceForm[ "which amount to: ", 0, " percent EPM"], Editable->False]], "Print", CellLabel->"From In[15]:="], Cell[BoxData[ \("____________________________"\)], "Print", CellLabel->"From In[15]:="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ The function below is the same as sidepayment[game] but without the print \ commands (used for the Monte Carlo simulations) \ \>", "Subsubsection"], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\(sidepayments[ game_]\)\(:=\)\(Module[{maxout, alternatives, n, arr, malepayoffs, femalepayoffs, satisfaction, \ sidepaymatrix, desired, rsfe, sr, sidep, sidearr, totmales, totfemales, minsidepmale, minsidepfemale}, \[IndentingNewLine]n = Length[game]; \[IndentingNewLine] (*We\ start\ by\ identifying\ the\ \ maximum\ output\ arrangements*) \[IndentingNewLine]maxout = maxOutput[ game]; \[IndentingNewLine]\[IndentingNewLine] (*The\ following\ \ computes\ whether\ and\ how\ much\ sidepayment\ is\ needed\ to\ whom\ to\ \ stabilize\ each\ of\ the\ mating\ arrangements\ that\ maximize\ the\ output\ *) \[IndentingNewLine]\[IndentingNewLine]sidep = \ \(Reap[\[IndentingNewLine]\(Do[\[IndentingNewLine]\[IndentingNewLine]malearr \ = maxout[\([i + 2]\)]; \ (*which\ female\ each\ male\ is\ mating\ *) \[IndentingNewLine]femalearr = Table[\(Position[malearr, x_?\((# \[Equal] j &)\)]\)[\([1, 1]\)], {j, 1, n}]; \ (*which\ male\ each\ female\ is\ mating\ *) \[IndentingNewLine]malepayoffs = Table[game[\([j, malearr[\([j]\)]]\)], {j, 1, n}]; \ (*the\ payoff\ to\ each\ male\ *) \[IndentingNewLine]femalepayoffs = Table[game[\([femalearr[\([j]\)], j]\)], {j, 1, n}]; \ (*the\ payoff\ to\ each\ female\ *) \[IndentingNewLine]\[IndentingNewLine] (*the\ following\ creates\ a\ \ matrix\ that\ has\ 1\ in\ a\ position\ if\ the\ corresponding\ pairing\ in\ \ the\ original\ game\ matrix\ is\ preferred\ by\ both\ the\ male\ and\ the\ \ female\ to\ their\ pairing\ under\ the\ maximum\ output\ mating\ arrangement\ \ *) \[IndentingNewLine]\[IndentingNewLine]satisfaction = Table[If[ game[\([k, j]\)] > malepayoffs[\([k]\)] && game[\([k, j]\)] > femalepayoffs[\([j]\)], \ 1, 0], {k, 1, n}, {j, 1, n}]; \ \[IndentingNewLine]\[IndentingNewLine] (*Now, \ \ the\ individuals\ who\ have\ a\ 1\ for\ any\ of\ their\ potential\ pairings\ \ need\ to\ be\ compansated\ in\ order\ to\ agree\ on\ the\ maximum\ output\ \ arrangement*) \[IndentingNewLine]\[IndentingNewLine]sidepaymatrix = Table[{"\<|\>"}, {k, 1, n}, {j, 1, n}]; \[IndentingNewLine]\[IndentingNewLine] (*The\ \ following\ provides\ information\ about\ which\ male\ should\ be\ getting\ \ how\ much\ sidepayment\ to\ prevent\ each\ particular\ pair\ from\ forming . \ \ The\ information\ is\ stored\ in\ a\ n\ by\ n\ matrix*) \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]desired = Flatten[ Position[satisfaction[\([m]\)], \ x_?\((# \[Equal] 1 &)\)]]; \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]sr = game[\([m, desired[\([l]\)]]\)] - malepayoffs[\([m]\)]; \ \[IndentingNewLine]sidepaymatrix = Insert[sidepaymatrix, \ x > sr, {m, desired[\([l]\)], 1}], \ {l, 1, Length[ desired]}\ ] (*End\ of\ Do[ (*Yakup*) ]*) ;\ \[IndentingNewLine], {m, 1, n}] (*End\ of\ Do[ (*Rasim*) ]*) ; \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]desired = Flatten[ Position[satisfaction[\([All, \ f]\)], \ x_?\((# \[Equal] 1 &)\)]]; \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]sr = game[\([desired[\([l]\)], f]\)] - femalepayoffs[\([f]\)]; \ \[IndentingNewLine]sidepaymatrix = Insert[sidepaymatrix, y > sr, {desired[\([l]\)], f\ , \(-1\)}], \ {l, 1, Length[ desired]}\ \ \[IndentingNewLine]];\[IndentingNewLine], {f, 1, n}]; \[IndentingNewLine]\[IndentingNewLine]Sow[ sidepaymatrix], {i, 1, maxout[\([2]\)]}];\)\[IndentingNewLine]]\)[\([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine] (*sidep\ is\ a\ \ list\ of\ matrices, \ where\ each\ matrix\ corresponds\ to\ one\ of\ the\ alternative\ \ maximum\ output\ arrangements . \ The\ entries\ in\ the\ matrix, \ where\ they\ exist, \ give\ how\ much\ the\ male\ and\ female\ need\ to\ be\ paid\ in\ \ order\ to\ forsake\ that\ particular\ pairing\ in\ favor\ of\ this\ specific\ \ maximum\ output\ arrangement . \ The\ entries\ are\ in\ the\ format\ {x > minimum\ sidepayment\ to\ the\ male | y > minimum\ sidepayment\ to\ the\ female}\ \ *) \[IndentingNewLine]\[IndentingNewLine] (*the\ following\ commands\ \ calculate\ the\ total\ amount\ of\ sidepayment\ required\ for\ each\ mating\ \ arrangement\ and\ take\ the\ three\ that\ require\ the\ least\ *) \[IndentingNewLine]\[IndentingNewLine]totsidep = \ \(Reap[\[IndentingNewLine]\[IndentingNewLine]Do[\[IndentingNewLine]sidearr = sidep[\([i]\)]; \[IndentingNewLine]totmales = Sum[Max[ Table[If[Length[sidearr[\([k, l]\)]] \[Equal] 3, Part[sidearr[\([k, l, 1]\)], 2], 0], {l, 1, n}]], {k, 1, n}]; \[IndentingNewLine]totfemales = Sum[Max[ Table[If[Length[sidearr[\([k, l]\)]] \[Equal] 3, Part[sidearr[\([k, l, 3]\)], 2], 0], {k, 1, n}]], {l, 1, n}]; \[IndentingNewLine]Sow[{totmales, totfemales}], \[IndentingNewLine]{i, 1, maxout[\([2]\)]}\[IndentingNewLine]] (*End\ of\ Do[ \ (*Nazmiye*) ]*) \[IndentingNewLine]\[IndentingNewLine]]\)[\([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine]minsidepmale = Ordering[totsidep[\([All, 1]\)], Min[3, maxout[\([2]\)]]]; \[IndentingNewLine]minsidepfemale = Ordering[totsidep[\([All, 2]\)], Min[3, maxout[\([2]\)]]]; \[IndentingNewLine]resultmale = Table[{maxout[\([minsidepmale[\([i]\)] + 2]\)], sidep[\([minsidepmale[\([i]\)]]\)], totsidep[\([minsidepmale[\([i]\)], 1]\)]}, {i, 1, Min[3, maxout[\([2]\)]]}]; \[IndentingNewLine]resultfemale = Table[{maxout[\([minsidepfemale[\([i]\)] + 2]\)], sidep[\([minsidepfemale[\([i]\)]]\)], \ totsidep[\([minsidepfemale[\([i]\)], 2]\)]}, {i, 1, Min[3, maxout[\([2]\)]]}]; \[IndentingNewLine]totsidep; \ \[IndentingNewLine]{resultmale[\([1, 3]\)]/maxout[\([1]\)]*100, \ resultfemale[\([1, 3]\)]/maxout[\([1]\)]*100, maxout[\([1]\)]}\[IndentingNewLine]]\)\( (*End\ of\ Module[]*) \)\)\ \)\)], "Input", CellLabel->"In[27]:="] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Monte Carlo simulations for the section \"Predicting Established Patterns\"\ \>", "Section"], Cell[CellGroupData[{ Cell["1. 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.56919 .63258 .58216 .64853 .60714 .64435 .59429 .62834 Metetra .607 .7 .91 r .59429 .62834 .60714 .64435 .63239 .64008 .61966 .624 Metetra .608 .701 .91 r .61966 .624 .63239 .64008 .6579 .63572 .6453 .61956 Metetra .609 .702 .91 r .6453 .61956 .6579 .63572 .68369 .63128 .67122 .61504 Metetra .609 .703 .91 r .67122 .61504 .68369 .63128 .70975 .62674 .69742 .61042 Metetra .61 .703 .911 r .69742 .61042 .70975 .62674 .73609 .62212 .7239 .60571 Metetra .61 .704 .911 r .7239 .60571 .73609 .62212 .76271 .61741 .75067 .60091 Metetra .611 .705 .911 r .75067 .60091 .76271 .61741 .78963 .61261 .77773 .59602 Metetra .611 .706 .912 r .77773 .59602 .78963 .61261 .81683 .60772 .80508 .59104 Metetra .612 .706 .912 r .80508 .59104 .81683 .60772 .84432 .60275 .83274 .58597 Metetra .612 .707 .912 r .83274 .58597 .84432 .60275 .87212 .59769 .8607 .58081 Metetra .613 .708 .912 r .8607 .58081 .87212 .59769 .90022 .59254 .88896 .57556 Metetra .613 .708 .913 r .88896 .57556 .90022 .59254 .92863 .58731 .91754 .57022 Metetra .613 .709 .913 r .91754 .57022 .92863 .58731 .95735 .58199 .94644 .56478 Metetra .595 .685 .904 r .31824 .65367 .33237 .66948 .35493 .66629 .34088 .65046 Metetra .596 .686 .905 r .34088 .65046 .35493 .66629 .37773 .66297 .36377 .64712 Metetra .598 .688 .905 r .36377 .64712 .37773 .66297 .40078 .65954 .38691 .64367 Metetra .599 .69 .906 r .38691 .64367 .40078 .65954 .42408 .656 .41029 .64009 Metetra .6 .691 .906 r .41029 .64009 .42408 .656 .44763 .65235 .43393 .6364 Metetra .601 .692 .907 r .43393 .6364 .44763 .65235 .47143 .6486 .45783 .6326 Metetra .602 .694 .907 r .45783 .6326 .47143 .6486 .49548 .64475 .48199 .62869 Metetra .603 .695 .908 r .48199 .62869 .49548 .64475 .51979 .64079 .5064 .62468 Metetra .604 .696 .908 r .5064 .62468 .51979 .64079 .54436 .63674 .53108 .62057 Metetra .605 .697 .908 r .53108 .62057 .54436 .63674 .56919 .63258 .55603 .61635 Metetra .606 .698 .909 r .55603 .61635 .56919 .63258 .59429 .62834 .58125 .61204 Metetra .607 .699 .909 r .58125 .61204 .59429 .62834 .61966 .624 .60674 .60762 Metetra .607 .7 .91 r .60674 .60762 .61966 .624 .6453 .61956 .63251 .60311 Metetra .608 .701 .91 r .63251 .60311 .6453 .61956 .67122 .61504 .65856 .59851 Metetra .609 .702 .91 r .65856 .59851 .67122 .61504 .69742 .61042 .68489 .59381 Metetra .609 .703 .91 r .68489 .59381 .69742 .61042 .7239 .60571 .71151 .58901 Metetra .61 .703 .911 r .71151 .58901 .7239 .60571 .75067 .60091 .73843 .58412 Metetra .61 .704 .911 r .73843 .58412 .75067 .60091 .77773 .59602 .76564 .57913 Metetra .611 .705 .911 r .76564 .57913 .77773 .59602 .80508 .59104 .79315 .57406 Metetra .611 .706 .912 r .79315 .57406 .80508 .59104 .83274 .58597 .82096 .56889 Metetra .612 .706 .912 r .82096 .56889 .83274 .58597 .8607 .58081 .84908 .56362 Metetra .612 .707 .912 r .84908 .56362 .8607 .58081 .88896 .57556 .87752 .55826 Metetra .613 .708 .912 r .87752 .55826 .88896 .57556 .91754 .57022 .90627 .55281 Metetra .613 .708 .913 r .90627 .55281 .91754 .57022 .94644 .56478 .93535 .54727 Metetra .593 .683 .904 r .30393 .63754 .31824 .65367 .34088 .65046 .32664 .63432 Metetra .595 .685 .904 r .32664 .63432 .34088 .65046 .36377 .64712 .34961 .63096 Metetra .596 .686 .905 r .34961 .63096 .36377 .64712 .38691 .64367 .37283 .62748 Metetra .598 .688 .905 r .37283 .62748 .38691 .64367 .41029 .64009 .39631 .62387 Metetra .599 .69 .906 r .39631 .62387 .41029 .64009 .43393 .6364 .42004 .62014 Metetra .6 .691 .906 r .42004 .62014 .43393 .6364 .45783 .6326 .44403 .6163 Metetra .601 .692 .907 r .44403 .6163 .45783 .6326 .48199 .62869 .46829 .61234 Metetra .602 .694 .907 r .46829 .61234 .48199 .62869 .5064 .62468 .49281 .60828 Metetra .603 .695 .908 r .49281 .60828 .5064 .62468 .53108 .62057 .51761 .6041 Metetra .604 .696 .908 r .51761 .6041 .53108 .62057 .55603 .61635 .54267 .59982 Metetra .605 .697 .908 r .54267 .59982 .55603 .61635 .58125 .61204 .568 .59544 Metetra .606 .698 .909 r .568 .59544 .58125 .61204 .60674 .60762 .59362 .59095 Metetra .607 .699 .909 r .59362 .59095 .60674 .60762 .63251 .60311 .61952 .58636 Metetra .607 .7 .91 r .61952 .58636 .63251 .60311 .65856 .59851 .6457 .58167 Metetra .608 .701 .91 r .6457 .58167 .65856 .59851 .68489 .59381 .67217 .57689 Metetra .609 .702 .91 r .67217 .57689 .68489 .59381 .71151 .58901 .69893 .572 Metetra .609 .703 .91 r .69893 .572 .71151 .58901 .73843 .58412 .72599 .56702 Metetra .61 .703 .911 r .72599 .56702 .73843 .58412 .76564 .57913 .75335 .56194 Metetra .61 .704 .911 r .75335 .56194 .76564 .57913 .79315 .57406 .78102 .55676 Metetra .611 .705 .911 r .78102 .55676 .79315 .57406 .82096 .56889 .80899 .55149 Metetra .611 .706 .912 r .80899 .55149 .82096 .56889 .84908 .56362 .83728 .54612 Metetra .612 .706 .912 r .83728 .54612 .84908 .56362 .87752 .55826 .86588 .54065 Metetra .612 .707 .912 r .86588 .54065 .87752 .55826 .90627 .55281 .89481 .53509 Metetra .613 .708 .912 r .89481 .53509 .90627 .55281 .93535 .54727 .92407 .52943 Metetra .591 .68 .903 r .28942 .62107 .30393 .63754 .32664 .63432 .31221 .61785 Metetra .593 .683 .904 r .31221 .61785 .32664 .63432 .34961 .63096 .33526 .61448 Metetra .595 .685 .904 r .33526 .61448 .34961 .63096 .37283 .62748 .35856 .61098 Metetra .596 .686 .905 r .35856 .61098 .37283 .62748 .39631 .62387 .38212 .60734 Metetra .598 .688 .905 r .38212 .60734 .39631 .62387 .42004 .62014 .40595 .60358 Metetra .599 .69 .906 r .40595 .60358 .42004 .62014 .44403 .6163 .43004 .59969 Metetra .6 .691 .906 r .43004 .59969 .44403 .6163 .46829 .61234 .4544 .59568 Metetra .601 .692 .907 r .4544 .59568 .46829 .61234 .49281 .60828 .47902 .59156 Metetra .602 .694 .907 r .47902 .59156 .49281 .60828 .51761 .6041 .50393 .58733 Metetra .603 .695 .908 r .50393 .58733 .51761 .6041 .54267 .59982 .5291 .58298 Metetra .604 .696 .908 r .5291 .58298 .54267 .59982 .568 .59544 .55456 .57853 Metetra .605 .697 .908 r .55456 .57853 .568 .59544 .59362 .59095 .5803 .57397 Metetra .606 .698 .909 r .5803 .57397 .59362 .59095 .61952 .58636 .60632 .5693 Metetra .607 .699 .909 r .60632 .5693 .61952 .58636 .6457 .58167 .63263 .56453 Metetra .607 .7 .91 r .63263 .56453 .6457 .58167 .67217 .57689 .65924 .55966 Metetra .608 .701 .91 r .65924 .55966 .67217 .57689 .69893 .572 .68615 .55468 Metetra .609 .702 .91 r .68615 .55468 .69893 .572 .72599 .56702 .71335 .54961 Metetra .609 .703 .91 r .71335 .54961 .72599 .56702 .75335 .56194 .74086 .54443 Metetra .61 .703 .911 r .74086 .54443 .75335 .56194 .78102 .55676 .76869 .53915 Metetra .61 .704 .911 r .76869 .53915 .78102 .55676 .80899 .55149 .79682 .53377 Metetra .611 .705 .911 r .79682 .53377 .80899 .55149 .83728 .54612 .82527 .52829 Metetra .611 .706 .912 r .82527 .52829 .83728 .54612 .86588 .54065 .85405 .52272 Metetra .612 .706 .912 r .85405 .52272 .86588 .54065 .89481 .53509 .88316 .51704 Metetra .612 .707 .912 r .88316 .51704 .89481 .53509 .92407 .52943 .9126 .51126 Metetra .589 .678 .902 r .27472 .60425 .28942 .62107 .31221 .61785 .29758 .60104 Metetra .591 .68 .903 r .29758 .60104 .31221 .61785 .33526 .61448 .3207 .59766 Metetra .593 .683 .904 r .3207 .59766 .33526 .61448 .35856 .61098 .34409 .59414 Metetra .595 .685 .904 r .34409 .59414 .35856 .61098 .38212 .60734 .36774 .59048 Metetra .596 .686 .905 r .36774 .59048 .38212 .60734 .40595 .60358 .39165 .58668 Metetra .598 .688 .905 r .39165 .58668 .40595 .60358 .43004 .59969 .41584 .58275 Metetra .599 .69 .906 r .41584 .58275 .43004 .59969 .4544 .59568 .4403 .5787 Metetra .6 .691 .906 r .4403 .5787 .4544 .59568 .47902 .59156 .46503 .57453 Metetra .601 .692 .907 r .46503 .57453 .47902 .59156 .50393 .58733 .49004 .57023 Metetra .602 .694 .907 r .49004 .57023 .50393 .58733 .5291 .58298 .51533 .56582 Metetra .603 .695 .908 r .51533 .56582 .5291 .58298 .55456 .57853 .5409 .5613 Metetra .604 .696 .908 r .5409 .5613 .55456 .57853 .5803 .57397 .56677 .55666 Metetra .605 .697 .908 r .56677 .55666 .5803 .57397 .60632 .5693 .59292 .55192 Metetra .606 .698 .909 r .59292 .55192 .60632 .5693 .63263 .56453 .61936 .54707 Metetra .607 .699 .909 r .61936 .54707 .63263 .56453 .65924 .55966 .64611 .54211 Metetra .607 .7 .91 r .64611 .54211 .65924 .55966 .68615 .55468 .67316 .53704 Metetra .608 .701 .91 r .67316 .53704 .68615 .55468 .71335 .54961 .70051 .53187 Metetra .609 .702 .91 r .70051 .53187 .71335 .54961 .74086 .54443 .72817 .52659 Metetra .609 .703 .91 r .72817 .52659 .74086 .54443 .76869 .53915 .75615 .52121 Metetra .61 .703 .911 r .75615 .52121 .76869 .53915 .79682 .53377 .78445 .51573 Metetra .61 .704 .911 r .78445 .51573 .79682 .53377 .82527 .52829 .81307 .51014 Metetra .611 .705 .911 r .81307 .51014 .82527 .52829 .85405 .52272 .84202 .50444 Metetra .611 .706 .912 r .84202 .50444 .85405 .52272 .88316 .51704 .8713 .49865 Metetra .612 .706 .912 r .8713 .49865 .88316 .51704 .9126 .51126 .90092 .49275 Metetra .587 .676 .901 r .25982 .58707 .27472 .60425 .29758 .60104 .28275 .58387 Metetra .589 .678 .902 r .28275 .58387 .29758 .60104 .3207 .59766 .30595 .58049 Metetra .591 .68 .903 r .30595 .58049 .3207 .59766 .34409 .59414 .32941 .57696 Metetra .593 .683 .904 r .32941 .57696 .34409 .59414 .36774 .59048 .35314 .57328 Metetra .595 .685 .904 r .35314 .57328 .36774 .59048 .39165 .58668 .37715 .56945 Metetra .596 .686 .905 r .37715 .56945 .39165 .58668 .41584 .58275 .40143 .56549 Metetra .598 .688 .905 r .40143 .56549 .41584 .58275 .4403 .5787 .42599 .56139 Metetra .599 .69 .906 r .42599 .56139 .4403 .5787 .46503 .57453 .45082 .55716 Metetra .6 .691 .906 r .45082 .55716 .46503 .57453 .49004 .57023 .47594 .55281 Metetra .601 .692 .907 r .47594 .55281 .49004 .57023 .51533 .56582 .50135 .54834 Metetra .602 .694 .907 r .50135 .54834 .51533 .56582 .5409 .5613 .52704 .54375 Metetra .603 .695 .908 r .52704 .54375 .5409 .5613 .56677 .55666 .55302 .53904 Metetra .604 .696 .908 r .55302 .53904 .56677 .55666 .59292 .55192 .5793 .53421 Metetra .605 .697 .908 r .5793 .53421 .59292 .55192 .61936 .54707 .60588 .52927 Metetra .606 .698 .909 r .60588 .52927 .61936 .54707 .64611 .54211 .63277 .52423 Metetra .607 .699 .909 r .63277 .52423 .64611 .54211 .67316 .53704 .65995 .51907 Metetra .607 .7 .91 r .65995 .51907 .67316 .53704 .70051 .53187 .68745 .5138 Metetra .608 .701 .91 r .68745 .5138 .70051 .53187 .72817 .52659 .71527 .50842 Metetra .609 .702 .91 r .71527 .50842 .72817 .52659 .75615 .52121 .74341 .50293 Metetra .609 .703 .91 r .74341 .50293 .75615 .52121 .78445 .51573 .77187 .49734 Metetra .61 .703 .911 r .77187 .49734 .78445 .51573 .81307 .51014 .80066 .49164 Metetra .61 .704 .911 r .80066 .49164 .81307 .51014 .84202 .50444 .82978 .48583 Metetra .611 .705 .911 r .82978 .48583 .84202 .50444 .8713 .49865 .85924 .47991 Metetra .611 .706 .912 r .85924 .47991 .8713 .49865 .90092 .49275 .88905 .47389 Metetra .585 .673 .9 r .24473 .5695 .25982 .58707 .28275 .58387 .26772 .56632 Metetra .587 .676 .901 r .26772 .56632 .28275 .58387 .30595 .58049 .29099 .56296 Metetra .589 .678 .902 r .29099 .56296 .30595 .58049 .32941 .57696 .31453 .55942 Metetra .591 .68 .903 r .31453 .55942 .32941 .57696 .35314 .57328 .33834 .55573 Metetra .593 .683 .904 r .33834 .55573 .35314 .57328 .37715 .56945 .36244 .55187 Metetra .595 .685 .904 r .36244 .55187 .37715 .56945 .40143 .56549 .38681 .54788 Metetra .596 .686 .905 r .38681 .54788 .40143 .56549 .42599 .56139 .41146 .54374 Metetra .598 .688 .905 r .41146 .54374 .42599 .56139 .45082 .55716 .4364 .53946 Metetra .599 .69 .906 r .4364 .53946 .45082 .55716 .47594 .55281 .46163 .53505 Metetra .6 .691 .906 r .46163 .53505 .47594 .55281 .50135 .54834 .48715 .53051 Metetra .601 .692 .907 r .48715 .53051 .50135 .54834 .52704 .54375 .51296 .52585 Metetra .602 .694 .907 r .51296 .52585 .52704 .54375 .55302 .53904 .53907 .52107 Metetra .603 .695 .908 r .53907 .52107 .55302 .53904 .5793 .53421 .56547 .51617 Metetra .604 .696 .908 r .56547 .51617 .5793 .53421 .60588 .52927 .59219 .51114 Metetra .605 .697 .908 r .59219 .51114 .60588 .52927 .63277 .52423 .61921 .50601 Metetra .606 .698 .909 r .61921 .50601 .63277 .52423 .65995 .51907 .64654 .50075 Metetra .607 .699 .909 r .64654 .50075 .65995 .51907 .68745 .5138 .67419 .49538 Metetra .607 .7 .91 r .67419 .49538 .68745 .5138 .71527 .50842 .70215 .4899 Metetra .608 .701 .91 r .70215 .4899 .71527 .50842 .74341 .50293 .73045 .48431 Metetra .609 .702 .91 r .73045 .48431 .74341 .50293 .77187 .49734 .75907 .4786 Metetra .609 .703 .91 r .75907 .4786 .77187 .49734 .80066 .49164 .78803 .47279 Metetra .61 .703 .911 r .78803 .47279 .80066 .49164 .82978 .48583 .81733 .46686 Metetra .61 .704 .911 r .81733 .46686 .82978 .48583 .85924 .47991 .84697 .46082 Metetra .611 .705 .911 r .84697 .46082 .85924 .47991 .88905 .47389 .87697 .45466 Metetra .582 .67 .899 r .22944 .55152 .24473 .5695 .26772 .56632 .25249 .54838 Metetra .585 .673 .9 r .25249 .54838 .26772 .56632 .29099 .56296 .27582 .54504 Metetra .587 .676 .901 r .27582 .54504 .29099 .56296 .31453 .55942 .29944 .54151 Metetra .589 .678 .902 r .29944 .54151 .31453 .55942 .33834 .55573 .32333 .5378 Metetra .591 .68 .903 r .32333 .5378 .33834 .55573 .36244 .55187 .34751 .53393 Metetra .593 .683 .904 r .34751 .53393 .36244 .55187 .38681 .54788 .37197 .5299 Metetra .595 .685 .904 r .37197 .5299 .38681 .54788 .41146 .54374 .39673 .52573 Metetra .596 .686 .905 r .39673 .52573 .41146 .54374 .4364 .53946 .42177 .5214 Metetra .598 .688 .905 r .42177 .5214 .4364 .53946 .46163 .53505 .4471 .51694 Metetra .599 .69 .906 r .4471 .51694 .46163 .53505 .48715 .53051 .47273 .51234 Metetra .6 .691 .906 r .47273 .51234 .48715 .53051 .51296 .52585 .49866 .50761 Metetra .601 .692 .907 r .49866 .50761 .51296 .52585 .53907 .52107 .52489 .50276 Metetra .602 .694 .907 r .52489 .50276 .53907 .52107 .56547 .51617 .55142 .49777 Metetra .603 .695 .908 r .55142 .49777 .56547 .51617 .59219 .51114 .57827 .49266 Metetra .604 .696 .908 r .57827 .49266 .59219 .51114 .61921 .50601 .60542 .48743 Metetra .605 .697 .908 r .60542 .48743 .61921 .50601 .64654 .50075 .6329 .48209 Metetra .606 .698 .909 r .6329 .48209 .64654 .50075 .67419 .49538 .6607 .47662 Metetra .607 .699 .909 r .6607 .47662 .67419 .49538 .70215 .4899 .68882 .47103 Metetra .607 .7 .91 r .68882 .47103 .70215 .4899 .73045 .48431 .71727 .46533 Metetra .608 .701 .91 r .71727 .46533 .73045 .48431 .75907 .4786 .74606 .45951 Metetra .609 .702 .91 r .74606 .45951 .75907 .4786 .78803 .47279 .77519 .45357 Metetra .609 .703 .91 r .77519 .45357 .78803 .47279 .81733 .46686 .80466 .44752 Metetra .61 .703 .911 r .80466 .44752 .81733 .46686 .84697 .46082 .83449 .44135 Metetra .61 .704 .911 r .83449 .44135 .84697 .46082 .87697 .45466 .86467 .43507 Metetra .579 .666 .898 r .21395 .5331 .22944 .55152 .25249 .54838 .23706 .53001 Metetra .582 .67 .899 r .23706 .53001 .25249 .54838 .27582 .54504 .26045 .52671 Metetra .585 .673 .9 r .26045 .52671 .27582 .54504 .29944 .54151 .28414 .5232 Metetra .587 .676 .901 r .28414 .5232 .29944 .54151 .32333 .5378 .30811 .51949 Metetra .589 .678 .902 r .30811 .51949 .32333 .5378 .34751 .53393 .33237 .51561 Metetra .591 .68 .903 r .33237 .51561 .34751 .53393 .37197 .5299 .35692 .51156 Metetra .593 .683 .904 r .35692 .51156 .37197 .5299 .39673 .52573 .38177 .50735 Metetra .595 .685 .904 r .38177 .50735 .39673 .52573 .42177 .5214 .40691 .50298 Metetra .596 .686 .905 r .40691 .50298 .42177 .5214 .4471 .51694 .43235 .49847 Metetra .598 .688 .905 r .43235 .49847 .4471 .51694 .47273 .51234 .45809 .49381 Metetra .599 .69 .906 r .45809 .49381 .47273 .51234 .49866 .50761 .48413 .48901 Metetra .6 .691 .906 r .48413 .48901 .49866 .50761 .52489 .50276 .51048 .48408 Metetra .601 .692 .907 r .51048 .48408 .52489 .50276 .55142 .49777 .53715 .47902 Metetra .602 .694 .907 r .53715 .47902 .55142 .49777 .57827 .49266 .56412 .47382 Metetra .603 .695 .908 r .56412 .47382 .57827 .49266 .60542 .48743 .59142 .4685 Metetra .604 .696 .908 r .59142 .4685 .60542 .48743 .6329 .48209 .61904 .46306 Metetra .605 .697 .908 r .61904 .46306 .6329 .48209 .6607 .47662 .64698 .45749 Metetra .606 .698 .909 r .64698 .45749 .6607 .47662 .68882 .47103 .67526 .4518 Metetra .607 .699 .909 r .67526 .4518 .68882 .47103 .71727 .46533 .70387 .44598 Metetra .607 .7 .91 r .70387 .44598 .71727 .46533 .74606 .45951 .73283 .44004 Metetra .608 .701 .91 r .73283 .44004 .74606 .45951 .77519 .45357 .76213 .43399 Metetra .609 .702 .91 r .76213 .43399 .77519 .45357 .80466 .44752 .79178 .42781 Metetra .609 .703 .91 r .79178 .42781 .80466 .44752 .83449 .44135 .82179 .42152 Metetra .61 .703 .911 r .82179 .42152 .83449 .44135 .86467 .43507 .85216 .4151 Metetra .575 .662 .897 r .19827 .51421 .21395 .5331 .23706 .53001 .22142 .5112 Metetra .579 .666 .898 r .22142 .5112 .23706 .53001 .26045 .52671 .24487 .50795 Metetra .582 .67 .899 r .24487 .50795 .26045 .52671 .28414 .5232 .26862 .50447 Metetra .585 .673 .9 r .26862 .50447 .28414 .5232 .30811 .51949 .29267 .50078 Metetra .587 .676 .901 r .29267 .50078 .30811 .51949 .33237 .51561 .31701 .49689 Metetra .589 .678 .902 r .31701 .49689 .33237 .51561 .35692 .51156 .34165 .49282 Metetra .591 .68 .903 r .34165 .49282 .35692 .51156 .38177 .50735 .36659 .48858 Metetra .593 .683 .904 r .36659 .48858 .38177 .50735 .40691 .50298 .39183 .48418 Metetra .595 .685 .904 r .39183 .48418 .40691 .50298 .43235 .49847 .41737 .47961 Metetra .596 .686 .905 r .41737 .47961 .43235 .49847 .45809 .49381 .44322 .4749 Metetra .598 .688 .905 r .44322 .4749 .45809 .49381 .48413 .48901 .46938 .47004 Metetra .599 .69 .906 r .46938 .47004 .48413 .48901 .51048 .48408 .49585 .46504 Metetra .6 .691 .906 r .49585 .46504 .51048 .48408 .53715 .47902 .52264 .45989 Metetra .601 .692 .907 r .52264 .45989 .53715 .47902 .56412 .47382 .54975 .45461 Metetra .602 .694 .907 r .54975 .45461 .56412 .47382 .59142 .4685 .57718 .4492 Metetra .603 .695 .908 r .57718 .4492 .59142 .4685 .61904 .46306 .60494 .44366 Metetra .604 .696 .908 r .60494 .44366 .61904 .46306 .64698 .45749 .63304 .43798 Metetra .605 .697 .908 r .63304 .43798 .64698 .45749 .67526 .4518 .66147 .43218 Metetra .606 .698 .909 r .66147 .43218 .67526 .4518 .70387 .44598 .69024 .42625 Metetra .607 .699 .909 r .69024 .42625 .70387 .44598 .73283 .44004 .71936 .4202 Metetra .607 .7 .91 r .71936 .4202 .73283 .44004 .76213 .43399 .74884 .41402 Metetra .608 .701 .91 r .74884 .41402 .76213 .43399 .79178 .42781 .77867 .40772 Metetra .609 .702 .91 r .77867 .40772 .79178 .42781 .82179 .42152 .80886 .40129 Metetra .609 .703 .91 r .80886 .40129 .82179 .42152 .85216 .4151 .83942 .39473 Metetra .571 .658 .896 r .18238 .49481 .19827 .51421 .22142 .5112 .20558 .49191 Metetra .575 .662 .897 r .20558 .49191 .22142 .5112 .24487 .50795 .22909 .48873 Metetra .579 .666 .898 r .22909 .48873 .24487 .50795 .26862 .50447 .2529 .4853 Metetra .582 .67 .899 r .2529 .4853 .26862 .50447 .29267 .50078 .27701 .48163 Metetra .585 .673 .9 r .27701 .48163 .29267 .50078 .31701 .49689 .30143 .47776 Metetra .587 .676 .901 r .30143 .47776 .31701 .49689 .34165 .49282 .32615 .47368 Metetra .589 .678 .902 r .32615 .47368 .34165 .49282 .36659 .48858 .35118 .46942 Metetra .591 .68 .903 r .35118 .46942 .36659 .48858 .39183 .48418 .37652 .46498 Metetra .593 .683 .904 r .37652 .46498 .39183 .48418 .41737 .47961 .40216 .46037 Metetra .595 .685 .904 r .40216 .46037 .41737 .47961 .44322 .4749 .42812 .4556 Metetra .596 .686 .905 r .42812 .4556 .44322 .4749 .46938 .47004 .45439 .45068 Metetra .598 .688 .905 r .45439 .45068 .46938 .47004 .49585 .46504 .48099 .4456 Metetra .599 .69 .906 r .48099 .4456 .49585 .46504 .52264 .45989 .5079 .44038 Metetra .6 .691 .906 r .5079 .44038 .52264 .45989 .54975 .45461 .53514 .43502 Metetra .601 .692 .907 r .53514 .43502 .54975 .45461 .57718 .4492 .56271 .42951 Metetra .602 .694 .907 r .56271 .42951 .57718 .4492 .60494 .44366 .59062 .42387 Metetra .603 .695 .908 r .59062 .42387 .60494 .44366 .63304 .43798 .61886 .4181 Metetra .604 .696 .908 r .61886 .4181 .63304 .43798 .66147 .43218 .64745 .41218 Metetra .605 .697 .908 r .64745 .41218 .66147 .43218 .69024 .42625 .67638 .40614 Metetra .606 .698 .909 r .67638 .40614 .69024 .42625 .71936 .4202 .70567 .39996 Metetra .607 .699 .909 r .70567 .39996 .71936 .4202 .74884 .41402 .73531 .39366 Metetra .607 .7 .91 r .73531 .39366 .74884 .41402 .77867 .40772 .76532 .38722 Metetra .608 .701 .91 r .76532 .38722 .77867 .40772 .80886 .40129 .7957 .38066 Metetra .609 .702 .91 r .7957 .38066 .80886 .40129 .83942 .39473 .82645 .37396 Metetra .566 .652 .894 r .16631 .47485 .18238 .49481 .20558 .49191 .18954 .4721 Metetra .571 .658 .896 r .18954 .4721 .20558 .49191 .22909 .48873 .21309 .46902 Metetra .575 .662 .897 r .21309 .46902 .22909 .48873 .2529 .4853 .23696 .46566 Metetra .579 .666 .898 r .23696 .46566 .2529 .4853 .27701 .48163 .26114 .46204 Metetra .582 .67 .899 r .26114 .46204 .27701 .48163 .30143 .47776 .28563 .45818 Metetra .585 .673 .9 r .28563 .45818 .30143 .47776 .32615 .47368 .31043 .45411 Metetra .587 .676 .901 r .31043 .45411 .32615 .47368 .35118 .46942 .33554 .44984 Metetra .589 .678 .902 r .33554 .44984 .35118 .46942 .37652 .46498 .36097 .44537 Metetra .591 .68 .903 r .36097 .44537 .37652 .46498 .40216 .46037 .38672 .44072 Metetra .593 .683 .904 r .38672 .44072 .40216 .46037 .42812 .4556 .41278 .4359 Metetra .595 .685 .904 r .41278 .4359 .42812 .4556 .45439 .45068 .43917 .43092 Metetra .596 .686 .905 r .43917 .43092 .45439 .45068 .48099 .4456 .46588 .42578 Metetra .598 .688 .905 r .46588 .42578 .48099 .4456 .5079 .44038 .49292 .42048 Metetra .599 .69 .906 r .49292 .42048 .5079 .44038 .53514 .43502 .52029 .41503 Metetra .6 .691 .906 r .52029 .41503 .53514 .43502 .56271 .42951 .548 .40943 Metetra .601 .692 .907 r .548 .40943 .56271 .42951 .59062 .42387 .57605 .40369 Metetra .602 .694 .907 r .57605 .40369 .59062 .42387 .61886 .4181 .60444 .39781 Metetra .603 .695 .908 r .60444 .39781 .61886 .4181 .64745 .41218 .63318 .39179 Metetra .604 .696 .908 r .63318 .39179 .64745 .41218 .67638 .40614 .66228 .38562 Metetra .605 .697 .908 r .66228 .38562 .67638 .40614 .70567 .39996 .69173 .37933 Metetra .606 .698 .909 r .69173 .37933 .70567 .39996 .73531 .39366 .72155 .37289 Metetra .607 .699 .909 r .72155 .37289 .73531 .39366 .76532 .38722 .75174 .36632 Metetra .607 .7 .91 r .75174 .36632 .76532 .38722 .7957 .38066 .7823 .35962 Metetra .608 .701 .91 r .7823 .35962 .7957 .38066 .82645 .37396 .81325 .35278 Metetra .56 .646 .892 r .15006 .45427 .16631 .47485 .18954 .4721 .17331 .45172 Metetra .566 .652 .894 r .17331 .45172 .18954 .4721 .21309 .46902 .19689 .44878 Metetra .571 .658 .896 r .19689 .44878 .21309 .46902 .23696 .46566 .22081 .44552 Metetra .575 .662 .897 r .22081 .44552 .23696 .46566 .26114 .46204 .24504 .44196 Metetra .579 .666 .898 r .24504 .44196 .26114 .46204 .28563 .45818 .2696 .43815 Metetra .582 .67 .899 r .2696 .43815 .28563 .45818 .31043 .45411 .29448 .43409 Metetra .585 .673 .9 r .29448 .43409 .31043 .45411 .33554 .44984 .31968 .42981 Metetra .587 .676 .901 r .31968 .42981 .33554 .44984 .36097 .44537 .3452 .42533 Metetra .589 .678 .902 r .3452 .42533 .36097 .44537 .38672 .44072 .37104 .42065 Metetra .591 .68 .903 r .37104 .42065 .38672 .44072 .41278 .4359 .39721 .41579 Metetra .593 .683 .904 r .39721 .41579 .41278 .4359 .43917 .43092 .42371 .41075 Metetra .595 .685 .904 r .42371 .41075 .43917 .43092 .46588 .42578 .45054 .40554 Metetra .596 .686 .905 r .45054 .40554 .46588 .42578 .49292 .42048 .4777 .40016 Metetra .598 .688 .905 r .4777 .40016 .49292 .42048 .52029 .41503 .5052 .39463 Metetra .599 .69 .906 r .5052 .39463 .52029 .41503 .548 .40943 .53304 .38894 Metetra .6 .691 .906 r .53304 .38894 .548 .40943 .57605 .40369 .56123 .3831 Metetra .601 .692 .907 r .56123 .3831 .57605 .40369 .60444 .39781 .58977 .37711 Metetra .602 .694 .907 r .58977 .37711 .60444 .39781 .63318 .39179 .61867 .37097 Metetra .603 .695 .908 r .61867 .37097 .63318 .39179 .66228 .38562 .64793 .36469 Metetra .604 .696 .908 r .64793 .36469 .66228 .38562 .69173 .37933 .67755 .35827 Metetra .605 .697 .908 r .67755 .35827 .69173 .37933 .72155 .37289 .70754 .35171 Metetra .606 .698 .909 r .70754 .35171 .72155 .37289 .75174 .36632 .73791 .345 Metetra .607 .699 .909 r .73791 .345 .75174 .36632 .7823 .35962 .76867 .33815 Metetra .607 .7 .91 r .76867 .33815 .7823 .35962 .81325 .35278 .79981 .33117 Metetra .552 .638 .889 r .13363 .433 .15006 .45427 .17331 .45172 .15689 .43071 Metetra .56 .646 .892 r .15689 .43071 .17331 .45172 .19689 .44878 .18049 .42796 Metetra .566 .652 .894 r .18049 .42796 .19689 .44878 .22081 .44552 .20444 .42484 Metetra .571 .658 .896 r .20444 .42484 .22081 .44552 .24504 .44196 .22873 .42138 Metetra .575 .662 .897 r .22873 .42138 .24504 .44196 .2696 .43815 .25335 .41762 Metetra .579 .666 .898 r .25335 .41762 .2696 .43815 .29448 .43409 .2783 .4136 Metetra .582 .67 .899 r .2783 .4136 .29448 .43409 .31968 .42981 .30357 .40933 Metetra .585 .673 .9 r .30357 .40933 .31968 .42981 .3452 .42533 .32918 .40484 Metetra .587 .676 .901 r .32918 .40484 .3452 .42533 .37104 .42065 .35512 .40013 Metetra .589 .678 .902 r .35512 .40013 .37104 .42065 .39721 .41579 .38139 .39523 Metetra .591 .68 .903 r .38139 .39523 .39721 .41579 .42371 .41075 .408 .39014 Metetra .593 .683 .904 r .408 .39014 .42371 .41075 .45054 .40554 .43494 .38487 Metetra .595 .685 .904 r .43494 .38487 .45054 .40554 .4777 .40016 .46223 .37942 Metetra .596 .686 .905 r .46223 .37942 .4777 .40016 .5052 .39463 .48986 .3738 Metetra .598 .688 .905 r .48986 .3738 .5052 .39463 .53304 .38894 .51784 .36802 Metetra .599 .69 .906 r .51784 .36802 .53304 .38894 .56123 .3831 .54617 .36208 Metetra .6 .691 .906 r .54617 .36208 .56123 .3831 .58977 .37711 .57486 .35599 Metetra .601 .692 .907 r .57486 .35599 .58977 .37711 .61867 .37097 .60391 .34974 Metetra .602 .694 .907 r .60391 .34974 .61867 .37097 .64793 .36469 .63333 .34334 Metetra .603 .695 .908 r .63333 .34334 .64793 .36469 .67755 .35827 .66312 .33679 Metetra .604 .696 .908 r .66312 .33679 .67755 .35827 .70754 .35171 .69329 .33009 Metetra .605 .697 .908 r .69329 .33009 .70754 .35171 .73791 .345 .72384 .32324 Metetra .606 .698 .909 r .72384 .32324 .73791 .345 .76867 .33815 .75478 .31625 Metetra .607 .699 .909 r .75478 .31625 .76867 .33815 .79981 .33117 .78612 .30912 Metetra .543 .628 .886 r .11704 .4109 .13363 .433 .15689 .43071 .14028 .40898 Metetra .552 .638 .889 r .14028 .40898 .15689 .43071 .18049 .42796 .1639 .4065 Metetra .56 .646 .892 r .1639 .4065 .18049 .42796 .20444 .42484 .18787 .40356 Metetra .566 .652 .894 r .18787 .40356 .20444 .42484 .22873 .42138 .2122 .40023 Metetra .571 .658 .896 r .2122 .40023 .22873 .42138 .25335 .41762 .23687 .39657 Metetra .575 .662 .897 r .23687 .39657 .25335 .41762 .2783 .4136 .26188 .3926 Metetra .579 .666 .898 r .26188 .3926 .2783 .4136 .30357 .40933 .28724 .38836 Metetra .582 .67 .899 r .28724 .38836 .30357 .40933 .32918 .40484 .31293 .38387 Metetra .585 .673 .9 r .31293 .38387 .32918 .40484 .35512 .40013 .33896 .37915 Metetra .587 .676 .901 r .33896 .37915 .35512 .40013 .38139 .39523 .36533 .37422 Metetra .589 .678 .902 r .36533 .37422 .38139 .39523 .408 .39014 .39204 .36908 Metetra .591 .68 .903 r .39204 .36908 .408 .39014 .43494 .38487 .4191 .36375 Metetra .593 .683 .904 r .4191 .36375 .43494 .38487 .46223 .37942 .4465 .35823 Metetra .595 .685 .904 r .4465 .35823 .46223 .37942 .48986 .3738 .47426 .35254 Metetra .596 .686 .905 r .47426 .35254 .48986 .3738 .51784 .36802 .50238 .34667 Metetra .598 .688 .905 r .50238 .34667 .51784 .36802 .54617 .36208 .53085 .34063 Metetra .599 .69 .906 r .53085 .34063 .54617 .36208 .57486 .35599 .55969 .33443 Metetra .6 .691 .906 r .55969 .33443 .57486 .35599 .60391 .34974 .58889 .32806 Metetra .601 .692 .907 r .58889 .32806 .60391 .34974 .63333 .34334 .61847 .32154 Metetra .602 .694 .907 r .61847 .32154 .63333 .34334 .66312 .33679 .64843 .31486 Metetra .603 .695 .908 r .64843 .31486 .66312 .33679 .69329 .33009 .67877 .30803 Metetra .604 .696 .908 r .67877 .30803 .69329 .33009 .72384 .32324 .70951 .30104 Metetra .605 .697 .908 r .70951 .30104 .72384 .32324 .75478 .31625 .74064 .2939 Metetra .606 .698 .909 r .74064 .2939 .75478 .31625 .78612 .30912 .77217 .28661 Metetra .53 .615 .882 r .10033 .38781 .11704 .4109 .14028 .40898 .12352 .38642 Metetra .543 .628 .886 r .12352 .38642 .14028 .40898 .1639 .4065 .14712 .38431 Metetra .552 .638 .889 r .14712 .38431 .1639 .4065 .18787 .40356 .1711 .38163 Metetra .56 .646 .892 r .1711 .38163 .18787 .40356 .2122 .40023 .19546 .37849 Metetra .566 .652 .894 r .19546 .37849 .2122 .40023 .23687 .39657 .22017 .37495 Metetra .571 .658 .896 r .22017 .37495 .23687 .39657 .26188 .3926 .24524 .37106 Metetra .575 .662 .897 r .24524 .37106 .26188 .3926 .28724 .38836 .27066 .36687 Metetra .579 .666 .898 r .27066 .36687 .28724 .38836 .31293 .38387 .29643 .36241 Metetra .582 .67 .899 r .29643 .36241 .31293 .38387 .33896 .37915 .32255 .35769 Metetra .585 .673 .9 r .32255 .35769 .33896 .37915 .36533 .37422 .34901 .35273 Metetra .587 .676 .901 r .34901 .35273 .36533 .37422 .39204 .36908 .37583 .34756 Metetra .589 .678 .902 r .37583 .34756 .39204 .36908 .4191 .36375 .403 .34217 Metetra .591 .68 .903 r .403 .34217 .4191 .36375 .4465 .35823 .43052 .33659 Metetra .593 .683 .904 r .43052 .33659 .4465 .35823 .47426 .35254 .45841 .33082 Metetra .595 .685 .904 r .45841 .33082 .47426 .35254 .50238 .34667 .48665 .32486 Metetra .596 .686 .905 r .48665 .32486 .50238 .34667 .53085 .34063 .51527 .31872 Metetra .598 .688 .905 r .51527 .31872 .53085 .34063 .55969 .33443 .54425 .31242 Metetra .599 .69 .906 r .54425 .31242 .55969 .33443 .58889 .32806 .57361 .30594 Metetra .6 .691 .906 r .57361 .30594 .58889 .32806 .61847 .32154 .60335 .29929 Metetra .601 .692 .907 r .60335 .29929 .61847 .32154 .64843 .31486 .63348 .29248 Metetra .602 .694 .907 r .63348 .29248 .64843 .31486 .67877 .30803 .664 .28551 Metetra .603 .695 .908 r .664 .28551 .67877 .30803 .70951 .30104 .69492 .27837 Metetra .604 .696 .908 r .69492 .27837 .70951 .30104 .74064 .2939 .72624 .27108 Metetra .605 .697 .908 r .72624 .27108 .74064 .2939 .77217 .28661 .75797 .26363 Metetra .512 .596 .875 r .08353 .36344 .10033 .38781 .12352 .38642 .10662 .36286 Metetra .53 .615 .882 r .10662 .36286 .12352 .38642 .14712 .38431 .13017 .36128 Metetra .543 .628 .886 r .13017 .36128 .14712 .38431 .1711 .38163 .15414 .35896 Metetra .552 .638 .889 r .15414 .35896 .1711 .38163 .19546 .37849 .17851 .35607 Metetra .56 .646 .892 r .17851 .35607 .19546 .37849 .22017 .37495 .20325 .35271 Metetra .566 .652 .894 r .20325 .35271 .22017 .37495 .24524 .37106 .22837 .34894 Metetra .571 .658 .896 r .22837 .34894 .24524 .37106 .27066 .36687 .25385 .34483 Metetra .575 .662 .897 r .25385 .34483 .27066 .36687 .29643 .36241 .27969 .34041 Metetra .579 .666 .898 r .27969 .34041 .29643 .36241 .32255 .35769 .30589 .33571 Metetra .582 .67 .899 r .30589 .33571 .32255 .35769 .34901 .35273 .33244 .33074 Metetra .585 .673 .9 r .33244 .33074 .34901 .35273 .37583 .34756 .35936 .32554 Metetra .587 .676 .901 r .35936 .32554 .37583 .34756 .403 .34217 .38664 .32011 Metetra .589 .678 .902 r .38664 .32011 .403 .34217 .43052 .33659 .41428 .31447 Metetra .591 .68 .903 r .41428 .31447 .43052 .33659 .45841 .33082 .44229 .30862 Metetra .593 .683 .904 r .44229 .30862 .45841 .33082 .48665 .32486 .47067 .30258 Metetra .595 .685 .904 r .47067 .30258 .48665 .32486 .51527 .31872 .49942 .29635 Metetra .596 .686 .905 r .49942 .29635 .51527 .31872 .54425 .31242 .52855 .28993 Metetra .598 .688 .905 r .52855 .28993 .54425 .31242 .57361 .30594 .55806 .28334 Metetra .599 .69 .906 r .55806 .28334 .57361 .30594 .60335 .29929 .58797 .27657 Metetra .6 .691 .906 r .58797 .27657 .60335 .29929 .63348 .29248 .61826 .26963 Metetra .601 .692 .907 r .61826 .26963 .63348 .29248 .664 .28551 .64896 .26251 Metetra .602 .694 .907 r .64896 .26251 .664 .28551 .69492 .27837 .68006 .25523 Metetra .603 .695 .908 r .68006 .25523 .69492 .27837 .72624 .27108 .71157 .24779 Metetra .604 .696 .908 r .71157 .24779 .72624 .27108 .75797 .26363 .7435 .24017 Metetra .484 .567 .864 r .06675 .33724 .08353 .36344 .10662 .36286 .08963 .338 Metetra .512 .596 .875 r .08963 .338 .10662 .36286 .13017 .36128 .11308 .33722 Metetra .53 .615 .882 r .11308 .33722 .13017 .36128 .15414 .35896 .137 .33543 Metetra .543 .628 .886 r .137 .33543 .15414 .35896 .17851 .35607 .16136 .3329 Metetra .552 .638 .889 r .16136 .3329 .17851 .35607 .20325 .35271 .18612 .32978 Metetra .56 .646 .892 r .18612 .32978 .20325 .35271 .22837 .34894 .21127 .32619 Metetra .566 .652 .894 r .21127 .32619 .22837 .34894 .25385 .34483 .2368 .3222 Metetra .571 .658 .896 r .2368 .3222 .25385 .34483 .27969 .34041 .26271 .31785 Metetra .575 .662 .897 r .26271 .31785 .27969 .34041 .30589 .33571 .28898 .31318 Metetra .579 .666 .898 r .28898 .31318 .30589 .33571 .33244 .33074 .31562 .30823 Metetra .582 .67 .899 r .31562 .30823 .33244 .33074 .35936 .32554 .34263 .30301 Metetra .585 .673 .9 r .34263 .30301 .35936 .32554 .38664 .32011 .37002 .29754 Metetra .587 .676 .901 r .37002 .29754 .38664 .32011 .41428 .31447 .39777 .29185 Metetra .589 .678 .902 r .39777 .29185 .41428 .31447 .44229 .30862 .4259 .28593 Metetra .591 .68 .903 r .4259 .28593 .44229 .30862 .47067 .30258 .45441 .27981 Metetra .593 .683 .904 r .45441 .27981 .47067 .30258 .49942 .29635 .4833 .27349 Metetra .595 .685 .904 r .4833 .27349 .49942 .29635 .52855 .28993 .51257 .26696 Metetra .596 .686 .905 r .51257 .26696 .52855 .28993 .55806 .28334 .54224 .26025 Metetra .598 .688 .905 r .54224 .26025 .55806 .28334 .58797 .27657 .5723 .25336 Metetra .599 .69 .906 r .5723 .25336 .58797 .27657 .61826 .26963 .60277 .24628 Metetra .6 .691 .906 r .60277 .24628 .61826 .26963 .64896 .26251 .63364 .23903 Metetra .601 .692 .907 r .63364 .23903 .64896 .26251 .68006 .25523 .66492 .2316 Metetra .602 .694 .907 r .66492 .2316 .68006 .25523 .71157 .24779 .69662 .22399 Metetra .603 .695 .908 r .69662 .22399 .71157 .24779 .7435 .24017 .72875 .21622 Metetra .428 .51 .841 r .05022 .30778 .06675 .33724 .08963 .338 .07265 .31128 Metetra .484 .567 .864 r .07265 .31128 .08963 .338 .11308 .33722 .0959 .31185 Metetra .512 .596 .875 r .0959 .31185 .11308 .33722 .137 .33543 .11972 .31086 Metetra .53 .615 .882 r .11972 .31086 .137 .33543 .16136 .3329 .14403 .30885 Metetra .543 .628 .886 r .14403 .30885 .16136 .3329 .18612 .32978 .16879 .30609 Metetra .552 .638 .889 r .16879 .30609 .18612 .32978 .21127 .32619 .19395 .30275 Metetra .56 .646 .892 r .19395 .30275 .21127 .32619 .2368 .3222 .21952 .29892 Metetra .566 .652 .894 r .21952 .29892 .2368 .3222 .26271 .31785 .24548 .29468 Metetra .571 .658 .896 r .24548 .29468 .26271 .31785 .28898 .31318 .27182 .29007 Metetra .575 .662 .897 r .27182 .29007 .28898 .31318 .31562 .30823 .29854 .28515 Metetra .579 .666 .898 r .29854 .28515 .31562 .30823 .34263 .30301 .32564 .27993 Metetra .582 .67 .899 r .32564 .27993 .34263 .30301 .37002 .29754 .35313 .27444 Metetra .585 .673 .9 r .35313 .27444 .37002 .29754 .39777 .29185 .38099 .26871 Metetra .587 .676 .901 r .38099 .26871 .39777 .29185 .4259 .28593 .40924 .26273 Metetra .589 .678 .902 r .40924 .26273 .4259 .28593 .45441 .27981 .43787 .25653 Metetra .591 .68 .903 r .43787 .25653 .45441 .27981 .4833 .27349 .4669 .25011 Metetra .593 .683 .904 r .4669 .25011 .4833 .27349 .51257 .26696 .49632 .24349 Metetra 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Male productivity and EPP", "Subsection"], Cell[CellGroupData[{ Cell["\<\ The function sidepaymentsmod[game] is the same as sidepayments[game] but \ gives more output: In addition to the minimum EPP each male requires to get \ at the core, it also reports the maximum paternity each male is willing to \ pay. This is then used for relating within-pair paternity to male \ productivity.\ \>", "Subsubsection"], Cell[BoxData[ \(\(\(sidepaymentsmod[ game_]\)\(:=\)\(Module[{maxout, alternatives, n, arr, malepayoffs, femalepayoffs, satisfaction, \ sidepaymatrix, desired, rsfe, sr, sidep, sidearr, totmales, totfemales, minsidepmale, minsidepfemale, malesidep, \ femalesidep, totsidep, default, maxpos, defgame, defaultarr, defaultpayoff, willpaymales, willpay}, \[IndentingNewLine]n = Length[game]; \[IndentingNewLine] (*We\ start\ by\ identifying\ the\ \ maximum\ output\ arrangements*) \[IndentingNewLine]maxout = maxOutput[ game]; \[IndentingNewLine]\[IndentingNewLine] (*The\ following\ \ computes\ whether\ and\ how\ much\ sidepayment\ is\ needed\ to\ whom\ to\ \ stabilize\ each\ of\ the\ mating\ arrangements\ that\ maximize\ the\ output\ *) \[IndentingNewLine]\[IndentingNewLine]sidep = \ \(Reap[\[IndentingNewLine]\(Do[\[IndentingNewLine]\[IndentingNewLine]malearr \ = maxout[\([i + 2]\)]; \ (*which\ female\ each\ male\ is\ mating\ *) \[IndentingNewLine]femalearr = Table[\(Position[malearr, x_?\((# \[Equal] j &)\)]\)[\([1, 1]\)], {j, 1, n}]; \ (*which\ male\ each\ female\ is\ mating\ *) \[IndentingNewLine]malepayoffs = Table[game[\([j, malearr[\([j]\)]]\)], {j, 1, n}]; \ (*the\ payoff\ to\ each\ male\ *) \[IndentingNewLine]femalepayoffs = Table[game[\([femalearr[\([j]\)], j]\)], {j, 1, n}]; \ (*the\ payoff\ to\ each\ female\ *) \[IndentingNewLine]\[IndentingNewLine] (*the\ following\ creates\ a\ \ matrix\ that\ has\ 1\ in\ a\ position\ if\ the\ corresponding\ pairing\ in\ \ the\ original\ game\ matrix\ is\ preferred\ by\ both\ the\ male\ and\ the\ \ female\ to\ their\ pairing\ under\ the\ maximum\ output\ mating\ arrangement\ \ *) \[IndentingNewLine]\[IndentingNewLine]satisfaction = Table[If[ game[\([k, j]\)] > malepayoffs[\([k]\)] && game[\([k, j]\)] > femalepayoffs[\([j]\)], \ 1, 0], {k, 1, n}, {j, 1, n}]; \ \[IndentingNewLine]\[IndentingNewLine] (*Now, \ \ the\ individuals\ who\ have\ a\ 1\ for\ any\ of\ their\ potential\ pairings\ \ need\ to\ be\ compansated\ in\ order\ to\ agree\ on\ the\ maximum\ output\ \ arrangement*) \[IndentingNewLine]\[IndentingNewLine]sidepaymatrix = Table[{"\<|\>"}, {k, 1, n}, {j, 1, n}]; \[IndentingNewLine]\[IndentingNewLine] (*The\ \ following\ provides\ information\ about\ which\ male\ should\ be\ getting\ \ how\ much\ sidepayment\ to\ prevent\ each\ particular\ pair\ from\ forming . \ \ The\ information\ is\ stored\ in\ a\ n\ by\ n\ matrix*) \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]desired = Flatten[ Position[satisfaction[\([m]\)], \ x_?\((# \[Equal] 1 &)\)]]; \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]sr = game[\([m, desired[\([l]\)]]\)] - malepayoffs[\([m]\)]; \ \[IndentingNewLine]sidepaymatrix = Insert[sidepaymatrix, \ x > sr, {m, desired[\([l]\)], 1}], \ {l, 1, Length[desired]}\ ];\[IndentingNewLine], {m, 1, n}]; \[IndentingNewLine]\[IndentingNewLine]Do[\ \[IndentingNewLine]\[IndentingNewLine]desired = Flatten[ Position[satisfaction[\([All, \ f]\)], \ x_?\((# \[Equal] 1 &)\)]]; \[IndentingNewLine]\ \[IndentingNewLine]Do[\[IndentingNewLine]\[IndentingNewLine]sr = game[\([desired[\([l]\)], f]\)] - femalepayoffs[\([f]\)]; \ \[IndentingNewLine]sidepaymatrix = Insert[sidepaymatrix, y > sr, {desired[\([l]\)], f\ , \(-1\)}], \ {l, 1, Length[ desired]}\ \ \[IndentingNewLine]];\[IndentingNewLine], {f, 1, n}]; \[IndentingNewLine]\[IndentingNewLine]Sow[ sidepaymatrix], {i, 1, maxout[\([2]\)]}];\)\[IndentingNewLine]]\)[\([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine] (*sidep\ is\ a\ \ list\ of\ matrices, \ where\ each\ matrix\ corresponds\ to\ one\ of\ the\ alternative\ \ maximum\ output\ arrangements . \ The\ entries\ in\ the\ matrix, \ where\ they\ exist, \ give\ how\ much\ the\ male\ and\ female\ need\ to\ be\ paid\ in\ \ order\ to\ forsake\ that\ particular\ pairing\ in\ favor\ of\ this\ specific\ \ maximum\ output\ arrangement . \ The\ entries\ are\ in\ the\ format\ {x > minimum\ sidepayment\ to\ the\ male | y > minimum\ sidepayment\ to\ the\ female}\ \ *) \[IndentingNewLine]\[IndentingNewLine] (*To\ see\ what\ each\ individual\ \ is\ willing\ to\ "\", \ we\ calculate\ their\ "\"\ payoffs\ \((i . e . \ without\ sidepayments)\)\ by\ the\ following\ algorithm . \ Take\ the\ highest\ number\ from\ the\ matrix, \ delete\ its\ row\ and\ column, \ and\ \(\(repeat\)\(.\)\)*) \[IndentingNewLine]\[IndentingNewLine]\ default = \(Reap[ defgame = game; \[IndentingNewLine]Do[ Sow[Max[ defgame]]; \[IndentingNewLine]maxpos = \(Position[ defgame, x_?\((# \[Equal] Max[defgame] &)\)]\)[\([1]\)]; \ \ \[IndentingNewLine]defgame = Delete[defgame, maxpos[\([1]\)]]; \[IndentingNewLine]defgame = Delete[defgame, \ Table[{g, maxpos[\([2]\)]}, {g, 1, Length[defgame]}]]\[IndentingNewLine], {b, 1, n}]\[IndentingNewLine]]\)[\([2, 1]\)]; \[IndentingNewLine]defaultarr = Sort[Table[\(Position[game, x_?\((# \[Equal] default[\([b]\)] &)\)]\)[\([1]\)], {b, 1, n}]]; \[IndentingNewLine]\[IndentingNewLine] (*defaultarr\ \ gives\ the\ pairings\ which\ are\ found\ according\ to\ the\ above\ \ algorithm, \ and\ would\ be\ the\ core\ if\ sidepayments\ were\ not\ allowed\ \ *) \[IndentingNewLine]\[IndentingNewLine]defaultpayoff = Table[game[\([defaultarr[\([k, 1]\)], defaultarr[\([k, 2]\)]]\)], {k, 1, n}]; \[IndentingNewLine] (*default\ payoff\ gives\ the\ payoff\ \ to\ males\ \((in\ numberical\ order)\)\ from\ the\ default\ \ \(\(pairing\)\(.\)\)\ *) \[IndentingNewLine]\[IndentingNewLine]willpaymales = \ \(Reap[\[IndentingNewLine]Do[ malearr = maxout[\([i + 2]\)]; \[IndentingNewLine]malepayoffs = Table[game[\([j, malearr[\([j]\)]]\)], {j, 1, n}]; \[IndentingNewLine]willpay = Table[Max[ 0, \((malepayoffs[\([j]\)] - defaultpayoff[\([j]\)])\) \ (*\(/\)\(malepayoffs[\([j]\)]\)*) ], {j, 1, n}]; \[IndentingNewLine]Sow[ willpay], {i, 1, maxout[\([2]\)]}\[IndentingNewLine]]]\)[\([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine]malesidep = \ \(Reap[\[IndentingNewLine]Do[ sidearr = sidep[\([i]\)]; \[IndentingNewLine]maleside = Table[Max[ Table[If[Length[sidearr[\([k, l]\)]] \[Equal] 3, Part[sidearr[\([k, l, 1]\)], 2], 0], {l, 1, n}]], {k, 1, n}]; \[IndentingNewLine]Sow[ maleside]\[IndentingNewLine], {i, 1, \ maxout[\([2]\)]}\[IndentingNewLine]]\[IndentingNewLine]]\)[\ \([2, 1]\)]; \[IndentingNewLine]femalesidep = \(Reap[\[IndentingNewLine]Do[ sidearr = sidep[\([i]\)]; \[IndentingNewLine]femaleside = Table[Max[ Table[If[Length[sidearr[\([k, l]\)]] \[Equal] 3, Part[sidearr[\([k, l, 3]\)], 2], 0], {k, 1, n}]], {l, 1, n}]; \[IndentingNewLine]Sow[ femaleside]\[IndentingNewLine], {i, 1, \ maxout[\([2]\)]}\[IndentingNewLine]]\[IndentingNewLine]]\)[\ \([2, 1]\)]; \[IndentingNewLine]\[IndentingNewLine] (*the\ following\ \ commands\ calculate\ the\ total\ amount\ of\ sidepayment\ required\ for\ each\ \ mating\ arrangement\ and\ take\ the\ three\ that\ require\ the\ least\ *) \[IndentingNewLine]\[IndentingNewLine]totsidep = Table[{Total[malesidep[\([k]\)]], Total[femalesidep[\([k]\)]]}, {k, 1, maxout[\([2]\)]}]; \ \[IndentingNewLine]\[IndentingNewLine]minsidepmale = Ordering[totsidep[\([All, 1]\)], Min[1, maxout[\([2]\)]]]; \[IndentingNewLine]minsidepfemale = Ordering[totsidep[\([All, 2]\)], Min[1, maxout[\([2]\)]]]; \[IndentingNewLine]resultmale = Table[{maxout[\([minsidepmale[\([i]\)] + 2]\)], sidep[\([minsidepmale[\([i]\)]]\)], totsidep[\([minsidepmale[\([i]\)], 1]\)]}, {i, 1, Min[1, maxout[\([2]\)]]}]; \[IndentingNewLine]resultfemale = Table[{maxout[\([minsidepfemale[\([i]\)] + 2]\)], sidep[\([minsidepfemale[\([i]\)]]\)], \ totsidep[\([minsidepfemale[\([i]\)], 2]\)]}, {i, 1, Min[1, maxout[\([2]\)]]}]; \[IndentingNewLine]totsidep; \ \[IndentingNewLine]{resultmale[\([1, 3]\)]/maxout[\([1]\)]*100, \ resultfemale[\([1, 3]\)]/maxout[\([1]\)]*100, maxout[\([1]\)], malesidep[\([minsidepmale[\([1]\)]]\)], femalesidep[\([minsidepfemale[\([1]\)]]\)], willpaymales[\([minsidepmale[\([1]\)]]\)]}\[IndentingNewLine]]\)\( \ (*End\ of\ Module[]*) \)\)\)], "Input", CellLabel->"In[24]:="], Cell[CellGroupData[{ Cell[BoxData[ \(game\ // MatrixForm\)], "Input", CellLabel->"In[25]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"8", "4"}, {"9", "7"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", CellLabel->"Out[25]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sidepaymentsmod[game]\)], "Input", CellLabel->"In[26]:="], Cell[BoxData[ \({40\/3, 20\/3, 15, {0, 2}, {1, 0}, {4, 0}}\)], "Output", CellLabel->"Out[26]="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ The function below carries out the Monte Carlo simulations for the relation \ between EPP gained and male productivity\ \>", "Subsubsection"], Cell[BoxData[ \(\(maletraitgain[a_, r_, n_] := Module[{list, randommales, randomfemales, randomgame, result}, \[IndentingNewLine]prod[male_, \ female_] := 5\ Sqrt[\((male + \ female)\)]; \[IndentingNewLine]list = \(Reap[ Do[randommales = Table[Random[Real, \ {0.0001, r}], \ {l, 1, n}]; \[IndentingNewLine]randomfemales = Table[Random[Real, \ {0.0001, r}], \ {k, 1, n}]; \[IndentingNewLine]randomgame = Table[N[ prod[randommales[\([i]\)], randomfemales[\([j]\)]]], \ {i, 1, n}, {j, 1, n}]; \[IndentingNewLine]result = sidepaymentsmod[randomgame]; \[IndentingNewLine]corr = Table[{randommales[\([j]\)], result[\([4, j]\)]}, {j, 1, n}]; \[IndentingNewLine]Sow[{result[\([1]\)], corr}], {i, 1, a}]]\)[\([2, 1]\)]; \[IndentingNewLine]Flatten[ Join[Table[list[\([i, 2]\)], {i, 1, a}]], 1]\[IndentingNewLine]];\)\)], "Input", CellLabel->"In[27]:="], Cell[BoxData[ \(\(corr = maletraitgain[30, 4, 4];\)\)], "Input", CellLabel->"In[28]:="], Cell[CellGroupData[{ Cell[BoxData[{ \(\(point1 = ListPlot[corr, \ Frame \[Rule] True, \ Axes \[Rule] False, FrameLabel \[Rule] {StyleForm["\", FontWeight \[Rule] "\", \ 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WPP and male \ productivity\ \>", "Subsubsection"], Cell[BoxData[ \(\(maletraitloss[a_, r_, n_] := Module[{list, randommales, randomfemales, randomgame, result}, \[IndentingNewLine]prod[male_, \ female_] := 5\ Sqrt[\((male + \ female)\)]; \[IndentingNewLine]list = \(Reap[ Do[randommales = Table[Random[Real, \ {0.0001, r}], \ {l, 1, n}]; \[IndentingNewLine]randomfemales = Table[Random[Real, \ {0.0001, r}], \ {k, 1, n}]; \[IndentingNewLine]randomgame = Table[N[ prod[randommales[\([i]\)], randomfemales[\([j]\)]]], \ {i, 1, n}, {j, 1, n}]; \[IndentingNewLine]result = sidepaymentsmod[randomgame]; \[IndentingNewLine]corr = Table[{randommales[\([j]\)], result[\([6, j]\)]}, {j, 1, n}]; \[IndentingNewLine]Sow[{result[\([1]\)], corr}], {i, 1, a}]]\)[\([2, 1]\)]; \[IndentingNewLine]Flatten[ Join[Table[list[\([i, 2]\)], {i, 1, a}]], 1]\[IndentingNewLine]];\)\)], "Input", CellLabel->"In[33]:="], Cell[BoxData[ \(\(corr1 = maletraitloss[30, 4, 4];\)\)], "Input", CellLabel->"In[34]:="], 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