(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 451021, 18908]*) (*NotebookOutlinePosition[ 536930, 21805]*) (* CellTagsIndexPosition[ 536662, 21794]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ \[LightBulb]\[LightBulb]\[LightBulb] DYNAMO 2x2 \[LightBulb]\ \[LightBulb]\[LightBulb] Phase Diagrams for Evolutionary Dynamics\ \>", "Title", CellFrame->True, TextAlignment->Center, FontSize->32, FontColor->GrayLevel[1], Background->RGBColor[0, 0, 0.500008]], Cell[CellGroupData[{ Cell["User-defined Parameters", "Subtitle", CellDingbat->None], Cell["\<\ When you have finished specifying parameters, click on the rightmost vertical \ bar and press Enter (or Shift-Enter) to run the program.\ \>", "Text", Evaluatable->False, FontFamily->"Palatino", FontSize->14], Cell[BoxData[ \(Off[\ General::spell1\ ]\ ; \ Off[\ General::spell]\ ;\)], "Input", CellOpen->False, InitializationCell->True], Cell[CellGroupData[{ Cell[TextData[StyleBox["Choice of game", "Section"]], "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "Choose a normal form game here. To use one of the built-in payoff \ matrices, select the matrix on the right hand side of \"", StyleBox["U", FontWeight->"Bold"], " = .\" (including the parentheses but not the semicolon); then the press \ the button corresponding to the game you desire." }], "Text", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[GridBox[{ { ButtonBox[\(\(12\)\(\ \)\(Coordination\)\(\ \)\), ButtonData:>RowBox[ {"(", "\[NegativeThinSpace]", GridBox[ {{ RowBox[ {"{", RowBox[ {"1", ",", "1"}], "}"}], RowBox[ {"{", RowBox[ {"0", ",", "0"}], "}"}]}, { RowBox[ {"{", RowBox[ {"0", ",", "0"}], "}"}], RowBox[ {"{", RowBox[ {"2", ",", "2"}], "}"}]}}], "\[NegativeThinSpace]", ")"}]], ButtonBox[\(Pure\ Coordination\), ButtonData:>RowBox[ {"(", "\[NegativeThinSpace]", GridBox[ {{ RowBox[ {"{", RowBox[ {"1", ",", "1"}], "}"}], RowBox[ {"{", RowBox[ {"0", ",", "0"}], "}"}]}, { RowBox[ {"{", RowBox[ {"0", ",", "0"}], "}"}], RowBox[ {"{", RowBox[ {"1", ",", "1"}], "}"}]}}], "\[NegativeThinSpace]", ")"}]], ButtonBox[\(\(Matching\)\(\ \)\(Pennies\)\(\ \)\), ButtonData:>RowBox[ {"(", "\[NegativeThinSpace]", GridBox[ {{ RowBox[ {"{", RowBox[ {"1", ",", RowBox[ {"-", "1"}]}], "}"}], RowBox[ {"{", RowBox[ { RowBox[ {"-", "1"}], ",", "1"}], "}"}]}, { RowBox[ {"{", RowBox[ { RowBox[ {"-", "1"}], ",", "1"}], "}"}], RowBox[ {"{", RowBox[ {"1", ",", RowBox[ {"-", "1"}]}], "}"}]}}], "\[NegativeThinSpace]", ")"}]], ButtonBox[\(\(Prisoner'\) \(s\)\(\ \)\(Dilemma\)\(\ \)\), ButtonData:>RowBox[ {"(", "\[NegativeThinSpace]", GridBox[ {{ RowBox[ {"{", RowBox[ {"2", ",", "2"}], "}"}], RowBox[ {"{", RowBox[ {"0", ",", "3"}], "}"}]}, { RowBox[ {"{", RowBox[ {"3", ",", "0"}], "}"}], RowBox[ {"{", RowBox[ {"1", ",", "1"}], "}"}]}}], "\[NegativeThinSpace]", ")"}]], ButtonBox[\(Stag\ Hunt\), ButtonData:>RowBox[ {"(", "\[NegativeThinSpace]", GridBox[ {{ RowBox[ {"{", RowBox[ {"5", ",", "5"}], "}"}], RowBox[ {"{", RowBox[ {"0", ",", "4"}], "}"}]}, { RowBox[ {"{", RowBox[ {"4", ",", "0"}], "}"}], RowBox[ {"{", RowBox[ {"2", ",", "2"}], "}"}]}}], "\[NegativeThinSpace]", ")"}]], ButtonBox[\(Chain\ Store\), ButtonData:>RowBox[ {"(", "\[NegativeThinSpace]", GridBox[ {{ RowBox[ {"{", RowBox[ {"0", ",", "4"}], "}"}], RowBox[ {"{", RowBox[ {"0", ",", "4"}], "}"}]}, { RowBox[ {"{", RowBox[ {"2", ",", "2"}], "}"}], RowBox[ {"{", RowBox[ { RowBox[ {"-", "4"}], ",", RowBox[ {"-", "4"}]}], "}"}]}}], "\[NegativeThinSpace]", ")"}]]} }, RowSpacings->0, ColumnSpacings->0, GridDefaultElement:>ButtonBox[ "\\[Placeholder]"]]], "Input", Active->True, Evaluatable->False], Cell[BoxData[ RowBox[{ RowBox[{"U", "=", RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\({1, \(-1\)}\), \({\(-1\), 1}\)}, {\({\(-1\), 1}\), \({1, \(-1\)}\)} }], "\[NegativeThinSpace]", ")"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Nonlinear population games", FontSlant->"Italic"]], "SmallText"], Cell[TextData[{ "To choose a nonlinear game, set ", StyleBox["nonlineargame", FontWeight->"Bold"], " = 1 and define ", StyleBox["F1[x_,y_]", FontWeight->"Bold"], " and ", StyleBox["F2[x_,y_]", FontWeight->"Bold"], " as you like. In doing so, the components of x should be entered as \ x[[1]], x[[2]], and the components of y should be entered similarly. The \ default value of F1[x_,y_] is A.y and F2[x_,y_] is B'.x, the payoff vector \ field for the normal form game U." }], "Text", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[{ RowBox[{\(nonlineargame\ = 0\ ;\), "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"A", "=", RowBox[{"(", GridBox[{ {\(U\[LeftDoubleBracket]1, 1, 1\[RightDoubleBracket]\), \(U\[LeftDoubleBracket]1, 2, 1\[RightDoubleBracket]\)}, {\(U\[LeftDoubleBracket]2, 1, 1\[RightDoubleBracket]\), \(U\[LeftDoubleBracket]2, 2, 1\[RightDoubleBracket]\)} }], ")"}]}], " ", ";", " ", RowBox[{"B", "=", RowBox[{"(", GridBox[{ {\(U\[LeftDoubleBracket]1, 1, 2\[RightDoubleBracket]\), \(U\[LeftDoubleBracket]1, 2, 2\[RightDoubleBracket]\)}, {\(U\[LeftDoubleBracket]2, 1, 2\[RightDoubleBracket]\), \(U\[LeftDoubleBracket]2, 2, 2\[RightDoubleBracket]\)} }], ")"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{\(F1[x_, y_]\ := A . y\ ;\), " "}], "\[IndentingNewLine]", \(F2[x_, y_]\ := Transpose[B] . x\ ; \ F[x_, y_] := {F1[x, y], F2[x, y]}\ ;\)}], "Input"] }, Closed]], Cell[TextData[{ "If the game you consider has a nontrivial component of Nash equilibria, \ the program will find a random subset of this component. If you'd prefer not \ to compute the Nash equilibria, set ", StyleBox["findnashequilibria", FontWeight->"Bold"], " to 0." }], "Text", FontFamily->"Palatino"], Cell[BoxData[ \(\(findnashequilibria = 1\ ;\)\)], "Input"], Cell["\<\ Give the strategies one-character names to be printed on the phase \ diagram.\ \>", "Text", FontFamily->"Palatino"], Cell[BoxData[{ \(\(strategy[1] = "\"\ ;\)\ \), "\[IndentingNewLine]", \(\(strategy[2] = "\"\ ;\)\ \), "\[IndentingNewLine]", \(\(strategy[3] = "\"\ ;\)\), "\[IndentingNewLine]", \(\(strategy[4] = "\"\ ;\)\)}], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Payoff-related definitions", FontSlant->"Italic"]], "SmallText"], Cell[BoxData[ \(Clear[Fbar]\ ; \ Clear[Fhat]\ ; \ \ Clear[Fhatplus]\ ;\)], "Input", InitializationCell->True], Cell["The population's average payoff", "Subsubsection", InitializationCell->True], Cell[BoxData[{ \(\(\(\(Fbar[1]\)[x_, y_, F1_] := \[Sum]\+\(i = 1\)\%2 x\[LeftDoubleBracket] i\[RightDoubleBracket]\ \(F1[x, y]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\ ;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fbar[2]\)[x_, y_, F2_] := \ \[Sum]\+\(i = 1\)\%2 y\[LeftDoubleBracket] i\[RightDoubleBracket]\ \(F2[x, y]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\ ;\)\(\[IndentingNewLine]\) \)\)}], "Input", InitializationCell->True], Cell["Excess payoff vector", "Subsubsection", InitializationCell->True], Cell[BoxData[{ \(\(\(\(Fhat[1]\)[x_, y_, F1_] := F1[x, y]\ - \ \(Fbar[1]\)[x, y, F1]\ ;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fhat[2]\)[x_, y_, F2_] := F2[x, y]\ - \ \(Fbar[2]\)[x, y, F2]\ ;\)\(\[IndentingNewLine]\) \)\)}], "Input", InitializationCell->True], Cell["Vector of positive parts of excess payoffs", "Subsubsection", InitializationCell->True], Cell[BoxData[{ \(\(\(\(Fhatplus[1]\)[x_, y_, F1_] := \ {Max[ 0, \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket]], Max[0, \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket]]}\ ;\)\(\ \[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(\(Fhatplus[2]\)[x_, y_, F2_] := \ {Max[ 0, \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket]], Max[0, \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]]}\ ;\)\(\ \[IndentingNewLine]\) \)\)}], "Input", InitializationCell->True], Cell["Projected payoff vector", "Subsubsection"], Cell[BoxData[ \(\(PhiF[x_, y_, F1_, F2_] := Flatten[{F1[x, y] - {1/2, 1/2} \(\[Sum]\+\(i = 1\)\%2\( F1[x, y]\)[\([i]\)]\), F2[x, y] - {1/2, 1/2} \(\[Sum]\+\(i = 1\)\%2\( F2[x, y]\)[\([i]\)]\)\ }, 1];\)\)], "Input", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Choice of dynamic", "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "To specify a dynamic, select the rhs of \"", StyleBox["Dynamic", FontWeight->"Bold"], " = (.)\" (excluding the semicolon), and then press the button \ corresponding to the dynamic you desire. Definitions of the dynamics can be \ found in the closed group at the end of this section.\nDetails: If you use \ Logit[\[Eta]] or ILogit[\[Eta]], be sure to enter a value for the noise \ parameter \[Eta] in the closed group below. Making \[Eta] very small \ generates close approximations of the best response dynamic. ", " If you use Projection and if you are not using ", StyleBox["Mathematica", FontSlant->"Italic"], " version 5 or above, do not take initial condtions on the boundary.", " EP (excess payoff dynamic), PC (pairwise comparison dynamic), ConvexComb, \ and Other must be specified in greater detail below." }], "Text", FontFamily->"Palatino"], Cell[CellGroupData[{ Cell["Noise level for the logit and i-logit dynamics", "SmallText"], Cell[BoxData[ \(\(\[Eta]\ = \ .01\ ;\)\)], "Input"] }, Closed]], Cell[BoxData[GridBox[{ { ButtonBox["Replicator"], ButtonBox[\(Logit[\[Eta]]\)], ButtonBox["BNN"], ButtonBox["PD"], ButtonBox["Projection"], ButtonBox["Combined"]}, { ButtonBox["MSReplicator"], ButtonBox[\(ILogit[\[Eta]]\)], ButtonBox["EP"], ButtonBox["PC"], "", ButtonBox["Other"]} }, RowSpacings->0, ColumnSpacings->0, GridDefaultElement:>ButtonBox[ "\\[Placeholder]"]]], "Input", Active->True, Evaluatable->False], Cell[BoxData[ \(\(Dynamic = Replicator\ ;\)\)], "Input"], Cell[TextData[{ "If the dynamic you consider has a nontrivial component of rest points, the \ program will compute and plot a random subset of this component. If you set \ ", StyleBox["findrestpoints", FontWeight->"Bold"], " equal to 0, the computation and plotting is skipped." }], "Text", FontFamily->"Palatino"], Cell[BoxData[ \(\(findrestpoints = 1;\)\)], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definition of combination of two dynamics", FontSlant->"Italic"]], "SmallText"], Cell["\<\ To define a combination of two dynamics, specify the two dynamics \ to be combined, the weights on the dynamics, and the characterization of the \ rest points of combined dynamic. Nash is the default setting for the set or \ rest points. This is correct, for example, with combinations of the \ replicator dynamic and an excess payoff dynamic like the BNN dynamic. If the \ rest points aren't identical to the Nash equilibria for the dynamics you have \ specified, you can replace Nash with Automatic if the combined dynamic is \ smooth. (If the combined dynamic isn't smooth, you're on your own!) The \ last line of code formally defines the combined dynamic according to your \ specificcations.\ \>", "Text", FontFamily->"Palatino"], Cell[BoxData[{ \(\(dyn[1] = Replicator;\)\), "\[IndentingNewLine]", \(\(dyn[2] = BNN;\)\), "\[IndentingNewLine]", \(\(weight[1] = .9;\)\), "\[IndentingNewLine]", \(\(weight[2] = .1;\)\), "\[IndentingNewLine]", \(\(RPCharacterization[Combined] = Nash;\)\), "\[IndentingNewLine]", \(\(Combined[x_, y_, F1_, F2_] := weight[1]\ \(dyn[1]\)[x, y, F1, F2] + weight[2]\ \(dyn[2]\)[x, y, F1, F2];\)\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definitions of dynamics", FontSlant->"Italic"]], "SmallText", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[{ \(\(Clear[Replicator]\ ;\)\ \ \), "\[IndentingNewLine]", \(\(Clear[BNN]\ \ ;\)\), "\[IndentingNewLine]", \(\(Clear[Logit]\ ;\)\), "\[IndentingNewLine]", \(\(Clear[rho]\ ;\)\), "\[IndentingNewLine]", \(\(Clear[PD]\ ;\)\ \), "\[IndentingNewLine]", \(\(Clear[rho1]\ ;\)\), "\[IndentingNewLine]", \(\(Clear[SelMut]\ ;\)\)}], "Input", CellOpen->False, InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Replicator Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(Replicator[x_, y_, F1_, F2_] := {x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \(\(Fhat[ 1]\)[x, y, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket], x\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket], y\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket], y\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]}\ ;\)\)], \ "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[Replicator] = Automatic\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Maynard Smith Replicator Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(MSReplicator[x_, y_, F1_, F2_] := {\(1\/\(Fbar[1]\)[x, y, F1]\) x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket], \ \(1\/\(Fbar[1]\)[x, y, F1]\) x\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket], \ \(1\/\(Fbar[2]\)[x, y, F2]\) y\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket], \ \(1\/\(Fbar[2]\)[x, y, F2]\) y\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]}\ ;\)\)], \ "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[MSReplicator] = Automatic\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Logit Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(Logit[\[Eta]_]\)[x_, y_, F1_, F2_] := {\[ExponentialE]\^\(\(F1[x, y]\)\[LeftDoubleBracket]1\ \[RightDoubleBracket]\/\[Eta]\)\/\(\[Sum]\+\(i = 1\)\%2 \ \[ExponentialE]\^\(\(F1[x, y]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\/\ \[Eta]\)\) - x\[LeftDoubleBracket]1\[RightDoubleBracket], \ \[ExponentialE]\^\(\(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket]\/\ \[Eta]\)\/\(\[Sum]\+\(i = 1\)\%2 \[ExponentialE]\^\(\(F1[x, y]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\) - x\[LeftDoubleBracket]2\[RightDoubleBracket], \ \[ExponentialE]\^\(\(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\/\ \[Eta]\)\/\(\[Sum]\+\(i = 1\)\%2 \[ExponentialE]\^\(\(F2[x, y]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\) - y\[LeftDoubleBracket]1\[RightDoubleBracket], \ \[ExponentialE]\^\(\(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket]\/\ \[Eta]\)\/\(\[Sum]\+\(i = 1\)\%2 \[ExponentialE]\^\(\(F2[x, y]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\) - y\[LeftDoubleBracket]2\[RightDoubleBracket]}\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[Logit[_]] = Automatic\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["I-Logit Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(ILogit[\[Eta]_]\)[x_, y_, F1_, F2_] := {\(x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \[ExponentialE]\^\(\(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\/\ \[Eta]\)\)\/\(\[Sum]\+\(i = 1\)\%2 \ x\[LeftDoubleBracket]i\[RightDoubleBracket] \[ExponentialE]\^\(\(F1[x, y]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\)\ - x\[LeftDoubleBracket]1\[RightDoubleBracket], \(x\ \[LeftDoubleBracket]2\[RightDoubleBracket]\ \[ExponentialE]\^\(\(F1[x, y]\)\ \[LeftDoubleBracket]2\[RightDoubleBracket]\/\[Eta]\)\)\/\(\[Sum]\+\(i = \ 1\)\%2 x\[LeftDoubleBracket]i\[RightDoubleBracket] \[ExponentialE]\^\(\(F1[x, \ y]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\) - x\[LeftDoubleBracket]2\[RightDoubleBracket], \(y\ \[LeftDoubleBracket]1\[RightDoubleBracket]\ \[ExponentialE]\^\(\(F2[x, y]\)\ \[LeftDoubleBracket]1\[RightDoubleBracket]\/\[Eta]\)\)\/\(\[Sum]\+\(i = \ 1\)\%2 y\[LeftDoubleBracket]i\[RightDoubleBracket] \[ExponentialE]\^\(\(F2[x, \ y]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\)\ - y\[LeftDoubleBracket]1\[RightDoubleBracket], \(y\ \[LeftDoubleBracket]2\[RightDoubleBracket]\ \[ExponentialE]\^\(\(F2[x, y]\)\ \[LeftDoubleBracket]2\[RightDoubleBracket]\/\[Eta]\)\)\/\(\[Sum]\+\(i = \ 1\)\%2 y\[LeftDoubleBracket]i\[RightDoubleBracket] \[ExponentialE]\^\(\(F2[x, \ y]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\/\[Eta]\)\) - y\[LeftDoubleBracket]2\[RightDoubleBracket]}\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[ILogit[_]] = Automatic\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["BNN dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(BNN[x_, y_, F1_, F2_] := {\(\(Fhatplus[1]\)[x, y, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\(\( Fhatplus[1]\)[x, y, F1]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(\(Fhatplus[1]\)[x, y, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - x\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\(\( Fhatplus[1]\)[x, y, F1]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(\(Fhatplus[2]\)[x, y, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - y\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\(\( Fhatplus[2]\)[x, y, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(\(Fhatplus[2]\)[x, y, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - y\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\(\( Fhatplus[2]\)[x, y, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\)}\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(\(RPCharacterization[BNN] = Nash\ ;\)\(\[IndentingNewLine]\) \)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Excess payoff dynamic", "Subsubsection", InitializationCell->True], Cell[TextData[{ "Here one specifies the vector field sigmatilde that defines an excess \ payoff dynamic. This definition should be stated in terms of the excess \ payoff vector Fhat[", StyleBox["i", FontSlant->"Italic"], "][x,y,F", StyleBox["i", FontSlant->"Italic"], "], which is defined as Fhat[", StyleBox["i", FontSlant->"Italic"], "][x,y,F", StyleBox["i", FontSlant->"Italic"], "] = F", StyleBox["i", FontSlant->"Italic"], "[x,y] - Fbar[", StyleBox["i", FontSlant->"Italic"], "][x,y,F", StyleBox["i", FontSlant->"Italic"], "], for each population ", StyleBox["i ", FontSlant->"Italic"], "= 1, 2. (", StyleBox["Mathematica", FontSlant->"Italic"], " subtracts the scalar from the vector correctly.) When computing rest \ points, the program assumes that sigmatilde is acute, so that the rest points \ of the dynamic are the Nash equilibria of the underlying game." }], "Text", InitializationCell->True, FontFamily->"Palatino"], Cell[BoxData[ \(\(sigmatilde[x_, y_, F1_, F2_] := \ {\((Max[ 0, \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket]])\)^2, \ \[IndentingNewLine]\((Max[ 0, \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket]])\)^2, \ \((Max[0, \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket]])\)^2, \ \((Max[0, \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]])\)^2};\)\ \)], "Input", InitializationCell->True], Cell[BoxData[ \(\(EP[x_, y_, F1_, F2_] := {\(sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\( sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - x\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 1\)\%2\( sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket]3\[RightDoubleBracket] - y\[LeftDoubleBracket]1\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 3\)\%4\( sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\), \(sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket]4\[RightDoubleBracket] - y\[LeftDoubleBracket]2\[RightDoubleBracket]\ \(\[Sum]\+\(i = \ 3\)\%4\( sigmatilde[x, y, F1, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]\)}\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(RPCharacterization[EP] = Nash\ \ ;\)\)], "Input", InitializationCell->True], Cell["Pairwise Difference Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[{ \(\(\(rho[1]\)[x_, y_, F1_] := {{0, Max[\(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F1[ x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}}\ ;\)\), "\[IndentingNewLine]", \(\(\(rho[2]\)[x_, y_, F2_] := {{0, Max[\(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F2[ x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}}\ ;\)\)}], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(PD[x_, y_, F1_, F2_] := Join[Flatten[ Transpose[\(rho[1]\)[x, y, F1]] . \ x - {{x\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, x\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho[ 1]\)[x, y, F1] . {1, 1}], Flatten[Transpose[\(rho[2]\)[x, y, F2]] . \ y - {{y\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, y\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho[ 2]\)[x, y, F2] . {1, 1}]]\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(RPCharacterization[PD] = Nash\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Pairwise Comparison Dynamic", "Subsubsection", InitializationCell->True], Cell["\<\ Here one specifies the vector field rho that defines an excess \ payoff dynamic. When computing rest points, the program assumes that rho is \ separable and sign-preserving, so that the rest points of the dynamic are the \ Nash equilibria of the underlying game.\ \>", "Text", InitializationCell->True], Cell[BoxData[{ \(\(\(rho1[1]\)[x_, y_, F1_] := {{0, Max[\(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F1[ x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}}\ ;\)\), "\[IndentingNewLine]", \(\(\(rho1[2]\)[x_, y_, F2_] := {{0, Max[\(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \(F2[ x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket], 0]}, {Max[\(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket], 0], 0}}\ ;\)\)}], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(PC[x_, y_, F1_, F2_] := Join[Flatten[ Transpose[\(rho1[1]\)[x, y, F1]] . \ x - {{x\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, x\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho1[ 1]\)[x, y, F1] . {1, 1}], Flatten[Transpose[\(rho1[2]\)[x, y, F2]] . \ y - {{y\[LeftDoubleBracket]1\[RightDoubleBracket], 0}, {0, y\[LeftDoubleBracket]2\[RightDoubleBracket]}} . \(rho1[ 2]\)[x, y, F2] . {1, 1}]]\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(RPCharacterization[PC] = Nash\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Projection Dynamic", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(closetozero = 10^\((\(-7\))\)\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(Projection[x_, y_, F1_, F2_] := {Evaluate[ If[x\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\), If[x\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\), \ \(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \((\(1\/2\) \ \((\[Sum]\+\(j = 1\)\%2\( F1[x, y]\)\[LeftDoubleBracket] j\[RightDoubleBracket])\))\), 0], 0]], Evaluate[ If[x\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\), If[x\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F1[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \ \(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\), \ \(F1[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \((\(1\/2\) \ \((\[Sum]\+\(j = 1\)\%2\( F1[x, y]\)\[LeftDoubleBracket] j\[RightDoubleBracket])\))\), 0], 0]], Evaluate[ If[\((y\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\))\)\ \ , If[\((y\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\))\ \), \(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F2[x, y]\)\[LeftDoubleBracket] j\[RightDoubleBracket])\))\), 0], 0]], Evaluate[ If[\((y\[LeftDoubleBracket]2\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ \[GreaterEqual] \ \(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket])\))\)\ , If[\((y\[LeftDoubleBracket]1\[RightDoubleBracket] > closetozero\ || \ \((\(F2[x, y]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ \[GreaterEqual] \(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket])\))\ \)\ , \(F2[x, y]\)\[LeftDoubleBracket]2\[RightDoubleBracket] - \((\(1\ \/2\) \((\[Sum]\+\(j = 1\)\%2\( F2[x, y]\)\[LeftDoubleBracket]j\[RightDoubleBracket])\ \))\), 0], 0]]\ }\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(RPCharacterization[Projection] = Nash\ ;\)\)], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["Other", "Subsubsection", InitializationCell->True, CellTags->"dynamicslibrary"], Cell["\<\ Define any other dynamic you want to use. When defining be sure you \ follow same style with previously defined dynamics. Otherwise, you may need \ to do major changes in the program.\ \>", "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(Other[x_, y_, F1_, F2_] := {x\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \(\(Fhat[ 1]\)[x, y, F1]\)\[LeftDoubleBracket]1\[RightDoubleBracket], x\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ \(\(Fhat[1]\)[x, y, F1]\)\[LeftDoubleBracket]2\[RightDoubleBracket], y\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]1\[RightDoubleBracket], y\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ \(\(Fhat[2]\)[x, y, F2]\)\[LeftDoubleBracket]2\[RightDoubleBracket]};\)\)], \ "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ \(\(RPCharacterization[Other] = Automatic\ \ ;\)\)], "Input", InitializationCell->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Choice of contour function", "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "Choose a contour function here. To use one of the ", ButtonBox["built-in contour functions"], ", select the rhs of \"", StyleBox["SimplexContourFunction", FontWeight->"Bold"], " = xxx\" (excluding the semicolon) and then press the button corresponding \ to the contour function you desire. If you choose \ StableGameLyapunov[Dynamic], the program will use the Lyapunov function that \ is appropriate for the dynamic you selected in the previous section. " }], "Text", FontFamily->"Palatino"], Cell[BoxData[GridBox[{ { ButtonBox[\(\(Speed\)\(\ \)\)], ButtonBox[\(\(L1Speed\)\(\ \)\)], ButtonBox[\(\(NormalFormPotential\)\(\ \)\)], ButtonBox[\(\(StableGameLyapunov[Dynamic]\)\(\ \)\)], ButtonBox["Other"]} }, RowSpacings->0, ColumnSpacings->0, GridDefaultElement:>ButtonBox[ "\\[Placeholder]"]]], "Input", Active->True, Evaluatable->False], Cell[BoxData[ \(\(SimplexContourFunction = Speed\ \ ;\)\)], "Input"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definitions of contour functions", FontSlant->"Italic"]], "SmallText", InitializationCell->True, CellTags->"contourfunctions"], Cell[CellGroupData[{ Cell["Speed functions", "Subsubsection", CellTags->"contourfunctions"], Cell["\<\ Speed is the standard (Euclidean) speed on the simplex. L1Speed is \ self-explanatory. RSSpeed is the speed of the replicator dynamic after \ solution trajectories have been moved to the sphere.\ \>", "Text", Evaluatable->False, InitializationCell->True, FontFamily->"Palatino", CellTags->"contourfunctions"], Cell[BoxData[ \(\(Speed[x_, y_] := If[Dynamic === \ Projection, Sqrt[\[Sum]\+\(i = 1\)\%4\( PhiF[x, y, F1, \ F2]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\^2]\ , Sqrt[\[Sum]\+\(i = 1\)\%4\( Dynamic[x, y, F1, F2]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket]\^2]\ ];\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(L1Speed[x_, y_] := \[Sum]\+\(i = 1\)\%4 Abs[\(Dynamic[x, y, F1, F2]\)\[LeftDoubleBracket] i\[RightDoubleBracket]]\ ;\)\)], "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["Potential functions", "Subsubsection", CellTags->"contourfunctions"], Cell[BoxData[ \(\(NormalFormPotential[x_, y_] := x . \((A . y\ )\)\ ;\)\)], "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["Lyapunov functions ", "Subsubsection", CellTags->"contourfunctions"], Cell[BoxData[ \(\(NEQ = If[findnashequilibria \[Equal] 1, NashEq[F1, F2]]\ ;\)\)], "Input"], Cell[BoxData[ \(\(\(StableGameLyapunov[Replicator]\)[x_, y_] := \(-\ \((\[Product]\+\(i = 1\)\%2 x[\([i]\)]\^NEQ\ \[LeftDoubleBracket]1, 1, i\[RightDoubleBracket])\)\) \((\[Product]\+\(j = \ 1\)\%2 y[\([j]\)]\^NEQ\[LeftDoubleBracket]1, 2, j\[RightDoubleBracket])\)\ \ \ \ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(StableGameLyapunov[Logit[\[Eta]]]\)[x_, y_] := \ \[Eta]\ Log[\[Sum]\+\(i = 1\)\%2 \ \[ExponentialE]\^\(\(F1[x, y]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\/\ \[Eta]\)] - \((x . F1[x, y] - \[Eta]\ \(\[Sum]\+\(i = 1\)\%2 x\[LeftDoubleBracket]i\[RightDoubleBracket] Log[Max[x\[LeftDoubleBracket]i\[RightDoubleBracket], 10^\((\(-7\))\)]]\))\)\ \ + \ \[Eta]\ \ Log[\[Sum]\+\(i = 1\)\%2 \[ExponentialE]\^\(\(F2[x, y]\)\[LeftDoubleBracket]i\ \[RightDoubleBracket]\/\[Eta]\)] - \((y . F2[x, y] - \[Eta]\ \(\[Sum]\+\(i = 1\)\%2 y\[LeftDoubleBracket]i\[RightDoubleBracket] Log[Max[y\[LeftDoubleBracket]i\[RightDoubleBracket], 10^\((\(-7\))\)]]\))\)\ ;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(StableGameLyapunov[Projection]\)[x_, y_] := \ \ \[Sum]\+\(i = 1\)\%2\((x[\([i]\)] - NEQ\[LeftDoubleBracket]1, 1, i\[RightDoubleBracket])\)^2\ \ + \[Sum]\+\(i = \ 1\)\%2\((y[\([i]\)] - NEQ\[LeftDoubleBracket]1, 2, i\[RightDoubleBracket])\)^2;\)\)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(StableGameLyapunov[BNN]\)[x_, y_] := \[Sum]\+\(i = 1\)\%2\(\( Fhatplus[1]\)[x, y, F1]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket]\^2\ \ + \[Sum]\+\(i = 1\)\%2\(\( \ Fhatplus[2]\)[x, y, F2]\)\[LeftDoubleBracket]i\[RightDoubleBracket]\^2\ \ ;\)\ \)], "Input", InitializationCell->True], Cell[BoxData[ \(\(\(StableGameLyapunov[PD]\)[x_, y_] := \[Sum]\+\(i = 1\)\%2 x\[LeftDoubleBracket] i\[RightDoubleBracket] \(\[Sum]\+\(j = 1\)\%2\((Max[\(F1[x, \ y]\)\[LeftDoubleBracket]j\[RightDoubleBracket] - \(F1[x, y]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket], 0])\)\^2\)\ \ + \[Sum]\+\(i = \ 1\)\%2 y\[LeftDoubleBracket] i\[RightDoubleBracket] \(\[Sum]\+\(j = 1\)\%2\((Max[\(F2[x, \ y]\)\[LeftDoubleBracket]j\[RightDoubleBracket] - \(F2[x, y]\)\ \[LeftDoubleBracket]i\[RightDoubleBracket], 0])\)\^2\)\ \ \ ;\)\)], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["Other contour functions", "Subsubsection", CellTags->{"contourfunctions", "othercontour"}], Cell["Define your own contour function here.", "Text", FontFamily->"Palatino", CellTags->{"contourfunctions", "othercontour"}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Specification of graphical output", "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Shared parameters for contour function output", "Subsection"], Cell[TextData[{ "These parameters are used for contour function output in all of the types \ of diagrams described below. If you do not include contour functions in your \ output, these parameters are not used.\n", StyleBox["color", FontWeight->"Bold"], " = 1 generates color output; color = 0 generates black and white. The \ scales used are drawn below.\n", StyleBox["colorbar", FontWeight->"Bold"], " = 1 to create a color scale (alternatively, a black and white scale) \ along with your contour plot.\n", StyleBox["plotprecision", FontWeight->"Bold"], " specifies the number of points sampled in each dimension when drawing the \ contour plots. Typicaly, this option is the main determinant of the \ program's running time. Settings between 50 and 200 are accurate enough for \ most purposes. 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The vector fields \ should take values in the tangent space of the simplex (i.e., values whose \ components sum to zero). \n", StyleBox["drawoncontour", FontWeight->"Bold"], " = 1 draws the vector field on top of a contour plot." }], "Text"], Cell[BoxData[{ \(\(vectorfielddiagram = 1\ ;\)\), "\[IndentingNewLine]", \(\(drawoncontour = 0\ ;\)\)}], "Input"], Cell[CellGroupData[{ Cell["Instructions for specification of vector fields", "SmallText"], Cell[TextData[{ "Either one or two vector fields is drawn, according to whether ", StyleBox["drawvectorfield1", FontWeight->"Bold"], ", ", StyleBox["drawvectorfield2", FontWeight->"Bold"], ", or both are set to 1.\n", StyleBox["vectorfield?", FontWeight->"Bold"], " specifies the vector field to be drawn. (Here and below, \"?\" equals 1 \ or 2.) Common specifications for this are Dynamic (the dynamic specified in \ the \"Choice of dynamic\" section) and PhiF (the projection of the payoff \ vector field onto the tangent space of the simplex - see \"Payoff-related \ definitions\" in the \"Choice of game\"section).\n", StyleBox["scale?", FontWeight->"Bold"], " rescales the vectors, as is often needed to prevent the vector field \ arrows from being too long. The program calibrates the output so that \ setting scale1 = scale2 makes the longest vector in each vector field have \ the same length.\n", StyleBox["vf?thickness", FontWeight->"Bold"], " is the thickness of the \"shafts\" of the arrows.\n", StyleBox["arrowheadlengtsvf?", FontWeight->"Bold"], " is self-explanatory; set it to zero if you do not want arrowheads.\n", StyleBox["colorvf?", FontWeight->"Bold"], " determines the color of the vector field. 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