(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 209020, 4997] NotebookOptionsPosition[ 202558, 4819] NotebookOutlinePosition[ 203020, 4837] CellTagsIndexPosition[ 202977, 4834] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ The Evolutionary Foundation of Probability Weighting and Hyperbolic \ Discounting\ \>", "Title", CellChangeTimes->{{3.4512251887676163`*^9, 3.4512252118315697`*^9}, { 3.451641627505931*^9, 3.451641631412181*^9}, {3.4517392586387463`*^9, 3.4517392617168713`*^9}, {3.5066123061347656`*^9, 3.5066123163554688`*^9}, 3.5088437620566406`*^9, 3.5088442638945312`*^9, {3.5163607300039062`*^9, 3.5163607394101562`*^9}, {3.517843149220703*^9, 3.5178431620927734`*^9}, { 3.5437685773876953`*^9, 3.543768583176758*^9}, 3.5442762067929688`*^9, 3.5460200388007812`*^9, {3.546195301796875*^9, 3.5461953063125*^9}}], Cell["And Their Intimate Connection", "Subtitle", CellChangeTimes->{{3.5442761739648438`*^9, 3.5442762002929688`*^9}, { 3.546195309484375*^9, 3.5461953175*^9}}], Cell["\<\ Laurens Bogaardt - 29-05-2012 Master\[CloseCurlyQuote]s Thesis in Economics at Lunds Universitet\ \>", "Subsubtitle", CellChangeTimes->{{3.5163607461445312`*^9, 3.5163607521289062`*^9}, { 3.5178431682783203`*^9, 3.5178431990234375`*^9}, {3.5182466543740234`*^9, 3.5182466552666016`*^9}, 3.518785013516594*^9, {3.543768660694336*^9, 3.543768674600586*^9}, {3.5460200580791016`*^9, 3.5460200703896484`*^9}}], Cell[CellGroupData[{ Cell["Introduction", "Subtitle", CellGroupingRules->{GroupTogetherGrouping, 10001.}, CellChangeTimes->{{3.451225222214694*^9, 3.4512252238347073`*^9}, 3.4514664013390656`*^9, {3.543681697473633*^9, 3.543681698883789*^9}}], Cell["\<\ This notebook is used to do the calculation for my Master\[CloseCurlyQuote]s \ Thesis in Economics at Lunds Universitet, 2012. It examines the cause of \ hyperbolic discounting by taking the position that the hyperbolic discount \ function is a version of an exponential function on which probability \ weighting is applied. As such, this notebook first explores the evolutionary \ foundation of Prospect Theory probability weighting. Some of the functions \ used in this notebook were based on a previous notebook by Elliott Wagner, \ who wrote the paper \[OpenCurlyQuote]The Dynamics of Costly Signaling\ \[CloseCurlyQuote].\ \>", "Text", CellChangeTimes->{{3.4514663936671906`*^9, 3.4514664013390656`*^9}, { 3.451720204061669*^9, 3.451720278749064*^9}, {3.4517203925326767`*^9, 3.4517206157436385`*^9}, {3.4517209787456093`*^9, 3.451721589984528*^9}, { 3.4517216355099907`*^9, 3.4517216564601154`*^9}, {3.45172169293256*^9, 3.451721696507701*^9}, {3.4517218576093535`*^9, 3.4517218867813005`*^9}, { 3.451721996939701*^9, 3.451722003549205*^9}, {3.4517220338928366`*^9, 3.4517221594633985`*^9}, {3.451739755623917*^9, 3.451739768014542*^9}, { 3.4517398276248617`*^9, 3.4517398600467367`*^9}, {3.4517399288592367`*^9, 3.4517400076404867`*^9}, {3.451756201732218*^9, 3.4517562236540923`*^9}, { 3.4517562634665923`*^9, 3.451756268294718*^9}, {3.451756306794718*^9, 3.451756308450968*^9}, {3.451756342607218*^9, 3.451751697900552*^9}, { 3.5066123507597656`*^9, 3.5066123513710938`*^9}, 3.5163561804570312`*^9, { 3.518246878551758*^9, 3.5182469792597656`*^9}, {3.5182524792304688`*^9, 3.518252497984375*^9}, {3.543683083298828*^9, 3.543683114298828*^9}, { 3.5442764298554688`*^9, 3.5442765152773438`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Initiation", "Subtitle", CellChangeTimes->{{3.451225222214694*^9, 3.4512252238347073`*^9}, 3.4514664013390656`*^9, 3.5163561804570312`*^9, {3.5163562169648438`*^9, 3.5163562182470703`*^9}, {3.5163606831367188`*^9, 3.5163606847460938`*^9}, 3.5172175692265625`*^9}], Cell["\<\ This section defines all the functions of this notebook. In particular, it \ starts with the objective functions and moves on to the subjective functions \ afterwards. In short, there is a function to solve for the position of the \ mixed equilibrium. There is a function which sets up the replicator equation. \ This can be used to make a vector plot or stream plot. There is also a \ function which creates the borders of the phase space. There is also a \ function for the labels and one to show the equilibria of the model, both as \ points and in terms of there utility value. Finally, these things are put \ together in a plot, where lines and arrows show the dynamics of the phase \ space.\ \>", "Text", CellChangeTimes->{{3.4514663936671906`*^9, 3.4514664013390656`*^9}, { 3.451720204061669*^9, 3.451720278749064*^9}, {3.4517203925326767`*^9, 3.4517206157436385`*^9}, {3.4517209787456093`*^9, 3.451721589984528*^9}, { 3.4517216355099907`*^9, 3.4517216564601154`*^9}, {3.45172169293256*^9, 3.451721696507701*^9}, {3.4517218576093535`*^9, 3.4517218867813005`*^9}, { 3.451721996939701*^9, 3.451722003549205*^9}, {3.4517220338928366`*^9, 3.4517221594633985`*^9}, {3.451739755623917*^9, 3.451739768014542*^9}, { 3.4517398276248617`*^9, 3.4517398600467367`*^9}, {3.4517399288592367`*^9, 3.4517400076404867`*^9}, {3.451756201732218*^9, 3.4517562236540923`*^9}, { 3.4517562634665923`*^9, 3.451756268294718*^9}, {3.451756306794718*^9, 3.451756308450968*^9}, {3.451756342607218*^9, 3.451751697900552*^9}, { 3.5066123507597656`*^9, 3.5066123513710938`*^9}, 3.5163561804570312`*^9, { 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