From ded898e213d0d43157f02c7ea4de466bb0dd0cc3 Mon Sep 17 00:00:00 2001 From: Holger Ingmar Meinhardt Date: Sat, 22 Apr 2023 17:17:25 +0200 Subject: [PATCH] V3.1.1 --- ChangeLog | 6 + ChangeLog.md | 13 + LICENSE.md | 2 +- PacletInfo.m | 2 +- ParaTuGames.wl | 14 +- README | 14 +- README.md | 18 +- TuGames.nb | 1774 +++++++++++++++++++++++++++++++----------------- 8 files changed, 1192 insertions(+), 651 deletions(-) diff --git a/ChangeLog b/ChangeLog index 5a0eba6..801a0c5 100644 --- a/ChangeLog +++ b/ChangeLog @@ -342,3 +342,9 @@ 1. Revision Update of the Documentation references pages and adjustment to the paclet system of Mathematica Version 13.0. + + Version 3.1.1 + + Adding the new functions: + + ProductGame, ProbabilityGame, HarsanyiValue, ShapAirProb, TauValAirProb, NucAirProb. diff --git a/ChangeLog.md b/ChangeLog.md index 859bad1..fbe54e5 100644 --- a/ChangeLog.md +++ b/ChangeLog.md @@ -346,3 +346,16 @@ Some minor bug fixes and code revision. #### 1. Revision Update of the Documentation references pages and adjustment to the paclet system of Mathematica Version 13.0. + +### Version 3.1.1 + +#### 1. Modification + +Adding the new functions: + +* `ProductGame[]` computes from a weight vector the product game and Harsanyi dividends. +* `ProbabilityGame[]` computes from a weight vector the probability game. +* `HarsanyiValue[]` the Harsanyi value of the game. +* `ShapAirProb[]` calculates the Shapley value from an airport cost allocation problem. +* `TauValAirProb[]` calculates the Tau value from an airport cost allocation problem. +* `NucAirProb[]` calculates the nucleolus from an airport cost allocation problem. diff --git a/LICENSE.md b/LICENSE.md index 7959c42..6f9c6cb 100644 --- a/LICENSE.md +++ b/LICENSE.md @@ -1,6 +1,6 @@ # MIT License -## Copyright (c) 2019-22, Holger I. Meinhardt +## Copyright (c) 2019-23, Holger I. Meinhardt Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: diff --git a/PacletInfo.m b/PacletInfo.m index 6207e07..a915afb 100644 --- a/PacletInfo.m +++ b/PacletInfo.m @@ -1,6 +1,6 @@ Paclet[ Name -> "TUG", - Version -> "3.1.0", + Version -> "3.1.1", MathematicaVersion -> "12+", Description -> "A Mathematica Package for Cooperative Game Theory", Creator -> "Holger Ingmar Meinhardt ", diff --git a/ParaTuGames.wl b/ParaTuGames.wl index 8f0e7d7..6d780fa 100644 --- a/ParaTuGames.wl +++ b/ParaTuGames.wl @@ -1,7 +1,7 @@ (* ::Package:: *) (* :Title: ParaTuGames.m - : Release Date : 15.03.2022 + : Release Date : 18.04.2023 *) @@ -21,7 +21,7 @@ Off[Needs::nocont] holger.meinhardt@wiwi.uni-karlsruhe.de *) -(* :Package Version: 1.0.3 *) +(* :Package Version: 1.0.4 *) (* :Mathematica Version: 12.x, 13.x @@ -779,7 +779,7 @@ ParaMaxSurplus[game_, pi_, pj_, payoff_List] := ParaMaxSijSurplus[game_,sij_List, payass_List] := - Block[{}, + Block[{z0}, Max[ReplaceAll[Map[v[#] - x[#] &, sij],payass]] ]; @@ -795,7 +795,7 @@ ParaAntiSurplus[game_, pi_, pj_, payoff_List] := ]; ParaAntiSijSurplus[game_,sij_List, payass_List] := - Block[{}, + Block[{z0}, Min[ReplaceAll[Map[v[#] - x[#] &, sij],payass]] ]; @@ -942,7 +942,7 @@ ParaMinExc[mg_List, asspay_List] := Min[ReplaceAll[(v[#] - x[#]) & /@ mg, asspay (* Deriving a game from unanimity coordinates. *) ParaCharacteristicValues[args___]:=(Message[ParaCharacteristicValues::argerr];$Failed); -ParaCharacteristicValues[coord_List,T_,opts:OptionsPattern[]]:= Block[{}, +ParaCharacteristicValues[coord_List,T_,opts:OptionsPattern[]]:= Block[{z0}, Which[ Length[coord] === 2^Length[T] , ParaDetWorth[coord,T] , True, ParaWrongCoordDimension[coord, T]] ]; @@ -1043,11 +1043,11 @@ ParaSupAddQ[teilmg_List] := Block[{tpws, valsubg, duval, leq}, ParaWrongDimension:=(Print["Payoff vector has not the correct dimension!"]); -ParaWrongCoordDimension[T_]:= Block[{}, +ParaWrongCoordDimension[T_]:= Block[{z0}, Print["List of unanimity coordinates of size 2 has not the correct length!"]; Print["The correct dimension is: ", Binomial[Length[T],2]]; ]; -ParaWrongCoordDimension[coord_List,T_]:= Block[{}, +ParaWrongCoordDimension[coord_List,T_]:= Block[{z0}, Print["List of unanimity coordinates of length ", Length[coord]]; Print["is not correct!"]; Print["The correct dimension is: ", 2^Length[T]]; diff --git a/README b/README index c25cbca..c8e24fa 100644 --- a/README +++ b/README @@ -1,4 +1,4 @@ -Mathematica Package: TuGames Version 3.1.0 +Mathematica Package: TuGames Version 3.1.1 ============================== Contents: 1. Introduction @@ -117,10 +117,10 @@ the command In[1]:= PacletInformation["TUG"] -Out[1]= {Name -> TUG, Version -> 3.1.0, BuildNumber -> , Qualifier -> , WolframVersion -> 12+, +Out[1]= {Name -> TUG, Version -> 3.1.1, BuildNumber -> , Qualifier -> , WolframVersion -> 12+, SystemID -> All, Description -> A Mathematica Package for Cooperative Game Theory, Category -> , Creator -> Holger Ingmar Meinhardt , - Publisher -> , Support -> , Internal -> False, Location -> /home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.0 + Publisher -> , Support -> , Internal -> False, Location -> /home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.1 Context -> {TUG`coop`, TUG`vertex`, TUG`}, Enabled -> True, Loading -> Manual} @@ -130,7 +130,7 @@ To get the same information and beyond that under Mathematica version 12.1, it i In[1]:= PacletObject["TUG"][All] -Out[1]= {"Name" -> "TUG", "Version" -> "3.1.0", "WolframVersion" -> "12+", +Out[1]= {"Name" -> "TUG", "Version" -> "3.1.1", "WolframVersion" -> "12+", "Qualifier" -> "", "SystemID" -> All, "Description" -> "A Mathematica Package for Cooperative Game Theory", "Category" -> Missing["NotAvailable"], "Keywords" -> Missing["NotAvailable"], "UUID" -> Missing["NotAvailable"], @@ -140,7 +140,7 @@ Out[1]= {"Name" -> "TUG", "Version" -> "3.1.0", "WolframVersion" -> "12+", "Internal" -> False, "Context" -> {"TUG`coop`", "TUG`vertex`", "TUG`"}, "Loading" -> Manual, "AutoUpdating" -> False, "Enabled" -> True, - "Location" -> "/home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.0"} + "Location" -> "/home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.1"} or alternatively/ @@ -265,8 +265,8 @@ In[1]:= Needs["TUG`"] =================================================== Loading Package 'TuGames' for Unix =================================================== -TuGames V3.1.0 by Holger I. Meinhardt -Release Date: 15.03.2022 +TuGames V3.1.1 by Holger I. Meinhardt +Release Date: 18.04.2023 Program runs under Mathematica Version 12.0 or later Version 12.x or higher is recommended =================================================== diff --git a/README.md b/README.md index 692d4a4..dde46de 100644 --- a/README.md +++ b/README.md @@ -1,8 +1,8 @@ [![GitHub (pre-)release](https://img.shields.io/github/release/himeinhardt/TuGames/all.svg)](https://github.com/himeinhardt/TuGames/releases) -[![Mathematica 12.0 - 13.0.1](https://img.shields.io/badge/Mathematica-12.0_--_13.0.1-brightgreen.svg)](#compatibility) +[![Mathematica 12.0 - 13.2.0](https://img.shields.io/badge/Mathematica-12.0_--_13.2.0-brightgreen.svg)](#compatibility) [![license MIT](https://img.shields.io/badge/license-MIT-blue.svg)](https://github.com/himeinhardt/TuGames/blob/master/LICENSE.md) -# *Mathematica* Package: *TuGames* Version 3.1.0 +# *Mathematica* Package: *TuGames* Version 3.1.1 ``` Contents: @@ -130,10 +130,10 @@ In order check for *Mathematica* versions smaller than 12.1 the paths where you ``` In[1]:= PacletInformation["TUG"] -Out[1]= {Name -> TUG, Version -> 3.1.0, BuildNumber -> , Qualifier -> , WolframVersion -> 12+, +Out[1]= {Name -> TUG, Version -> 3.1.1 BuildNumber -> , Qualifier -> , WolframVersion -> 12+, SystemID -> All, Description -> A Mathematica Package for Cooperative Game Theory, Category -> , Creator -> Holger Ingmar Meinhardt , - Publisher -> , Support -> , Internal -> False, Location -> /home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.0 + Publisher -> , Support -> , Internal -> False, Location -> /home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.1 Context -> {TUG`coop`, TUG`vertex`, TUG`}, Enabled -> True, Loading -> Manual} ``` @@ -143,7 +143,7 @@ To get the same information and beyond that under *Mathematica* version 12.1, it In[1]:= PacletObject["TUG"][All] ``` ``` -Out[1]= {"Name" -> "TUG", "Version" -> "3.1.0", "WolframVersion" -> "12+", +Out[1]= {"Name" -> "TUG", "Version" -> "3.1.1", "WolframVersion" -> "12+", "Qualifier" -> "", "SystemID" -> All, "Description" -> "A Mathematica Package for Cooperative Game Theory", "Category" -> Missing["NotAvailable"], "Keywords" -> Missing["NotAvailable"], "UUID" -> Missing["NotAvailable"], @@ -153,7 +153,7 @@ Out[1]= {"Name" -> "TUG", "Version" -> "3.1.0", "WolframVersion" -> "12+", "Internal" -> False, "Context" -> {"TUG`coop`", "TUG`vertex`", "TUG`"}, "Loading" -> Manual, "AutoUpdating" -> False, "Enabled" -> True, - "Location" -> "/home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.0"} + "Location" -> "/home/kit/xxx/xxxx/.Mathematica/Paclets/Repository/TUG-3.1.1"} ``` or alternatively @@ -186,7 +186,7 @@ occur on these operating systems to run the basic functions of the package. ## 2. Custom Installation -Since `Version 2.5.1` the package is distributed as a `Paclet`, which allows a custom installation. The latest version is `TUG-3.1.0`, which is only compatible for Mathematica version 12.0 or higher. This version is not anymore usable for versions that are smaller than 12.0. Notice that `TUG-2.6.2` is the latest version that is compatible with Mathematica versions smaller than 12.0, and will remain compatible with the most recent Mathematica version as long as `ConstrainedMax/ConstrainedMin` and `LinearProgramming/DualLinearProgramming` are supported by Wolfram Research, otherwise one has to update to `TUG-3.0.0` or later. The installation of the package requires about 90 MB free hard-disk space, and the Mathematica version should not be smaller than 10 while installing Version `TUG-2.6.2`. For Mathematica versions smaller than Version 10, a manual installation is requested. In that case one has to follow the guidelines related to the associated operating system that can be found from the Mathematica documentation. +Since `Version 2.5.1` the package is distributed as a `Paclet`, which allows a custom installation. The latest version is `TUG-3.1.1`, which is only compatible for Mathematica version 12.0 or higher. This version is not anymore usable for versions that are smaller than 12.0. Notice that `TUG-2.6.2` is the latest version that is compatible with Mathematica versions smaller than 12.0, and will remain compatible with the most recent Mathematica version as long as `ConstrainedMax/ConstrainedMin` and `LinearProgramming/DualLinearProgramming` are supported by Wolfram Research, otherwise one has to update to `TUG-3.0.0` or later. The installation of the package requires about 90 MB free hard-disk space, and the Mathematica version should not be smaller than 10 while installing Version `TUG-2.6.2`. For Mathematica versions smaller than Version 10, a manual installation is requested. In that case one has to follow the guidelines related to the associated operating system that can be found from the Mathematica documentation. The most simplest method is to install the `Paclet` directly from GitHub under Mathematica V12.0 or later while executing @@ -275,8 +275,8 @@ In[1]:= Needs["TUG`"] =================================================== Loading Package 'TuGames' for Unix =================================================== -TuGames V3.1.0 by Holger I. Meinhardt -Release Date: 15.03.2022 +TuGames V3.1.1 by Holger I. Meinhardt +Release Date: 18.04.2023 Program runs under Mathematica Version 12.0 or later Version 12.x or higher is recommended =================================================== diff --git a/TuGames.nb b/TuGames.nb index ddaad16..2081b48 100644 --- a/TuGames.nb +++ b/TuGames.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 1229052, 30821] -NotebookOptionsPosition[ 1208087, 30597] -NotebookOutlinePosition[ 1208553, 30614] -CellTagsIndexPosition[ 1208510, 30611] +NotebookDataLength[ 1249554, 31343] +NotebookOptionsPosition[ 1228191, 31115] +NotebookOutlinePosition[ 1228657, 31132] +CellTagsIndexPosition[ 1228614, 31129] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -56,7 +56,7 @@ Cell[BoxData[ RowBox[{"(*", " ", RowBox[{":", RowBox[{"Package", " ", "Version"}], ":", " ", - RowBox[{"3.1", ".0"}]}], " ", "*)"}], "\n", "\n", + RowBox[{"3.1", ".1"}]}], " ", "*)"}], "\n", "\n", RowBox[{"(*", " ", "\n", " ", RowBox[{ RowBox[{":", @@ -165,7 +165,21 @@ Cell[BoxData[ RowBox[{"Vol", ".", " ", "4"}], ",", " ", RowBox[{"No", ".", " ", "3"}], ",", " ", RowBox[{"201", "-", "211"}], ",", " ", - RowBox[{"2002.", " ", "\n", "\n", " ", "Theo", " ", "Driessen"}], ",", + RowBox[{"2002.", " ", "\n", "\n", " ", "Pierre", " ", "Dehez", " ", + RowBox[{"(", "2023", ")"}]}], ",", " ", + RowBox[{"COOPERATIVE", " ", "PRODUCT", " ", "GAMES"}], ",", " ", + RowBox[{"LIDAM", " ", "Discussion", " ", "Paper", " ", "CORE", " ", + RowBox[{"2023", " ", "/", " ", "10"}], "\n", "\n", " ", "Pierre", " ", + "Dehez", " ", + RowBox[{"(", "2023", ")"}]}], ",", " ", + RowBox[{ + "Sharing", " ", "a", " ", "collective", " ", "probability", " ", "of", + " ", "success"}], ",", " ", + RowBox[{ + "Mathematical", " ", "Social", "\n", " ", "Sciences", " ", "123"}], + ",", " ", + RowBox[{"122", "-", + RowBox[{"127.", "\n", "\n", " ", "Theo", " ", "Driessen"}]}], ",", " ", RowBox[{"Cooperative", " ", "Games"}], ",", " ", RowBox[{"Solutions", " ", "and", " ", "Applications"}], ",", " ", @@ -177,16 +191,16 @@ Cell[BoxData[ RowBox[{"Game", ":", " ", RowBox[{ "An", " ", "Alternative", " ", "Game", " ", "Theoretic", " ", - "Analysis", " ", "of", " ", "a", " ", "Bankruptcy", " ", - RowBox[{"Problem", ".", " ", "In"}], "\n", " ", + "Analysis", " ", "of", " ", "a", "\n", " ", "Bankruptcy", " ", + RowBox[{"Problem", ".", " ", "In"}], " ", RowBox[{"L", ".", "A", ".", " ", "Petrosjan"}], " ", "and", " ", RowBox[{"V", ".", "V", ".", " ", "Mazalov"}]}]}]}], ",", " ", "editors", ",", " ", RowBox[{"Game", " ", "Theory", " ", "and", " ", "Applications"}], ",", - " ", + "\n", " ", RowBox[{"volume", " ", "IV"}], ",", " ", RowBox[{"pages", " ", "45"}], "\[Dash]", "61", ",", " ", "Commack", ",", - "\n", " ", + " ", RowBox[{"New", " ", "York"}], ",", " ", RowBox[{"1998.", " ", "Nova", " ", "Science", " ", "Publishers", " ", RowBox[{"Inc", ".", "\n", "\n", "\n", " ", "E", ".", " ", "Inarra"}], @@ -232,20 +246,32 @@ Cell[BoxData[ "Science", " ", "and", " ", "Economics"}], ",", "\n", " ", "Waseda", ",", " ", "Japan", ",", " ", RowBox[{"2006.", "\n", "\n", " ", - RowBox[{"J", ".", " ", "Get\[AAcute]n"}]}], ",", " ", + RowBox[{"J", ".", " ", "Getan"}]}], ",", " ", RowBox[{"J", ".", " ", "M", ".", " ", "Izquierdo"}], ",", " ", RowBox[{"J", ".", " ", "Montes"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"C", ".", " ", "Rafels", ".", " ", "The"}], " ", "bargaining", - " ", "set", " ", "and", " ", "the", " ", "kernel", " ", "for", " ", - "almost"}], "-", - RowBox[{"convex", "\n", " ", "games"}]}], ",", " ", - RowBox[{ - RowBox[{ - RowBox[{"(", "2012", ")"}], ".", " ", "mimeo", ".", "\n", "\n", "\n", - " ", "I", ".", " ", "Katsev"}], " ", "and", " ", - RowBox[{"E", ".", " ", "Yanovskaya"}]}], ",", " ", + " ", "set", " ", "and", " ", "the", " ", "kernel", "\n", " ", "for", + " ", "almost"}], "-", + RowBox[{"convex", " ", "games"}]}], ",", " ", + RowBox[{ + RowBox[{"(", "2012", ")"}], ".", " ", "mimeo", ".", "\n", "\n", " ", + "Hou"}], ",", " ", + RowBox[{"D", "."}], ",", " ", "Xu", ",", " ", + RowBox[{"G", "."}], ",", " ", "Sun", ",", " ", + RowBox[{"P", "."}], ",", " ", "Driessen", ",", " ", + RowBox[{"T", "."}], ",", " ", + RowBox[{ + "2018.", " ", "The", " ", "Shapley", " ", "value", " ", "for", " ", + "the", " ", "probability", " ", + RowBox[{ + "game", ".", "\n", " ", "Oper", ".", " ", "Res", ".", " ", "Lett", + ".", " ", "46"}]}], ",", " ", + RowBox[{"457", "-", + RowBox[{"461.", "\n", "\n", " ", + RowBox[{"I", ".", " ", "Katsev"}], " ", "and", " ", + RowBox[{"E", ".", " ", "Yanovskaya"}]}]}], ",", " ", RowBox[{ "Between", " ", "the", " ", "Prekernel", " ", "and", " ", "the", " ", "Prenucleolus"}], ",", " ", "mimeo", ",", " ", @@ -317,17 +343,92 @@ Cell[BoxData[ RowBox[{"L", ".", " ", "Liang", ".", " ", "Multi"}], "-", RowBox[{ "Player", " ", "Allocations", " ", "in", " ", "the", " ", "Presence", - " ", "of", " ", "Diminishing", " ", "Marginal", " ", - RowBox[{"Contributions", ":", "\n", " ", + " ", "of", " ", "Diminishing", " ", "Marginal", "\n", " ", + RowBox[{"Contributions", ":", " ", RowBox[{ "Cooperative", " ", "Game", " ", "Analysis", " ", "and", " ", "Applications", " ", "in", " ", "Management", " ", "Science"}]}]}]}], - ",", " ", "2020", ",", " ", + ",", " ", "2020", ",", "\n", " ", RowBox[{ "to", " ", "appear", " ", "in", " ", "Management", " ", "Science", "\n", "\n", " ", - RowBox[{"SC", ".", " ", "Littlechild"}], " ", "and", " ", - RowBox[{"KG", ".", " ", "Vaidya"}]}], ",", " ", + RowBox[{"S", ".", " ", "C", ".", " ", "Littlechild", ".", " ", "A"}], + " ", "simple", " ", "expression", " ", "for", " ", "the", " ", + "nucleolus", " ", "in", " ", "a", " ", "special", " ", + RowBox[{"case", ".", " ", "International"}], "\n", " ", "Journal", + " ", "of", " ", "Game", " ", "Theory"}], ",", " ", + RowBox[{"3", ":", + RowBox[{"21", "-", "29"}]}], ",", " ", + RowBox[{ + RowBox[{"1974.", " ", "URL", " ", + RowBox[{"https", ":"}]}], "//", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"doi", ".", "org"}], "/", "10.1007"}], "/", + RowBox[{ + "BF01766216", ".", "\n", "\n", " ", "S", ".", " ", "C", ".", " ", + "Littlechild"}]}], " ", "and", " ", + RowBox[{"G", ".", " ", "Owen", ".", " ", "A"}], " ", "simple", " ", + "expression", " ", "for", " ", "the", " ", "shapely", " ", "value", + " ", "in", " ", "a", " ", "special", " ", + RowBox[{"case", ".", "\n", " ", "Management"}], " ", "Science"}]}], + ",", " ", + RowBox[{ + RowBox[{"20", + RowBox[{"(", "3", ")"}]}], ":", + RowBox[{"370", "-", "372"}]}], ",", " ", + RowBox[{"1973.", " ", "ISSN", " ", "00251909"}], ",", " ", + RowBox[{ + RowBox[{"15265501.", "\n", " ", "URL", " ", + RowBox[{"http", ":"}]}], "//", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"www", ".", "jstor", ".", "org"}], "/", "stable"}], "/", + "2629727."}], "\n", "\n", " ", + RowBox[{"S", ".", " ", "C", ".", " ", "Littlechild"}], " ", "and", " ", + RowBox[{"G", ".", " ", "Owen", ".", " ", "A"}], " ", "further", " ", + "note", " ", "on", " ", "the", " ", "nucleolus", " ", "of", " ", "the", + " ", "airport", " ", + RowBox[{"game", ".", "\n", " ", "International"}], " ", "Journal", + " ", "of", " ", "Game", " ", "Theory"}]}], ",", " ", + RowBox[{ + RowBox[{"5", + RowBox[{"(", "2", ")"}]}], ":", + RowBox[{"91", "-", "95"}]}], ",", " ", + RowBox[{ + RowBox[{"1976.", " ", "URL", " ", + RowBox[{"https", ":"}]}], "//", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"doi", ".", "org"}], "/", "10.1007"}], "/", + RowBox[{ + "BF01753311", ".", "\n", "\n", " ", "S", ".", " ", "C", ".", " ", + "Littlechild"}]}], " ", "and", " ", + RowBox[{ + "G", ".", " ", "F", ".", " ", "Thompson", ".", " ", "Aircraft"}], " ", + "landing", " ", + RowBox[{"fees", ":", " ", + RowBox[{"A", " ", "game", " ", "theory", " ", + RowBox[{"approach", ".", "\n", " ", "The"}], " ", "Bell", " ", + "Journal", " ", "of", " ", "Economics"}]}]}]}], ",", " ", + RowBox[{ + RowBox[{"8", + RowBox[{"(", "1", ")"}]}], ":", + RowBox[{"186", "-", "204"}]}], ",", " ", + RowBox[{ + RowBox[{"1977.", " ", "ISSN", " ", "0361915", + RowBox[{"X", ".", "\n", " ", "URL"}], " ", + RowBox[{"http", ":"}]}], "//", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"www", ".", "jstor", ".", "org"}], "/", "stable"}], "/", + "3003493."}], "\n", "\n", " ", + RowBox[{"S", ".", " ", "C", ".", " ", "Littlechild"}], " ", "and", " ", + RowBox[{"KG", ".", " ", "Vaidya"}]}]}], ",", " ", RowBox[{ RowBox[{ "The", " ", "propensity", " ", "to", " ", "disrupt", " ", "and", " ", @@ -504,7 +605,14 @@ Cell[BoxData[ RowBox[{"R", ".", " ", "T", ".", " ", "Rockafellar"}]}], ",", " ", RowBox[{"Convex", " ", "Analysis"}], ",", " ", RowBox[{"Princeton", " ", "University", " ", "Press"}], ",", " ", - RowBox[{"1970.", "\n", "\n", " ", + RowBox[{"1970.", "\n", "\n", " ", "Rosales"}], ",", " ", + RowBox[{"D", ".", " ", + RowBox[{"(", "2014", ")"}]}], ",", " ", + RowBox[{"Cooperative", " ", "product", " ", "games", " ", + RowBox[{"(", + RowBox[{ + RowBox[{"www", ".", "academia", ".", "edu"}], "/", "401764"}], ")"}], + "\n", "\n", " ", RowBox[{"J", ".", " ", "M", ".", " ", "Solano"}], " ", "and", " ", RowBox[{"C", ".", " ", "Rafels"}]}], ",", " ", RowBox[{"Convexity", " ", "versus", " ", "average", " ", @@ -557,8 +665,8 @@ Cell[BoxData[ RowBox[{"Ed", "."}], ")"}], ".", " ", "Economics"}], " ", "and", " ", "Financial", " ", "Modeling", " ", "with", " ", "Mathematica"}]}], ",", " ", "\n", " ", "Springer", ",", " ", "1992."}], " ", "\n", - "*)"}]}]}]], "Code",ExpressionUUID->"ffb30ab2-19ec-495a-af4d-\ -57b73eff3533"], + "*)"}]}]}]], "Code",ExpressionUUID->"f99c0bc6-3678-41a8-affc-\ +b9097faae5f5"], Cell[BoxData[ RowBox[{ @@ -1082,7 +1190,13 @@ Cell[BoxData[ "3.1", ".0", "\n", "\n", " ", "Update", " ", "of", " ", "the", " ", "Documentation", " ", "references", " ", "pages", " ", "and", " ", "adjustment", " ", "to", " ", "Mathematica", " ", "Version", " ", - RowBox[{"13.0", "."}]}]}], "\n", "\n", "*)"}], "\n", " ", "\n", "\n", + RowBox[{"13.0", ".", "\n", "\n", " ", "Version"}], " ", "3.1", ".1", + "\n", "\n", " ", "Adding", " ", "the", " ", "new", " ", + RowBox[{"functions", ":", "\n", "\n", " ", "ProductGame"}]}], ",", + " ", "ProbabilityGame", ",", " ", "HarsanyiValue", ",", " ", + "ShapAirProb", ",", " ", "TauValAirProb", ",", " ", + RowBox[{"NucAirProb", "."}]}], "\n", "\n", "\n", "*)"}], "\n", " ", "\n", + "\n", RowBox[{"(*", " ", "\n", " ", RowBox[{":", "Limitations", ":", " ", "\n", " ", RowBox[{"see", " ", @@ -1090,7 +1204,7 @@ Cell[BoxData[ RowBox[{"TUG", "/", "Guides"}], "/", "ManualTuGames"}], " ", "from", " ", "the", " ", "Documentation", " ", RowBox[{"Center", "."}]}]}], " ", "\n", "*)"}]}]], "Code",ExpressionUUID->\ -"6d4fdbf7-8930-4757-913c-b58ef50311b6"], +"ee7bcee2-3c94-4dc9-86fb-bd9f346d2c17"], Cell[BoxData[ RowBox[{ @@ -1103,7 +1217,7 @@ Cell[BoxData[ "this", " ", "project", " ", "is", " ", "licensed", " ", "under", " ", "the", " ", "MIT", " ", "License", " ", RowBox[{"terms", "."}]}]}], "\n", " ", "\n", "*)"}], "\n"}]], "Code",E\ -xpressionUUID->"13bd1b37-d06c-4a32-a6b5-35405ec368da"], +xpressionUUID->"c03f1ed0-9040-406e-bbf4-48496357385c"], Cell[BoxData[ RowBox[{ @@ -1178,7 +1292,7 @@ Cell[BoxData[ "state", " ", "of", " ", "Baden"}], "-", RowBox[{"W\[UDoubleDot]rttemberg", " ", "through", " ", RowBox[{"bwHPC", "."}]}]}]}], "\n", "*)"}], " "}]], "Code",ExpressionU\ -UID->"b183305f-8888-4f79-97a8-f808de821890"], +UID->"49ad5287-e922-408f-a56b-634cb71a9e7a"], Cell[BoxData[{ RowBox[{ @@ -1209,9 +1323,9 @@ Cell[BoxData[{ "\"\<===================================================\>\"", "]"}], ";", "\n", RowBox[{ - "Print", "[", "\"\\"", "]"}], + "Print", "[", "\"\\"", "]"}], ";", "\n", - RowBox[{"Print", "[", "\"\\"", "]"}], ";", + RowBox[{"Print", "[", "\"\\"", "]"}], ";", "\n", RowBox[{ "Print", "[", @@ -1237,7 +1351,7 @@ Cell[BoxData[{ analyzed. T is the player set and values are the worth for the coalitions.\n \ Do not forget the semicolons, otherwise some compatibly problems with\n M. \ Carter's ShapleyValue[] occurs\>\""}], ";"}]}], "Code",ExpressionUUID->\ -"55492e9b-f214-490e-a658-584fef28fc5a"], +"8add5606-5c74-4067-aed8-98a6dc9e05ca"], Cell[BoxData[{ RowBox[{ @@ -1293,7 +1407,7 @@ contributions of player i is increasing.\>\""}], ";"}], "\n"}], "\n", "\"\<{True/False,{pg1,pg2,cg}}=DecomposeInPositiveGames[game] decomposes a \ TU game into a difference of two positive (i.e., convex) games, denoted by \ pg1 and pg2. The symbol cg is the recomposed game.\>\""}], ";"}]}], "Code",Exp\ -ressionUUID->"9731237e-1306-48b2-bca2-2636ab54b2c6"], +ressionUUID->"d9746731-4350-4ef5-b0df-8ee0fbb18894"], Cell[BoxData[{ RowBox[{ @@ -1369,7 +1483,7 @@ returns only 'True' or 'False'.\>\""}], ";"}], "\n"}], "\n", It returns 'True' or 'False'. Calling the function with the option will \ return\n the sum of the marginal contributions for each coalition S w.r.t. to \ each \n superset S union {j}. These values must be non-negative.\>\""}], - ";"}]}], "Code",ExpressionUUID->"9ccddaf5-ef3a-4312-87a1-92b535530a3e"], + ";"}]}], "Code",ExpressionUUID->"7e7dfd9d-db19-4ec2-8a7b-ec16c33f6941"], Cell[BoxData[{ RowBox[{ @@ -1475,8 +1589,8 @@ See Funaki (1986).\>\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{"TIJsets", "::", "usage"}], " ", "=", " ", "\n", "\"\\""}], ";"}]}], "Code",ExpressionUUID->"daee2f39-9057-43ab-bee6-\ -d7bfd7d31d99"], +j.\>\""}], ";"}]}], "Code",ExpressionUUID->"61ec959c-986f-44f5-a87a-\ +4f7684dbc31f"], Cell[BoxData[{ RowBox[{ @@ -1585,7 +1699,7 @@ computational reliability in \n cases of numerical issues the following \ methods can be used: RevisedSimplex, CLP, \n MOSEK, or Automatic. Default \ setting is Automatic. For getting more precise results \n one can even set \ Method->{InteriorPoint, Tolerance->10^-10}.\>\""}], ";"}]}], "Code",Expression\ -UUID->"1cc258d4-bd7a-43bd-bbf9-9db67d6fb4f3"], +UUID->"63075c82-abb5-4b28-bb9f-96804a4af17f"], Cell[BoxData[ RowBox[{ @@ -1599,7 +1713,7 @@ the computational reliability in \n cases of numerical issues the following \ methods can be used: RevisedSimplex, CLP, \n MOSEK, or Automatic. Default \ setting is Automatic. For getting more precise results \n one can even set \ Method->{InteriorPoint, Tolerance->10^-10}.\>\""}], ";"}]], "Code",ExpressionU\ -UID->"6ac10f25-fe5a-45fb-8329-fded970723d0"], +UID->"151c4c06-1a50-4e63-bb68-fadd9b82e899"], Cell[BoxData[{ RowBox[{ @@ -1713,8 +1827,8 @@ pre-imputation set.\n To increases the computational reliability in cases of \ numerical issues the following methods\n can be used: RevisedSimplex, CLP, \ MOSEK, or Automatic. Default setting is Automatic. For getting more precise \ results one can even set \n Method->{InteriorPoint, \ -Tolerance->10^-10}.\>\""}], ";"}]}], "Code",ExpressionUUID->"a141cd8e-7f30-\ -4f41-bb25-9ba0118a72e6"], +Tolerance->10^-10}.\>\""}], ";"}]}], "Code",ExpressionUUID->"eeca83f3-db2d-\ +4556-8960-199410c3af90"], Cell[BoxData[ RowBox[{ @@ -1725,8 +1839,8 @@ vector is the modiclus of the game.\n To increases the computational \ reliability in cases of numerical issues the following methods\n can be used: \ RevisedSimplex, CLP, MOSEK, or Automatic. Default setting is Automatic. For \ getting more precise results one can even set \n Method->{InteriorPoint, \ -Tolerance->10^-10}\>\""}], ";"}]], "Code",ExpressionUUID->"10366f71-0cdf-4de4-\ -afa7-bc30d9370378"], +Tolerance->10^-10}\>\""}], ";"}]], "Code",ExpressionUUID->"4514f44f-5967-4c94-\ +9da1-c58cc70e74c9"], Cell[BoxData[{ RowBox[{ @@ -1842,8 +1956,8 @@ otherwise 'False'. To increases the computational reliability \n in cases of \ numerical issues the following methods can be used: RevisedSimplex, CLP, \ GUROBI, MOSEK, \n or Automatic. Default setting is RevisedSimplex. For \ getting more precise results one can even set \n Method->{InteriorPoint, \ -Tolerance->10^-10}.\>\""}], ";"}]}], "Code",ExpressionUUID->"21f61c24-a24b-\ -4ae4-9791-36415128fab6"], +Tolerance->10^-10}.\>\""}], ";"}]}], "Code",ExpressionUUID->"939a877d-a728-\ +4db9-8758-68684eb60670"], Cell[BoxData[{ RowBox[{ @@ -1864,7 +1978,7 @@ Method->{InteriorPoint, Tolerance->10^-10}.\>\""}], ";"}], "\n"}], "\n", "\"\\""}], ";"}]}], "Code",ExpressionUUID->\ -"896b97d5-30ff-4d3f-9952-8bc8c8ccf733"], +"2052ba4d-c921-456d-b872-9878bd13ee81"], Cell[BoxData[{ RowBox[{ @@ -1987,7 +2101,7 @@ This information can be obtained by invoking the option InFavor. Notice that \ \n whenever the option EffVector is set to 'True', then the first vector must \ be positive, since it is \n related to the grand coalition. Similar to \ SetsToVec[]. See also SetsToVec[].\>\""}], ";"}]}], "Code",ExpressionUUID->\ -"3152861f-e515-45fe-b4fe-f6a8decdc36a"], +"5f0e2055-8bbc-40d9-a9bb-0c651da243b3"], Cell[BoxData[{ RowBox[{ @@ -2012,8 +2126,8 @@ the function BargainUnanMatrix[game,payoff,EffVector -> False].\>\""}], ";"}], "\"\\""}], ";"}]}], "Code",ExpressionUUID->"455a8601-b886-4483-a72a-\ -bd175bb43328"], +(2013).\>\""}], ";"}]}], "Code",ExpressionUUID->"ff2698d9-10f7-4dc7-9476-\ +116373c036fd"], Cell[BoxData[ RowBox[{ @@ -2022,7 +2136,7 @@ Cell[BoxData[ "\"\\""}], ";"}]], "Code",Expressio\ -nUUID->"5f161572-66e5-401f-bff6-c6c88eaae3d5"], +nUUID->"dcfbc817-e581-4908-a46b-19d763b72ee6"], Cell[BoxData[{ RowBox[{ @@ -2059,7 +2173,7 @@ improvement in order reduce \n the maximum surpluses.\>\""}], ";"}], solution by iteratively carrying \n out transfers between pairs of players. \ The suggested algorithm is due to M. Maschler. For details \n see U. Faigle, \ W. Kern and J. Kuipers (1998).\>\""}], ";"}]}], "Code",ExpressionUUID->\ -"39c8879d-31bf-402a-b62d-6b1cb364b7d1"], +"730fc579-42d7-4e79-bf0a-f6c3b73c1bda"], Cell[BoxData[ RowBox[{ @@ -2069,7 +2183,7 @@ Cell[BoxData[ solution by iteratively carrying \n out transfers between pairs of players. \ The suggested algorithm is due to M. Maschler. For details \n see U. Faigle, \ W. Kern and J. Kuipers (1998).\>\""}], ";"}]], "Code",ExpressionUUID->\ -"f74d3d68-463d-4175-881b-658eed718da3"], +"005589d2-3041-47c1-9bb8-c3b05fed4912"], Cell[BoxData[{ RowBox[{ @@ -2162,7 +2276,7 @@ checked.\>\""}], ";"}], "\n"}], "\n", "\"\\""}], ";"}]}], "Code",ExpressionUU\ -ID->"92d8ed8b-ee43-4390-a707-70fc369cf33f"], +ID->"e7669ffe-c621-4651-b286-a7ac253c7583"], Cell[BoxData[{ RowBox[{ @@ -2446,11 +2560,29 @@ into a vector of dimension 3.\>\""}], ";"}], "\n"}], "\n", RowBox[{"EANSCValue", "::", "usage"}], " ", "=", " ", "\n", "\"\\""}], ";"}], "\n"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"TauValAirProb", "::", "usage"}], " ", "=", " ", "\n", + "\"\\""}], ";"}], "\n"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"NucAirProb", "::", "usage"}], " ", "=", " ", "\n", + "\"\\""}], ";"}], "\n"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"ShapAirProb", "::", "usage"}], " ", "=", " ", "\n", + "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{ RowBox[{"NewShapley", "::", "usage"}], " ", "=", " ", "\n", - "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ @@ -2463,7 +2595,7 @@ the marginal contributions of players. Function not very efficient!\>\""}], RowBox[{ RowBox[{ RowBox[{"ShapleyValueML", "::", "usage"}], " ", "=", "\n", - "\"\\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{ @@ -2471,6 +2603,12 @@ the multi-linear extension.\>\""}], ";"}], "\n"}], "\n", RowBox[{"MLExtension", "::", "usage"}], " ", "=", "\n", "\"\\ \""}], ";"}], "\n"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"HarsanyiValue", "::", "usage"}], " ", "=", "\n", + "\"\\""}], + ";"}], "\n"}], "\n", RowBox[{ RowBox[{ RowBox[{ @@ -2529,7 +2667,7 @@ payoffs for coalition S.\>\""}], ";"}], "\n"}], "\n", RowBox[{ RowBox[{"SemiConvexQ", "::", "usagge"}], " ", "=", " ", "\n", " ", "\"\\""}], - ";"}]}], "Code",ExpressionUUID->"27b4b989-343e-4baa-a7c6-c04dde83c5cb"], + ";"}]}], "Code",ExpressionUUID->"438d79d6-aec7-4ee7-af59-77bf707d1b4b"], Cell[BoxData[{ RowBox[{ @@ -2649,7 +2787,7 @@ allocations. An imputation x \n is in the core iff x =< dual v.\>\""}], ";"}], "\"\\""}], - ";"}]}], "Code",ExpressionUUID->"e7282c95-6183-4a1d-84c6-cfa0b8c15e87"], + ";"}]}], "Code",ExpressionUUID->"c2688f83-44d2-4783-b1e7-b6c8cd33bcc2"], Cell[BoxData[{ RowBox[{ @@ -2703,8 +2841,8 @@ coordinate for each coalition size.\>\""}], ";"}], "\n"}], "\n", inequalities of the unanimity coordinates \n constraints for strict positive \ sums. It examines if the sufficient condition of convexity in terms \n of \ unanimity coordinates is satisfied. The return value is 'True' or 'False'. \ -See also EvalSumMinCoord[].\>\""}], ";"}]}], "Code",ExpressionUUID->"04e4ef05-\ -6a75-4070-bf45-38634ef15b6a"], +See also EvalSumMinCoord[].\>\""}], ";"}]}], "Code",ExpressionUUID->"12091eb3-\ +c600-4f3d-a056-69551eca20f5"], Cell[BoxData[ RowBox[{ @@ -2715,8 +2853,8 @@ Cell[BoxData[ unanimity coordinates constraints \n for positive sums. It examines if the \ sufficient condition of convexity in terms of unanimity \n coordinates is \ satisfied. The return value is 'True' or 'False'. See also EvalSumMinCoord[].\ -\>\""}], ";"}], " "}]], "Code",ExpressionUUID->"627a526f-55de-4197-a75d-\ -e406295fa124"], +\>\""}], ";"}], " "}]], "Code",ExpressionUUID->"1fcb946b-7341-40be-9d26-\ +da051cd99675"], Cell[BoxData[{ RowBox[{ @@ -2734,8 +2872,8 @@ on the results, all terms must be non-negative.\>\""}], ";"}], "\n"}], "\n", sufficient and necessary condition \n of average convexity of the game in \ terms of unanimity coordinates. Calling the function with its options\n open \ a glance on the results, all terms must be non-negative. See Solano and \ -Rafels (1996).\>\""}], ";"}]}], "Code",ExpressionUUID->"b16e920d-6727-465a-\ -8011-1ae3cef9b749"], +Rafels (1996).\>\""}], ";"}]}], "Code",ExpressionUUID->"1200b642-3ef5-4de3-\ +a2cd-33855c26cc07"], Cell[BoxData[{ RowBox[{ @@ -2780,8 +2918,8 @@ non-negative vector [q; p1, ..., pt], \n where T={1,...t}=Range[t]. It is \ admissible to specify the vector of weights by the following \n format of \ lists {q, p1, ...,pt} or {q, {p1, ..., pt}} or {{q}, {p1, ...,pt}}. The \ resultant list can \n then be used to define a game by using the function \ -DefineGame[].\>\""}], ";"}]}], "Code",ExpressionUUID->"b9cb5132-1444-4218-\ -a9f3-06b1357f04c9"], +DefineGame[].\>\""}], ";"}]}], "Code",ExpressionUUID->"2b196139-3cb5-4459-\ +9bc8-359a727ae8db"], Cell[BoxData[ RowBox[{ @@ -2898,7 +3036,7 @@ line segment of the (pre)-kernel.\>\""}], ";"}], "\n", " ", "*)"}], "\n", is a kernel catcher.\n This function may useful in connection with the \ package 'TuGamesView3D' to visualize for \n four person games the upper set. \ This set can coincide with the reasonable set.\>\""}], ";"}]}]}]], "Code",Expr\ -essionUUID->"4aa1b2a5-30e6-47b8-a5b3-846cb6bc0ce5"], +essionUUID->"c1cf53ae-79f2-4a49-9f58-4176354b1280"], Cell[BoxData[ RowBox[{ @@ -3633,20 +3771,19 @@ Cell[BoxData[ " ", RowBox[{ RowBox[{"Options", "[", "BalancedSelectionQ", "]"}], " ", "=", " ", - RowBox[{ + RowBox[{"{", RowBox[{ - RowBox[{"{", - RowBox[{ - RowBox[{"DisplayAllResults", " ", "->", " ", "False"}], ",", " ", - RowBox[{"Silent", " ", "->", " ", "True"}], ",", " ", - RowBox[{"Tight", "->", "False"}]}], "}"}], "\n", " ", - RowBox[{"Options", "[", "WeaklyBalancedSelectionQ", "]"}]}], " ", "=", - " ", - RowBox[{"{", - RowBox[{ - RowBox[{"DisplayAllResults", " ", "->", " ", "False"}], ",", " ", - RowBox[{"Silent", " ", "->", " ", "True"}], ",", " ", - RowBox[{"Tight", "->", "False"}]}], "}"}]}]}], ";", "\n", " ", + RowBox[{"DisplayAllResults", " ", "->", " ", "False"}], ",", " ", + RowBox[{"Silent", " ", "->", " ", "True"}], ",", " ", + RowBox[{"Tight", "->", "False"}]}], "}"}]}], ";", "\n", " ", + RowBox[{ + RowBox[{"Options", "[", "WeaklyBalancedSelectionQ", "]"}], " ", "=", + " ", + RowBox[{"{", + RowBox[{ + RowBox[{"DisplayAllResults", " ", "->", " ", "False"}], ",", " ", + RowBox[{"Silent", " ", "->", " ", "True"}], ",", " ", + RowBox[{"Tight", "->", "False"}]}], "}"}]}], ";", "\n", " ", RowBox[{ RowBox[{"Options", "[", "BalancedCollectionQ", "]"}], " ", "=", " ", RowBox[{"{", @@ -3888,7 +4025,7 @@ Cell[BoxData[ RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "12"}], ")"}]}]}]}], "}"}]}], ";"}]}], "\n", "]"}], - ";"}]], "Code",ExpressionUUID->"73318c9e-05be-4bea-9c14-89b462a605fe"], + ";"}]], "Code",ExpressionUUID->"fd735623-54cb-49c0-8a6c-c27025fe60c7"], Cell[BoxData[ RowBox[{ @@ -4139,6 +4276,10 @@ Cell[BoxData[ RowBox[{ RowBox[{"HarsanyiDividends", "::", "argerr"}], "=", "\"\\""}], ";"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"HarsanyiValue", "::", "argerr"}], "=", + "\"\\""}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"IntersectionUpperLowerSetQ", "::", "argerr"}], "=", @@ -4438,7 +4579,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"ZeroOneNormalization", "::", "argerr"}], "=", "\"\\""}], ";"}]}]}]], "Code",ExpressionUUID\ -->"c5feb781-2bf3-46bd-9c00-113548328677"], +->"4a0f952c-444b-4a11-91e4-9db915a982c6"], Cell[BoxData[ RowBox[{ @@ -4622,6 +4763,10 @@ Cell[BoxData[ RowBox[{ RowBox[{"ModCoalArray", "::", "argerr"}], "=", "\"\\""}], ";"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"NucAirProb", "::", "argerr"}], "=", + "\"\\""}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"OptStepSize", "::", "argerr"}], "=", @@ -4638,6 +4783,10 @@ Cell[BoxData[ RowBox[{ RowBox[{"SetsToVec", "::", "argerr"}], "=", "\"\\""}], ";"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"ShapAirProb", "::", "argerr"}], "=", + "\"\\""}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"SmallestContribution", "::", "argerr"}], "=", @@ -4658,6 +4807,10 @@ Cell[BoxData[ RowBox[{ RowBox[{"SbgAlmostAvCoQ", "::", "argerr"}], "=", "\"\\""}], ";"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"TauValAirProb", "::", "argerr"}], "=", + "\"\\""}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"TIJsets", "::", "argerr"}], "=", @@ -4686,7 +4839,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"WekalyBalancedCollectionQ", "::", "argerr"}], "=", "\"\\""}], ";"}]}]}]], "Code",ExpressionUU\ -ID->"1da76f78-8cf2-41fc-b728-4bd0c9ba7b2c"], +ID->"1f4eb31a-1782-4b4c-927a-ffe76d45edf5"], Cell[BoxData[ RowBox[{ @@ -4809,8 +4962,8 @@ Cell[BoxData[ 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"Code",ExpressionUUID->"a9203b57-07a2-4415-b0dd-\ -d3ee7943cb13"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"d5bbd145-5d6f-4970-acb5-\ +1463406afa1f"], Cell[BoxData[ RowBox[{ @@ -6775,8 +6928,8 @@ Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ "Old", " ", "Average", " ", "Convex", " ", "Function", " ", "is", " ", - "deprecated"}], " ", "*)"}]}]}]], "Code",ExpressionUUID->"d93c9e89-9797-\ -4259-b722-99af1bd802ef"], + "deprecated"}], " ", "*)"}]}]}]], "Code",ExpressionUUID->"4e23499f-a8a9-\ +409e-a54e-a707275a9d0c"], Cell[BoxData[ RowBox[{ @@ -6963,8 +7116,8 @@ Cell[BoxData[ RowBox[{"And", ",", RowBox[{"Apply", "[", RowBox[{"And", ",", "liste", ",", "1"}], "]"}]}], "]"}]}]}], "\n", - "\t", "]"}]}], ";"}], "\n"}]}]], "Code",ExpressionUUID->"2e5c3c69-865e-\ -4884-96fb-58294a90130d"], + "\t", "]"}]}], ";"}], "\n"}]}]], "Code",ExpressionUUID->"70b35cc0-3839-\ +4d71-93b0-13d1aa4bbd7c"], Cell[BoxData[ RowBox[{ @@ -6997,7 +7150,7 @@ Cell[BoxData[ RowBox[{"j", ",", RowBox[{"Length", "[", "margli", 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RowBox[{"{", "}"}], ",", + RowBox[{"{", "z0", "}"}], ",", RowBox[{"Max", "[", RowBox[{ RowBox[{ @@ -7773,7 +7926,7 @@ Cell[BoxData[ "]"}]}], "}"}], "]"}], " ", "&"}], " ", "/@", " ", "ProperCoalitions"}], " ", "/.", " ", "lwpara"}], " ", "/.", " ", "uppara"}], "]"}]}], "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->\ -"a644b476-eb7c-4935-a63a-5e99fa41af3c"], +"b8c1d624-8679-4489-87bb-619c1947ea21"], Cell[BoxData[{ RowBox[{ @@ -7887,7 +8040,7 @@ Cell[BoxData[{ RowBox[{"up", "[", "T", "]"}], " ", "/.", " ", "uppara"}], ")"}], " ", ">=", " ", RowBox[{"v", "[", "T", "]"}]}]}]}], "\n", " ", "]"}]}], - ";"}]}], "Code",ExpressionUUID->"025396c3-2deb-4f6d-a74f-e47585c529aa"], + ";"}]}], "Code",ExpressionUUID->"5b2c0422-bce3-42bc-87f7-4605b155ebe2"], Cell[BoxData[{ RowBox[{ @@ -8035,7 +8188,7 @@ Cell[BoxData[{ RowBox[{ "Print", "[", "\"\\"", "]"}]}], "]"}]}]}], "\n", " ", "]"}]}], ";"}]}], "Code",ExpressionUUI\ -D->"7896d419-144a-4243-998b-277d3b5cdeb1"], 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"-", "1"}], ")"}]}]}], - "]"}]}], "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"c3e0d35a-d867-\ -4e67-a749-4ee9702381b6"], + "]"}]}], "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"75ff5ba2-87b1-\ +4c7a-b860-b018c21ec45b"], Cell[BoxData[{ RowBox[{ @@ -17217,8 +17749,8 @@ Cell[BoxData[{ RowBox[{"Length", "[", "T", "]"}]}]}], ";", "\n", " ", RowBox[{"FindPreKernelSolution", "[", RowBox[{"game", ",", "pay", ",", "opts"}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}], "\n"}], "Code",ExpressionUUID->"0e12676b-6934-4e4a-b005-\ -e14b51ffd282"], + "]"}]}], ";"}], "\n"}], "Code",ExpressionUUID->"c1093441-5ee1-4fca-9c86-\ +4a8a70870666"], Cell[BoxData[{ RowBox[{ @@ -17400,8 +17932,8 @@ Cell[BoxData[{ RowBox[{"Length", "[", "T", "]"}]}]}], ";", "\n", " ", RowBox[{"FindKernelSolution", "[", RowBox[{"game", ",", "pay", ",", "opts"}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"4bbf7f8b-4d9d-4cfb-b55c-\ -3a050c083681"], + "]"}]}], ";"}]}], 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+UID->"128f03a1-8dd0-435d-aa5f-6a645b156a4c"], Cell[BoxData[{ RowBox[{ @@ -18042,8 +18574,8 @@ Cell[BoxData[{ RowBox[{"j", ",", " ", "i", ",", " ", RowBox[{"-", "Global`\[Delta]"}], ",", " ", "eps"}], "]"}], ",", " ", "\n", " ", "delconst"}], "}"}]}], "]"}], " ", "//", - " ", "Flatten"}]}], ";"}]}], "Code",ExpressionUUID->"298afda1-8335-4126-\ -ba1c-398e07293fec"], + " ", "Flatten"}]}], ";"}]}], "Code",ExpressionUUID->"c0a2dcac-50be-4ea4-\ +8b46-5e1366dc603d"], Cell[BoxData[{ RowBox[{ @@ -18162,7 +18694,7 @@ Cell[BoxData[{ RowBox[{"delconst", " ", "=", " ", RowBox[{"{", RowBox[{"Global`\[Delta]", " ", ">=", " ", "0"}], "}"}]}], - ";"}]}], "Code",ExpressionUUID->"261f311c-0c1a-46e9-bec8-3735f6e3c00c"], + ";"}]}], "Code",ExpressionUUID->"de1ded52-37a6-4e33-ba19-2317657fe23b"], Cell[BoxData[{ RowBox[{ @@ -18308,7 +18840,7 @@ Cell[BoxData[{ RowBox[{"anf", ",", " ", "1"}], "]"}]}], ";"}]}], "]"}], ";", "\n", " ", RowBox[{"Return", "[", "menge", "]"}]}]}], "]"}]}], ";"}]}], "Code",Expr\ 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-ssionUUID->"f44879c1-b1df-4611-934a-7e8cc5448468"], +ssionUUID->"00899f95-9b6f-4f4f-9dba-aef2fb996bf5"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ "Auxiliary", " ", "functions", " ", "to", " ", "verify", " ", "balancedness", " ", "of", " ", "the", " ", "excess", " ", "vector"}], " ", - "*)"}]], "Code",ExpressionUUID->"08302b30-5df4-4837-a82c-ee79e912e5f7"], + "*)"}]], "Code",ExpressionUUID->"52a248a3-e45b-4750-91ed-3d03a2ea4fa9"], Cell[BoxData[ RowBox[{ @@ -18594,7 +19126,7 @@ Cell[BoxData[ RowBox[{"MaxExcessBalanced", "[", RowBox[{"newgame", ",", " ", "pay"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "\n", "]"}]}], ";"}]], "Code",Expre\ -ssionUUID->"88e17862-fd19-4f1c-b626-7a5bf24af401"], +ssionUUID->"98b160b9-8eda-4530-b610-d8ee77436728"], Cell[BoxData[{ RowBox[{ @@ -18689,8 +19221,8 @@ Cell[BoxData[{ RowBox[{"{", "#", "}"}], "]"}]}], ")"}], " ", "&"}], " ", "/@", " ", RowBox[{"{", RowBox[{"Last", "[", "plj", "]"}], "}"}]}], " ", "/.", " ", - "asspay"}]}], ";"}], " "}]}], "Code",ExpressionUUID->"91ad307f-66f0-\ -4809-839d-2b5b05de47fa"], + "asspay"}]}], ";"}], " "}]}], "Code",ExpressionUUID->"62a1b286-abf5-\ +4d07-a796-660ed414397e"], Cell[BoxData[{ RowBox[{ @@ -18775,7 +19307,7 @@ Cell[BoxData[{ RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";", RowBox[{"Return", "[", "]"}]}]}], "]"}]}]}], "\n", " ", "]"}]}], - ";"}]}], "Code",ExpressionUUID->"6e8de231-b1fa-44f4-8eb6-102dce42b558"], + ";"}]}], "Code",ExpressionUUID->"49ca856b-10bb-4c0b-81cd-705ec5bc1295"], Cell[BoxData[ RowBox[{ @@ -18786,7 +19318,7 @@ Cell[BoxData[ " ", ":=", " ", "\n", "\t", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{"Max", "[", RowBox[{"ReplaceAll", "[", RowBox[{ @@ -18797,8 +19329,8 @@ Cell[BoxData[ RowBox[{"v", "[", "#", "]"}], " ", "-", " ", RowBox[{"x", "[", "#", "]"}]}], " ", "&"}], ",", " ", "sij"}], "]"}], ",", "payass"}], "]"}], "]"}]}], "\n", " ", "]"}]}], - ";"}], "\n"}]], "Code",ExpressionUUID->"e7680021-c592-4113-8264-\ -dc13951cc1b5"], + ";"}], "\n"}]], "Code",ExpressionUUID->"44582ffc-c4ae-42d7-bd1a-\ +7fe9c75179d4"], Cell[BoxData[ RowBox[{ @@ -18875,7 +19407,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";", RowBox[{"Return", "[", "]"}]}]}], "]"}]}]}], "\n", " ", "]"}]}], - ";"}]], "Code",ExpressionUUID->"e1516541-5da1-4e1b-8114-074a11b596d0"], + ";"}]], "Code",ExpressionUUID->"dff57537-0756-4139-9fa7-b343281251c1"], Cell[BoxData[ RowBox[{ @@ -18885,7 +19417,7 @@ Cell[BoxData[ " ", ":=", " ", "\n", "\t", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{"Min", "[", RowBox[{"ReplaceAll", "[", RowBox[{ @@ -18896,7 +19428,7 @@ Cell[BoxData[ RowBox[{"v", "[", "#", "]"}], " ", "-", " ", RowBox[{"x", "[", "#", "]"}]}], " ", "&"}], ",", " ", "sij"}], "]"}], ",", "payass"}], "]"}], "]"}]}], "\n", " ", "]"}]}], - ";"}]], "Code",ExpressionUUID->"4ff62652-83f0-4c4f-bdfb-4e0ae4ebcd86"], + ";"}]], "Code",ExpressionUUID->"68347b6b-5e34-4ad2-8c39-429c06143c58"], Cell[BoxData[{ RowBox[{ @@ -19035,8 +19567,8 @@ Cell[BoxData[{ RowBox[{"List", ",", RowBox[{"{", RowBox[{"minpi", ",", "minpj"}], "}"}]}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"fd17a012-e408-472b-8fe4-\ -e61d446f2451"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"7f66fefa-57fe-4d75-9e92-\ +3ff883e9f052"], Cell[BoxData[{ RowBox[{ @@ -19121,8 +19653,8 @@ Cell[BoxData[{ RowBox[{"dispmat", " ", "==", " ", "False"}], ",", " ", "ergb", ",", " ", "True", ",", " ", RowBox[{"DisplayResult", "[", "ergb", "]"}]}], "]"}]}]}], "\n", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"8dc4bf26-4b14-4322-a9f2-\ -bd4a97d2c7b0"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"c0fb774b-0a80-48cf-a760-\ +ac3d9c164950"], Cell[BoxData[{ RowBox[{ @@ -19213,7 +19745,7 @@ Cell[BoxData[{ RowBox[{"MatrixForm", "[", RowBox[{"PrependTo", "[", RowBox[{"surpl", ",", "mgij"}], "]"}], "]"}]}]}], "\n", "]"}]}], - ";"}]}], "Code",ExpressionUUID->"90d959c3-c705-4084-9211-8660871e3a22"], + ";"}]}], "Code",ExpressionUUID->"d918eff8-627a-4e36-9c07-9bc2eda59553"], Cell[BoxData[ RowBox[{ @@ -19426,7 +19958,7 @@ Cell[BoxData[ " ", RowBox[{"Apply", "[", RowBox[{"And", ",", " ", "neq"}], "]"}]}]}], "\n", " ", "]"}]}], - ";"}]}]}]], "Code",ExpressionUUID->"a0e7e1f4-45a0-420e-ba1e-d8561e715aee"], + ";"}]}]}]], "Code",ExpressionUUID->"0bebe6da-9a62-465e-8f0c-429ebccbb57d"], Cell[BoxData[{ RowBox[{ @@ -19552,7 +20084,7 @@ payoffs.\>\"", "]"}]}], "\n", ")"}]}], ";"}], "\n"}], "\n", " ", "True", ",", " ", RowBox[{"DisplayMessage", "[", "payoff", "]"}]}], "\n", " ", "\n", " ", "]"}]}], "\n", "]"}]}], ";"}]}], "Code",ExpressionUUID->\ -"b8843301-4798-4891-8819-68b26213d206"], +"0eed58ab-beff-4d40-8fa6-2d6c072944a3"], Cell[BoxData[{ RowBox[{ @@ -19569,7 +20101,7 @@ Cell[BoxData[{ RowBox[{"game_", ",", "payoff_List"}], "]"}], ":=", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{"Which", "[", RowBox[{ RowBox[{ @@ -19587,8 +20119,8 @@ Cell[BoxData[{ RowBox[{"game", ",", "payoff"}], "]"}], ",", "\n", " ", "True", ",", " ", RowBox[{"DisplayMessage", "[", "payoff", "]"}]}], "\n", " ", "]"}]}], - "\n", "]"}]}], ";"}]}], "Code",ExpressionUUID->"71e9fdca-76ae-4bdf-afbe-\ -e96647b5c03f"], + "\n", "]"}]}], ";"}]}], "Code",ExpressionUUID->"eed75b1c-e938-4fed-86f6-\ +fb889693a5b7"], Cell[BoxData[{ RowBox[{ @@ -19649,7 +20181,7 @@ Cell[BoxData[{ "\n", " ", RowBox[{"Append", "[", RowBox[{"indrat", ",", "eff"}], "]"}]}]}], "\n", "]"}]}], - ";"}]}], "Code",ExpressionUUID->"2de6515e-cccf-4185-ac94-0f013d36016e"], + ";"}]}], "Code",ExpressionUUID->"a9b85844-fc08-4221-b0be-5eeb04abd4e0"], Cell[BoxData[{ RowBox[{ @@ -19879,7 +20411,7 @@ single payoff vector.\>\"", "]"}]}], "\n", "\n", ")"}]}], ";"}], "\n", "\n", " ", "True", ",", " ", RowBox[{"PrintRemark", "[", "payoff", "]"}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}], ";"}]}], "Code",ExpressionUUID->\ -"88a302f5-5421-465b-95c6-aea5477bf471"], +"26e58c96-5c01-4ad9-89b7-f788ae7a2873"], Cell[BoxData[ RowBox[{ @@ -20129,20 +20661,6 @@ Cell[BoxData[ RowBox[{ "SetGameToNonZeroMonotonic", " ", "->", " ", "notzeromono"}], ",", " ", - RowBox[{"Method", "->", " ", "mth"}]}], "]"}]}], ",", - "\n", " ", - RowBox[{ - RowBox[{"DisplayAvcQ", "[", "avcQ", "]"}], ";", "\n", - " ", - RowBox[{"KernelSubCall", "[", - RowBox[{ - "orggame", ",", "callm", ",", " ", "changeps", ",", " ", - "dispres", ",", " ", - RowBox[{"EpsilonValue", " ", "->", " ", "epsilon"}], ",", - " ", - RowBox[{ - "SetGameToNonZeroMonotonic", " ", "->", " ", - "notzeromono"}], ",", " ", RowBox[{"Method", "->", " ", "mth"}]}], "]"}]}]}], "\n", " ", "]"}]}], "\n", " ", "]"}]}], "\n", " ", "]"}]}], "\n", " ", @@ -20162,7 +20680,7 @@ Cell[BoxData[ RowBox[{"zmQ_", ",", "coreQ_"}], "]"}], " ", ":=", " ", "\n", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", "zmQ"}], "]"}], ";", @@ -20181,7 +20699,7 @@ Cell[BoxData[ RowBox[{"zmQ_", ",", "coreQ_"}], "]"}], " ", ":=", " ", "\n", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", "zmQ"}], "]"}], ";", @@ -20199,7 +20717,7 @@ Cell[BoxData[ RowBox[{"zmQ_", ",", "coreQ_"}], "]"}], " ", ":=", "\n", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", "zmQ"}], "]"}], ";", @@ -20221,7 +20739,7 @@ Cell[BoxData[ " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", @@ -20243,7 +20761,7 @@ list.\>\"", "]"}], ";", "\n", " ", "Print", "[", "\"\\"", "]"}]}]}], "\n", " ", "]"}]}], ";"}], - "\n"}]}]], "Code",ExpressionUUID->"ca00a3a5-2e6a-4b6d-ad2a-802522345ce3"], + "\n"}]}]], "Code",ExpressionUUID->"a4a2c467-ca63-4146-ae03-38915f42913f"], Cell[BoxData[{ RowBox[{ @@ -20332,8 +20850,8 @@ Cell[BoxData[{ RowBox[{"SetGameToNonZeroMonotonic", " ", "->", " ", "notzeromono"}], ",", RowBox[{"Method", "->", "mth"}]}], "]"}]}]}]}], "\n", "\n", "\n", - " ", "]"}]}], ";"}]}], "Code",ExpressionUUID->"55abe7ab-e7e2-4d7a-82a6-\ -c0387be4f221"], + " ", "]"}]}], ";"}]}], "Code",ExpressionUUID->"49e5d7d7-ce3d-4c6c-99ac-\ +18a452b0e054"], Cell[BoxData[ RowBox[{ @@ -20421,7 +20939,7 @@ Cell[BoxData[ RowBox[{"Method", "->", "mth"}]}], "]"}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}], ";"}], "\n"}]], "Code",ExpressionUUID->\ -"a14d4bb6-54cb-43bc-b3dd-8320adce3da0"], +"01b5e813-59a9-46b1-b490-2927f27e22a4"], Cell[BoxData[ RowBox[{ @@ -20437,7 +20955,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"KernelPoints", "[", RowBox[{"game_", ",", " ", - RowBox[{"storepay_", ":", + RowBox[{"storepay_List", ":", RowBox[{"{", "}"}]}], ",", " ", "callm_", ",", " ", "changeps_", ",", " ", "dispres_", ",", " ", RowBox[{"opts", ":", @@ -20811,7 +21329,7 @@ Calculation!\>\"", "]"}], ";", "\n", RowBox[{"Method", "->", "mth"}]}], "]"}]}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}], ";"}]}]], "Code",Express\ -ionUUID->"9cf07b12-20aa-4298-a128-332156bc1eab"], +ionUUID->"28dc6c80-2eda-4a45-942e-3843914d3425"], Cell[BoxData[{ RowBox[{ @@ -20821,7 +21339,7 @@ Cell[BoxData[{ " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{ "Print", "[", "\"\\"", @@ -20835,7 +21353,7 @@ Cell[BoxData[{ RowBox[{"MessageKerPoints02", " ", ":=", "\n", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";", "\n", " ", @@ -21049,7 +21567,7 @@ MaxExcessBalanced.\>\"", "]"}], ";"}]}], "\n", " ", "]"}]}], ";"}], "\n", RowBox[{ "kersol", ",", "objfunc", ",", "nb", ",", "var", ",", "tra"}], "}"}]}], "]"}]}]}], "\n", "]"}]}], ";"}]}], "Code",ExpressionUUID->\ -"65f12498-2b5b-428b-a0c2-1444aa11f6e4"], +"ffcd9151-4fbf-44f8-9d01-feea13e5b236"], Cell[BoxData[{ RowBox[{ @@ -21248,7 +21766,7 @@ Cell[BoxData[{ RowBox[{ "kersol", ",", "objfunc", ",", "nb", ",", "var", ",", "tra"}], "}"}]}], "]"}]}]}], "\n", "\n", "]"}]}], ";"}]}], "Code",ExpressionUU\ -ID->"10ee9273-24df-4bb8-958a-274dbaf2c32c"], +ID->"74f4e529-fa6d-4c79-b1ca-b4ea18e076ed"], Cell[BoxData[ RowBox[{ @@ -21487,8 +22005,8 @@ Cell[BoxData[ RowBox[{ RowBox[{"Print", "[", "\"\\"", "]"}], ";", "pkl"}]}], "]"}], ",", "kl"}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"932d0cd2-8edb-480c-95ef-\ -e6525900aa2f"], + "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"3645536e-5c7c-4d24-a758-\ +7972ea7f786c"], Cell[BoxData[ RowBox[{ @@ -21498,7 +22016,7 @@ Cell[BoxData[ "sol_", ",", " ", "obj_", ",", " ", "const_", " ", ",", " ", "var_", " ", ",", " ", "T_", ",", " ", "callm_", ",", "sil_", ",", " ", "mth_", ",", " ", - RowBox[{"zf_", ":", + RowBox[{"zf_List", ":", RowBox[{"{", "}"}]}]}], "]"}], " ", ":=", " ", "\n", " ", RowBox[{"Block", "[", RowBox[{ @@ -21639,15 +22157,15 @@ Cell[BoxData[ "oldres", ",", " ", "obj", ",", " ", "newineq", ",", " ", "var", ",", " ", "T", ",", " ", "callm", ",", " ", "sil", ",", " ", "mth", " ", ",", " ", "valzf"}], "]"}]}], "]"}]}]}], "\n", "]"}]}], - ";"}]], "Code",ExpressionUUID->"48e568c3-5cce-46c9-840f-76515443d6dc"], + ";"}]], "Code",ExpressionUUID->"0c41d348-aca1-4190-9b6f-9a62da91e3d8"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ "Section", " ", "ends", " ", "to", " ", "determine", " ", "a", " ", "Kernel", " ", "Range", " ", "from", " ", "an", " ", - RowBox[{"LP", "."}]}], " ", "*)"}]], "Code",ExpressionUUID->"04f23a67-a7b6-\ -457f-988b-b1631b7157e7"], + RowBox[{"LP", "."}]}], " ", "*)"}]], "Code",ExpressionUUID->"b405c6aa-f023-\ +4ae2-bc27-28d646e95f18"], Cell[BoxData[ RowBox[{ @@ -21712,8 +22230,8 @@ Cell[BoxData[ RowBox[{"Length", "[", "T", "]"}]}]}], ";", "\n", " ", RowBox[{"AntiPreKernelSolution", "[", RowBox[{"game", ",", "pay", ",", "opts"}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"c512fedd-fe1c-4751-8734-\ -8577debc7ca0"], + "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"af7a3fc5-0cad-4160-a03a-\ +b7fecf7d18b0"], Cell[BoxData[{ RowBox[{ @@ -21818,8 +22336,8 @@ Cell[BoxData[{ RowBox[{"Length", "[", "T", "]"}]}]}], ";", "\n", " ", RowBox[{"PreKernelSolution", "[", RowBox[{"game", ",", "pay", ",", "opts"}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"fec2f53d-4844-4cee-be8b-\ -d2841f72d114"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"d2bc61c9-cad2-4a7a-a7e5-\ +d45c62b38544"], Cell[BoxData[{ RowBox[{ @@ -22185,7 +22703,7 @@ Cell[BoxData[{ RowBox[{"WrongCoordDimension", "[", "T_", "]"}], ":=", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{ "Print", "[", @@ -22203,7 +22721,7 @@ length!\>\"", "]"}], ";", "\n", " ", RowBox[{"coord_List", ",", "T_"}], "]"}], ":=", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", " ", @@ -22214,8 +22732,8 @@ length!\>\"", "]"}], ";", "\n", " ", RowBox[{"\"\\"", ",", " ", RowBox[{"2", "^", RowBox[{"Length", "[", "T", "]"}]}]}], "]"}], ";"}]}], "\n", "]"}]}], - ";"}], "\n"}], "Code",ExpressionUUID->"6403d79a-5e0e-4dae-b596-\ -5a600b3bd67b"], + ";"}], "\n"}], "Code",ExpressionUUID->"4abb12c4-d356-4114-83cf-\ +2dbbf0b761c6"], Cell[BoxData[{ RowBox[{ @@ -22540,12 +23058,12 @@ Cell[BoxData[{ RowBox[{ RowBox[{"MessageSDMKer", "[", RowBox[{ - RowBox[{"zfc_", ":", + RowBox[{"zfc_List", ":", RowBox[{"{", "}"}]}], ",", "minw_", ",", "nwaz_", ",", " ", "fucval_", ",", " ", "addexc_"}], "]"}], " ", ":=", "\n", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", "zfc"}], "]"}], @@ -22579,8 +23097,8 @@ Cell[BoxData[{ ",", RowBox[{"N", "[", RowBox[{"addexc", " ", "-", " ", "fucval"}], "]"}]}], "]"}], ";"}]}], - "\n", " ", "]"}]}], ";"}]}], "Code",ExpressionUUID->"fa439c24-d457-4e4a-\ -a5bc-e3423ecbe058"], + "\n", " ", "]"}]}], ";"}]}], "Code",ExpressionUUID->"bac6044c-3bc9-4361-\ +afd0-a6dab3ca7033"], Cell[BoxData[ RowBox[{ @@ -22699,7 +23217,7 @@ Cell[BoxData[ RowBox[{ "\"\\"", ",", " ", "alpscal"}], "]"}], ";"}]}], "\n", " ", "]"}]}], - ";"}]}]}]], "Code",ExpressionUUID->"89960918-5593-4f11-8569-2f1d40dfd612"], + ";"}]}]}]], "Code",ExpressionUUID->"ee704b0b-2565-424a-b0a3-e3d37aa1ec78"], Cell[BoxData[ RowBox[{ @@ -22846,8 +23364,8 @@ Cell[BoxData[ RowBox[{ RowBox[{"Length", "[", "extps", "]"}], "===", "0"}], ",", "pvec", ",", "extps"}], "]"}]}], ";", "\n", " ", "res"}]}], "\n", - "]"}]}], ";"}], "\n", "\n"}]}]], "Code",ExpressionUUID->"34f6ba6f-2528-\ -4efb-8eab-60aab8d38305"], + "]"}]}], ";"}], "\n", "\n"}]}]], "Code",ExpressionUUID->"91b09a77-4909-\ +4c74-975d-8f858c074587"], Cell[BoxData[ RowBox[{ @@ -22964,7 +23482,7 @@ Cell[BoxData[ " ", "effective", " ", "coalitions", " ", "to", " ", "balance", " ", "the", " ", "maximum", " ", RowBox[{"surpluses", "."}]}], "\n", "*)"}]}]}]], "Code",ExpressionUUID->\ -"c4af0540-b23e-4a5f-a01d-2dfebb8a9d5c"], +"46994335-332d-4a64-9fbc-de92b1285834"], Cell[BoxData[{ RowBox[{ @@ -22974,7 +23492,7 @@ Cell[BoxData[{ RowBox[{"payoff_List", ",", " ", "meffc_List"}], "]"}], " ", ":=", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{"Print", "[", RowBox[{ @@ -23257,8 +23775,8 @@ Cell[BoxData[{ RowBox[{"maxsurp", ",", "False"}], "]"}], ",", " ", "sigcoal", ",", RowBox[{"{", RowBox[{"sigcoal", ",", 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"payoff", "]"}]}], "\n", " ", "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"21f9b067-c59c-43b6-aadc-\ -5acc84d76df2"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"d6a0c6ce-c7a2-4f7f-97a9-\ +610f36fd243d"], Cell[BoxData[{ RowBox[{ @@ -23866,8 +24384,8 @@ Cell[BoxData[{ " ", "True", ",", " ", RowBox[{"PrintRemark", "[", "payoff", "]"}]}], "\n", " ", "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"cb0dfa75-11e5-42f0-9e9a-\ -90a953237fb6"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"59c027e9-6488-4ff5-8e47-\ +efc067a6b895"], Cell[BoxData[{ RowBox[{ @@ -23916,7 +24434,7 @@ Cell[BoxData[{ RowBox[{"mat_List", ",", "T_"}], "]"}], ":=", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{"Which", "[", RowBox[{ RowBox[{ @@ -23941,7 +24459,7 @@ Cell[BoxData[{ RowBox[{"WrongMatDimension", "[", "T_", "]"}], ":=", " ", RowBox[{"Block", "[", RowBox[{ - RowBox[{"{", "}"}], ",", "\n", " ", + RowBox[{"{", "z0", "}"}], ",", "\n", " ", RowBox[{ RowBox[{ "Print", "[", @@ -24055,8 +24573,8 @@ Cell[BoxData[{ RowBox[{"effvec", "==", "True"}], ",", " ", RowBox[{"Prepend", "[", RowBox[{"detunan", ",", "onesv"}], "]"}], ",", " ", "detunan"}], - "]"}]}]}], "\n", "]"}]}], ";"}]}], "Code",ExpressionUUID->"5ffb1b3e-\ -9123-4fce-985e-2accc0f39de6"], + "]"}]}]}], "\n", "]"}]}], ";"}]}], "Code",ExpressionUUID->"92d5cb02-\ +2d51-4a68-b0ae-d658393c4864"], Cell[BoxData[ RowBox[{ @@ -24077,7 +24595,7 @@ Cell[BoxData[ RowBox[{"DetDircSetIJ", "[", RowBox[{"#", ",", " ", "powers"}], "]"}], " ", "&"}], " ", "/@", " ", "bsccoal"}]}]}], "\n", " ", "]"}]}], ";"}]], "Code",ExpressionUUID->\ -"a344fa12-ca7d-42e7-a24a-c2b4ac87a196"], +"ec60b118-dc84-461d-beb5-38c8d4a7ec49"], Cell[BoxData[{ RowBox[{ @@ -24211,8 +24729,8 @@ Cell[BoxData[{ " ", "True", ",", " ", RowBox[{"PrintRemark", "[", "payoff", "]"}]}], "\n", " ", "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"df01c213-0a2d-4ba7-9cd7-\ -7c0edff9a081"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"9366530e-3348-470c-b5fa-\ +ffb7fdb1141c"], Cell[BoxData[{ RowBox[{ @@ -24377,8 +24895,8 @@ Cell[BoxData[{ RowBox[{"Length", "[", "T", "]"}]}]}], ";", "\n", " ", RowBox[{"PreKernel", "[", RowBox[{"game", ",", "pay", ",", "opts"}], "]"}]}]}], "\n", " ", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"811a6b11-5465-4ca2-9eeb-\ -f308b3752024"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"b90714d2-2b1d-4da4-a9b6-\ +82a3517b14a7"], Cell[BoxData[ RowBox[{ @@ -24456,8 +24974,8 @@ Cell[BoxData[ " ", "True", ",", " ", RowBox[{"PrintRemark", "[", "payoff", "]"}]}], "\n", " ", "]"}]}]}], "\n", " ", - "]"}]}], ";"}]], "Code",ExpressionUUID->"552ab4de-eeec-447f-a1a6-\ -ac468388a895"], + "]"}]}], ";"}]], "Code",ExpressionUUID->"fe9cf4bd-81ae-46ff-8b81-\ +ed94a4a737e2"], Cell[BoxData[ RowBox[{ @@ -24534,8 +25052,8 @@ Cell[BoxData[ ";", "\n", " ", RowBox[{"PreKernelAlg2", "[", RowBox[{"game", ",", "xvec", ",", "opts"}], "]"}]}]}], "]"}]}]}], - " ", "\n", " ", "]"}]}], ";"}]], "Code",ExpressionUUID->"a8c7d4e3-ebdc-\ -46b5-adcc-3b5669b2eaf8"], + " ", "\n", " ", "]"}]}], ";"}]], "Code",ExpressionUUID->"dafdf54a-b196-\ +4192-af6e-5c39673411a3"], Cell[BoxData[ RowBox[{ @@ -24759,7 +25277,7 @@ Cell[BoxData[ RowBox[{"Silent", " ", "->", " ", "sil"}], ",", " ", RowBox[{"SmallestCardinality", " ", "->", " ", "smc"}]}], "]"}]}], "]"}]}]}], " ", "\n", "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->\ -"eb486161-4c83-433d-a9c4-74fa09a880bb"], +"e7168b20-0666-49dd-af55-d0fc68091287"], Cell[BoxData[{ RowBox[{ @@ -24919,8 +25437,8 @@ Cell[BoxData[{ RowBox[{ RowBox[{"-", " ", RowBox[{"smex", ".", "edvec"}]}], "/", "nrsq"}]}], "]"}]}]}], "\n", - "]"}]}], ";"}]}], "Code",ExpressionUUID->"2f457008-14ff-4b54-8d83-\ -6dae12d8c940"], + "]"}]}], ";"}]}], "Code",ExpressionUUID->"748fd2c6-c485-4c9c-9fbb-\ +89ae213343e9"], Cell[BoxData[ RowBox[{ @@ -25133,8 +25651,8 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"gradpv", ",", " ", RowBox[{"Flatten", "[", "cgate", "]"}]}], "}"}]}]}], "\n", " ", - "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"ce63dcc1-0b2c-4d3d-8b97-\ -4d43d8645c65"], + "]"}]}], ";"}]}]}]], "Code",ExpressionUUID->"4afc1611-27f3-4973-815b-\ +646f003cf17a"], Cell[BoxData[{ RowBox[{ @@ -25229,7 +25747,7 @@ of h has no solution.\>\"", "]"}]}], ";"}], "\n"}], "\n", RowBox[{ "\"\\"", ",", " ", RowBox[{"Length", "[", "hstfunc", "]"}]}], "]"}]}], ")"}]}], - ";"}]}], "Code",ExpressionUUID->"1c2efcfb-2f4d-4ff4-80ad-577be963989f"], + ";"}]}], "Code",ExpressionUUID->"56564cbf-2d70-4d8f-b0dd-a0266501a44c"], Cell[BoxData[ RowBox[{ @@ -25257,8 +25775,8 @@ objective function h,\>\"", "]"}], ";", "\n", " ", solution is not a unique vector!\>\"", "]"}], ";", "\n", " ", RowBox[{ "Print", "[", "\"\\"", - "]"}]}], "\n", ")"}]}], ";"}]], "Code",ExpressionUUID->"41dc2545-81f3-\ -4181-8f75-20099a622aa6"], + "]"}]}], "\n", ")"}]}], ";"}]], "Code",ExpressionUUID->"121a0363-4575-\ +4aa6-9204-237a38e878e8"], Cell[BoxData[{ RowBox[{ @@ -25351,7 +25869,7 @@ vector.\>\"", "]"}], ";", "\n", " ", RowBox[{ RowBox[{"(*", " ", RowBox[{"Kernel", " ", "section", " ", "ends"}], " ", "*)"}]}]}], "Code",Ex\ -pressionUUID->"c4698953-5cc7-4e2d-98f1-e5614c178757"], +pressionUUID->"11ba8546-7dd8-4dd4-8c6c-1df1a2f5a33b"], Cell[BoxData[ RowBox[{ @@ -25784,7 +26302,7 @@ Cell[BoxData[ RowBox[{"Drop", "[", RowBox[{"#", ",", " ", "1"}], "]"}], " ", "&"}], " ", "/@", " ", "sortlist"}]}]}], "\n", " ", "]"}]}], ";"}], "\n"}]}]], "Code",Expr\ -essionUUID->"403f6640-1c76-4401-afdb-e4bc79b79f28"], +essionUUID->"9a498202-4e52-4fc9-b322-2ef7d2661a2f"], Cell[BoxData[{ RowBox[{ @@ -25915,7 +26433,7 @@ Cell[BoxData[{ RowBox[{"Drop", "[", RowBox[{"#", ",", " ", "1"}], "]"}], " ", "&"}], " ", "/@", " ", "sortlist"}]}]}], "\n", " ", "]"}]}], ";"}], "\n"}], "Code",Expressio\ -nUUID->"c25b3027-2686-440b-a34e-e6cae5191bcb"], +nUUID->"1bc2c34f-9dbe-4e08-b208-222c4a3a1ca2"], Cell[BoxData[{ RowBox[{ @@ 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