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Notebook[{
Cell["\<\
Supply chain game.  There are 2 suppliers in sequence feeding into a consumer \
with value v.  They both bid to produce their components and if their bids \
sum to less than v, they both get what they bid.  If it's more than v, they \
both get nothing.  This is isomorphic to a standard bargaining problem where \
the buyer and seller each say a price and if they overlap, they transact and \
get whatever surplus, and if they don't overlap, they both get nothing.\
\>", "Text"],

Cell[CellGroupData[{

Cell["Libraries and Constants and stuff", "Section"],

Cell[BoxData[
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          Join[$Path, {Environment["\<HOME\>"] <> "\</lib/\>", 
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\[IndentingNewLine]"\<windows\>", $Path = 
          Join[$Path, {"\<E:\\lib\\\>", "\<E:\\equilibria\\\>"}], \
\[IndentingNewLine]"\<home\>", $Path = 
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
    \(\(\( (*\ 
      Supply\ chain\ game\ with\ 2\ suppliers\ in\ sequence ... \ *) \)\(\
\[IndentingNewLine]\)\(payoff[myCost_, myBid_, otherBids_List] := 
      If[myBid + Plus @@ otherBids \[LessEqual] v, myBid - myCost, 
        0]\)\)\)], "Input"],

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    \(minAction[myCost_:  0] := 
      First[bidRange[myCost]]\), "\[IndentingNewLine]", 
    \(maxAction[myCost_:  0] := Last[bidRange[myCost]]\)}], "Input"],

Cell[BoxData[{
    \(\(paperStrategy[v_]\)[c_] := 
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        3/4*c + v/4]\), "\[IndentingNewLine]", 
    \(\(fixedPriceStrategy[p_, v_]\)[c_] := 
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        p \[LessEqual] c \[LessEqual] 1, v]\), "\[IndentingNewLine]", 
    \(\(linearStrategy[v_]\)[c_] := 
      Which[0 \[LessEqual] c \[LessEqual] 1, 
        c/2 + v/3]\), "\[IndentingNewLine]", 
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      Which[0 \[LessEqual] c \[LessEqual] 2/3*v - 1, 2/3*v - 1/2, 
        2/3*v - 1 \[LessEqual] c \[LessEqual] 1, 
        c/2 + v/3]\), "\[IndentingNewLine]", 
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      Which[0 \[LessEqual] c \[LessEqual] 1, c]\)}], "Input"],

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