{"id":386,"date":"2018-04-16T04:55:10","date_gmt":"2018-04-16T04:55:10","guid":{"rendered":"http:\/\/chwe.net\/michael\/?page_id=386"},"modified":"2018-04-16T04:55:10","modified_gmt":"2018-04-16T04:55:10","slug":"mathematica-code-for-computing-largest-consistent-set","status":"publish","type":"page","link":"http:\/\/chwe.net\/michael\/index.php\/mathematica-code-for-computing-largest-consistent-set\/","title":{"rendered":"Mathematica code for computing largest consistent set"},"content":{"rendered":"
(*************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* preliminary functions *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(*************************)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* logical operations on matrices *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
matrixAnd[list_]:= MapThread[And, list, Depth[list]-2];<\/span><\/div>\n
matrixOr[list_]:= MapThread[Or, list, \u00a0Depth[list]-2];<\/span><\/div>\n
logicalmatrixmult[g_,h_]:=<\/span><\/div>\n
\u00a0 Map[#>0 &, Map[If[#,1,0]&,g,{2}].Map[If[#,1,0]&,h,{2}], {2}];<\/span><\/div>\n
logicalident:= Map[#==1&, IdentityMatrix[z], {2}];<\/span><\/div>\n
logicalzero:= Table[False, {z},{z}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* all nonempty subsets of {1,2,..,i} *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
nonemptysubsets[i_]:= Table[<\/span><\/div>\n
\u00a0 Flatten[Position[Reverse[IntegerDigits[j,2]],1]],{j,1,2^i-1}];<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(****************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* initialization procedure *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(****************************)<\/span><\/div>\n
initialize:= ClearAll[n, z, preferences, effective, outcomes,<\/span><\/div>\n
\u00a0 activecoalitions, coalpref, dirdom, inddom, inddomident, u, ord,<\/span><\/div>\n
\u00a0 num, name, payoff];<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(************************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0main procedure \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0inputs: \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* \u00a0 n, z, preferences, effective \u00a0 *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0returns the lcs \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(************************************)<\/span><\/div>\n
lcs:=Block[{i},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 find the coalitions which have *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* nonempty effectiveness relations *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 activecoalitions=<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Select[nonemptysubsets[n], Apply[Or,Flatten[effective[#]]]&];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* define coalitional preferences *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 coalpref[s_]:= coalpref[s]= matrixAnd[ preferences[[s]] ];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* compute direct dominance relation *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 dirdomproc[s_]:= matrixAnd[ {coalpref[s], effective[s]} ];<\/span><\/div>\n
\u00a0 dirdom= matrixOr[ Map[dirdomproc, activecoalitions] ];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* compute indirect dominance relation *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 inddomproc2[s_, g_]:=<\/span><\/div>\n
\u00a0 \u00a0 \u00a0matrixAnd[{logicalmatrixmult[effective[s],g], coalpref[s]}];<\/span><\/div>\n
\u00a0 inddomproc1[g_]:=<\/span><\/div>\n
\u00a0 \u00a0 \u00a0matrixOr[Prepend[Map[inddomproc2[#,g]&, activecoalitions], g]];<\/span><\/div>\n
\u00a0 inddom= FixedPoint[inddomproc1,dirdom];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* compute union of indirect dominance *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0relation and the identity relation *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 inddomident= matrixOr[{inddom, logicalident}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0given a set x of presumably stable *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0outcomes, the deviation of coalition s *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0from a to d is not deterred if the *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* deviation is feasible, and all outcomes *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 either do not indirectly dominate d *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0or are preferred by s over a *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 unstableproc3[x_,a_,d_,s_]:= effective[s][[a,d]] && matrixAnd[<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Map[Not[inddomident[[d,#]]] || coalpref[s][[a,#]]&, x]];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0given a set x of presumably stable *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* outcomes, the deviation from a to d *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 will not happen if each coalition *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 is deterred *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 stableproc2[x_,a_,d_]:=<\/span><\/div>\n
\u00a0 \u00a0 \u00a0matrixAnd[Map[Not[unstableproc3[x,a,d,#]]&, activecoalitions]];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* given a set x of presumably stable *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0outcomes, the outcome a is stable *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 if every deviation is deterred *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 stableproc1[x_,a_]:=<\/span><\/div>\n
\u00a0 \u00a0 \u00a0matrixAnd[ Map[stableproc2[x,a,#]&, Table[i,{i,1,z}] ] ];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* given a set x of presumably stable *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 outcomes, f[x] is the set of *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0outcomes which are stable *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 f[x_]:= Select[x, stableproc1[x, #]&];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* the lcs is the largest *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 fixed point of f *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 FixedPoint[f, Table[i,{i,1,z}]]<\/span><\/div>\n
];<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(*******************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* convenient input procedures *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0for general games \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(*******************************)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* basic setup procedure *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
setup[i_,list_]:= Block[{},<\/span><\/div>\n
\u00a0 n=i;<\/span><\/div>\n
\u00a0 outcomes=list; \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* a list of the names of outcomes *)<\/span><\/div>\n
\u00a0 z=Length[outcomes];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* make preference and effectivness *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 relations null *)<\/span><\/div>\n
\u00a0 preferences= Table[False, {n},{z},{z}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Scan[Block[{},effective[#]=Table[False,{z},{z}]]&,<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 nonemptysubsets[n]];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 functions which translate *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* between outcome names and numbers *)<\/span><\/div>\n
\u00a0 name[exp_]:= Map[outcomes[[#]]&, exp, {-1}];<\/span><\/div>\n
\u00a0 num[exp_]:= Map[Position[outcomes,#][[1,1]]&, exp, {-1}];<\/span><\/div>\n
];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* convert utility representation *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0to preference relations *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
u2preferences:= Block[{i,j,k},<\/span><\/div>\n
\u00a0 preferences= Table[ u[name[j]][[i]] <u[name[k]][[i]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0{i,1,n},{j,1,z},{k,1,z}];<\/span><\/div>\n
];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* convert preference order representation *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 to preference relations *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
ord2preferences:= Block[{i,j,k},<\/span><\/div>\n
\u00a0 \u00a0preferences= Table[<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 Position[ord[i],name[j]][[1,1]]<<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 Position[ord[i],name[k]][[1,1]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0{i,1,n},{j,1,z},{k,1,z}];<\/span><\/div>\n
];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* input: \u00a0player i *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 prefers b to a *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
lt[i_][a_,b_]:= preferences[[i,num[a],num[b]]]=True;<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* input: \u00a0coalition coal *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 can move from a to b *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
to[coal_][a_,b_]:= Block[{temp}, temp=effective[coal];<\/span><\/div>\n
\u00a0 temp[[num[a],num[b]]]=True; effective[coal]=temp;];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* input: \u00a0coalition coal *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 can move from a to b *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0and from b to a *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
btwn[coal_][a_,b_]:= Block[{}, to[coal][a,b]; to[coal][b,a];];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0input: \u00a0coalition coal *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* can move from any outcome *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 to outcomes in list *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
fromanywhere[coal_, list_]:= Block[{i},<\/span><\/div>\n
\u00a0 effective[coal]= Transpose[Table[ If[MemberQ[list,name[i]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Table[True,{z}], Table[False,{z}]], {i,1,z}]];];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* input: \u00a0players decide *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 by majority rule *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
majorityrule:= Scan[Block[{}, effective[#]=Table[True,{z},{z}]]&,<\/span><\/div>\n
\u00a0 Select[nonemptysubsets[n], Length[#]>Quotient[n,2]&]];<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(****************************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* strategic form game input procedures *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(****************************************)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0individual contingent threats: *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* input strategy sets and utility *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* profiles in lexicographic order *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
indivcontthreats[stratsets_,ulist_]:=<\/span><\/div>\n
\u00a0 Block[{i,j,k,comp,singletoncoalitions},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0n= Length[stratsets];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0outcomes= Flatten[Apply[Outer, Prepend[stratsets, List]],n-1];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0z= Length[outcomes];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 functions which translate *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* between outcome names and numbers *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0name[exp_]:= Map[outcomes[[#]]&, exp, {-1}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0num[exp_]:= Map[Position[outcomes,#][[1,1]]&, exp, {-2}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* generate preference and *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* effectiveness relations *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0preferences= Table[ ulist[[j,i]]<ulist[[k,i]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {i,1,n},{j,1,z},{k,1,z}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0singletoncoalitions= Select[nonemptysubsets[n], Length[#]==1&];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Scan[Block[{},effective[#]=Table[False,{z},{z}]]&,<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 nonemptysubsets[n]];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Scan[Block[{},comp=Complement[Table[i,{i,1,n}],#];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 effective[#]=Table[name[i][[comp]]===name[j][[comp]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{i,1,z},{j,1,z}];]&, singletoncoalitions];<\/span><\/div>\n
];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* coalitional contingent threats: *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* input strategy sets and utility *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* profiles in lexicographic order *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
coalcontthreats[stratsets_,ulist_]:=<\/span><\/div>\n
\u00a0 Block[{i,j,k,comp,singletoncoalitions},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0n= Length[stratsets];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0outcomes= Flatten[Apply[Outer, Prepend[stratsets, List]],n-1];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0z= Length[outcomes];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* \u00a0 \u00a0 \u00a0 \u00a0 functions which translate *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* between outcome names and numbers *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0name[exp_]:= Map[outcomes[[#]]&, exp, {-1}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0num[exp_]:= Map[Position[outcomes,#][[1,1]]&, exp, {-2}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* generate preference and *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* effectiveness relations *)<\/span><\/div>\n
\u00a0 \u00a0 \u00a0preferences= Table[ ulist[[j,i]]<ulist[[k,i]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {i,1,n},{j,1,z},{k,1,z}];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0Scan[Block[{},comp=Complement[Table[i,{i,1,n}],#];<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 effective[#]=Table[name[i][[comp]]===name[j][[comp]],<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{i,1,z},{j,1,z}];]&, nonemptysubsets[n]];<\/span><\/div>\n
];<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(***************************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* \u00a0examples: how to use the program \u00a0 *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* (the same game is shown throughout) *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(***************************************)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Can input n, z, preferences, effective directly *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
n=3;<\/span><\/div>\n
z=3;<\/span><\/div>\n
preferences={ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* player 1’s preference relation *)<\/span><\/div>\n
\u00a0 {{False,True,True}, {False,False,True}, {False,False,False}},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* player 2’s preference relation *)<\/span><\/div>\n
\u00a0 {{False,False,True}, {True,False,True}, {False,False,False}},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* player 3’s preference relation *)<\/span><\/div>\n
\u00a0 {{False,True,True}, {False,False,True}, {False,False,False}}<\/span><\/div>\n
};<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* {1,2}’s effectiveness relation *)<\/span><\/div>\n
effective[{1,2}]=<\/span><\/div>\n
\u00a0 {{False,True,False}, {True,False,False}, {False,False,False}};<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* {3}’s effectiveness relation *)<\/span><\/div>\n
effective[{3}]=<\/span><\/div>\n
\u00a0 {{False,False,False}, {False,False,True}, {False,True,False}};<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* other coalitions can’t do anything *)<\/span><\/div>\n
effective[{1}]=<\/span><\/div>\n
\u00a0 {{False,False,False}, {False,False,False}, {False,False,False}};<\/span><\/div>\n
effective[{2}]=<\/span><\/div>\n
\u00a0 {{False,False,False}, {False,False,False}, {False,False,False}};<\/span><\/div>\n
effective[{1,3}]=<\/span><\/div>\n
\u00a0 {{False,False,False}, {False,False,False}, {False,False,False}};<\/span><\/div>\n
effective[{2,3}]=<\/span><\/div>\n
\u00a0 {{False,False,False}, {False,False,False}, {False,False,False}};<\/span><\/div>\n
lcs<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{3}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* It’s easier to use convenient \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0input procedures \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
initialize; <\/span><\/div>\n
setup[3,{a,b,c}];<\/span><\/div>\n
a~lt[1]~b; b~lt[1]~c; a~lt[1]~c; \u00a0 (* specify preference relations *)<\/span><\/div>\n
b~lt[2]~a; b~lt[2]~c; a~lt[2]~c;<\/span><\/div>\n
a~lt[3]~b; b~lt[3]~c; a~lt[3]~c;<\/span><\/div>\n
a~btwn[{1,2}]~b; \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* specify effectiveness relations *)<\/span><\/div>\n
b~btwn[{3}]~c;<\/span><\/div>\n
lcs<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{3}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Can specify preferences using utility profiles *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3,{a,b,c}];<\/span><\/div>\n
u[a]={1,1,2}; \u00a0 \u00a0 \u00a0 \u00a0 (* utility profiles for each of the outcomes *)<\/span><\/div>\n
u[b]={2,0,0};<\/span><\/div>\n
u[c]={3,2,1};<\/span><\/div>\n
u2preferences; \u00a0 \u00a0(* convert utility representation to preferences *)<\/span><\/div>\n
a~btwn[{1,2}]~b;<\/span><\/div>\n
b~btwn[{3}]~c;<\/span><\/div>\n
name[lcs] \u00a0 \u00a0 (* output names, not numbers, of outcomes in the lcs *)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Can specify preferences using *)<\/span><\/div>\n
(* \u00a0linear preference ordering \u00a0 *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3,{a,b,c}];<\/span><\/div>\n
ord[1]={a,b,c}; \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* each player’s preference ordering *)<\/span><\/div>\n
ord[2]={b,a,c};<\/span><\/div>\n
ord[3]={a,b,c};<\/span><\/div>\n
\u00a0<\/span><\/div>\n
ord2preferences; \u00a0 \u00a0(* convert order representation to preferences *)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
a~btwn[{1,2}]~b;<\/span><\/div>\n
b~btwn[{3}]~c;<\/span><\/div>\n
\u00a0<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(********************************)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* examples in the dissertation *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(********************************)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Example in “How to compute the LCS \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* when the number of outcomes is finite”, page 14 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[2,{a,b,c,d}];<\/span><\/div>\n
ord[1]={a,b,c,d}; ord[2]={d,a,b,c};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; b~to[{2}]~c; c~to[{1}]~d; d~to[{2}]~a; a~to[{1,2}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Condorcet “paradox”, page 16 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3,{a,b,c}];<\/span><\/div>\n
ord[1]={a,b,c}; ord[2]={c,a,b}; ord[3]={b,c,a};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1,2}]~b; b~to[{1,3}]~c; c~to[{2,3}]~a;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a, b, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* The LCS versus the stable set, pages 16–17 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[2,{a,b,c}];<\/span><\/div>\n
ord[1]={a,c,b}; ord[2]={a,b,c};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; b~to[{2}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[2,{a,b,c}];<\/span><\/div>\n
ord[1]={c,a,b}; ord[2]={a,b,c};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; b~to[{2}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 2. The stable set is arbitrary, page 19 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3,{123, 231, 312, 124, 210, 120, 211}];<\/span><\/div>\n
u[123]={1,2,3}; u[231]={2,3,1}; u[312]={3,1,2};<\/span><\/div>\n
u[124]={1,2,4}; u[210]={2,1,0}; u[120]={1,2,0}; u[211]={2,1,1};<\/span><\/div>\n
u2preferences;<\/span><\/div>\n
123~to[{1,2}]~231; 231~to[{1,3}]~312; 312~to[{2,3}]~123;<\/span><\/div>\n
312~to[{3}]~124; 124~to[{1}]~210; 210~to[{2}]~120;<\/span><\/div>\n
120~to[{1}]~211; 211~to[{2}]~124;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{123, 231, 312, 124, 210, 120, 211}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Figure 3. The LCS predicts one of the *)<\/span><\/div>\n
(* three Nash equilibria, page 21 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[4,{“(1a,2a,3a,4a)”, “(1b,2b,3a,4a)”, “(1a,2a,3b,4b)”}];<\/span><\/div>\n
u[“(1a,2a,3a,4a)”]={3,3,1,1};<\/span><\/div>\n
u[“(1b,2b,3a,4a)”]={2,2,3,3};<\/span><\/div>\n
u[“(1a,2a,3b,4b)”]={1,1,2,2};<\/span><\/div>\n
u2preferences;<\/span><\/div>\n
“(1a,2a,3a,4a)”~btwn[{1,2}]~”(1b,2b,3a,4a)”;<\/span><\/div>\n
“(1b,2b,3a,4a)”~btwn[{1,2,3,4}]~”(1a,2a,3b,4b)”;<\/span><\/div>\n
“(1a,2a,3b,4b)”~btwn[{3,4}]~”(1a,2a,3a,4a)”;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{(1b,2b,3a,4a)}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 4. No stable set exists but \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* the LCS predicts a unique outcome, page 23 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
indivcontthreats[{{“1a”,”1b”,”1c”},{“2a”,”2b”},{“3a”,”3b”}},<\/span><\/div>\n
{{1,1,4}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,7,1},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {0,0,0}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{6,6,5},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* *)<\/span><\/div>\n
{2,2,6}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {3,3,7}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* *)<\/span><\/div>\n
{0,0,0}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {4,4,2}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{5,5,3}}<\/span><\/div>\n
];<\/span><\/div>\n
(* put utility profiles in lexicographic order:<\/span><\/div>\n
\u00a0 u(1a,2a,3a), u(1a,2a,3b), u(1a,2b,3a), u(1a,2b,3b),<\/span><\/div>\n
\u00a0 u(1b,2a,3a), u(1b,2a,3b), etc. *)<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2b, 3b}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 5.\u00a0 The stable set is misleading, page 23 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
indivcontthreats[{{“1a”,”1b”},{“2a”,”2b”}},<\/span><\/div>\n
{{3,3}, {2,2},<\/span><\/div>\n
{0,0}, {1,1}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2a}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* The Prisoners’ Dilemma, page 24 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
indivcontthreats[{{“Cooperate”,”Defect”},{“Cooperate”,”Defect”}},<\/span><\/div>\n
{{3,3}, {0,4},<\/span><\/div>\n
{4,0}, {1,1}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{Cooperate, Cooperate}, {Defect, Defect}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 6. Strict, not all, Nash equilibria *)<\/span><\/div>\n
(* are contained in the LCS, page 25 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
initialize;<\/span><\/div>\n
indivcontthreats[{{“1a”,”1b”,”1c”},{“2a”,”2b”,”2c”}},<\/span><\/div>\n
{{1,1}, {0,0}, {0,0},<\/span><\/div>\n
{1,1}, {2,2}, {0,0},<\/span><\/div>\n
{0,0}, {0,0}, {3,3}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1b, 2b}, {1c, 2c}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 7. The LCS makes the sharpest prediction, page 26 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
indivcontthreats[{{“1a”,”1b”},{“2a”,”2b”,”2c”}},<\/span><\/div>\n
{{3,3}, {0,0}, {0,4},<\/span><\/div>\n
{5,0}, {4,2}, {0,0}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1b, 2b}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 8. The LCS is the only \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* nonempty solution concept, page 27 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
coalcontthreats[{{“1a”,”1b”},{“2a”,”2b”},{“3a”,”3b”}},<\/span><\/div>\n
{{1,2,3}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{4,0,4},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {0,0,0}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{3,1,2},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* *)<\/span><\/div>\n
{0,4,4}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {2,3,1}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{4,4,0}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2a, 3a}, {1a, 2b, 3b}, {1b, 2b, 3a}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Figure 9. The LCS and strong Nash equilibrium differ, page 27 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
coalcontthreats[{{“1a”,”1b”},{“2a”,”2b”},{“3a”,”3b”}},<\/span><\/div>\n
{{2,2,4}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{5,5,3},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {0,2,0}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,2,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* *)<\/span><\/div>\n
{0,0,0}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {1,4,1}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{3,3,0}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2a, 3b}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 10. An outcome in the LCS is Pareto dominated *)<\/span><\/div>\n
(* by another outcome in the LCS, page 28 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
coalcontthreats[{{“1a”,”1b”,”1c”},{“2a”,”2b”,”2c”}},<\/span><\/div>\n
{{2,4}, {0,0}, {0,0},<\/span><\/div>\n
{0,0}, {3,5}, {1,7},<\/span><\/div>\n
{0,0}, {7,1}, {5,3}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2a}, {1b, 2b}, {1b, 2c}, {1c, 2b}, {1c, 2c}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* The Prisoners’ Dilemma, page 28 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
coalcontthreats[{{“Cooperate”,“Defect”},{“Cooperate”,”Defect“}},<\/span><\/div>\n
{{3,3}, {0,4},<\/span><\/div>\n
{4,0}, {1,1}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{Cooperate, Cooperate}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Figure 11. The LCS in the coalitional contingent threats *)<\/span><\/div>\n
(* situation is not a subset of the LCS in the individual \u00a0 *)<\/span><\/div>\n
(* contingent threats situation, page 29 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
initialize;<\/span><\/div>\n
indivcontthreats[{{“1a”,”1b”},{“2a”,”2b”},{“3a”,”3b”}},<\/span><\/div>\n
{{3,3,2}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{1,1,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {0,4,3}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* *)<\/span><\/div>\n
{4,0,3}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {1,1,4}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{2,2,3}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2a, 3a}, {1b, 2b, 3a}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
coalcontthreats[{{“1a”,”1b”},{“2a”,”2b”},{“3a”,”3b”}},<\/span><\/div>\n
{{3,3,2}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{1,1,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {0,4,3}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(* *)<\/span><\/div>\n
{4,0,3}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{0,0,0},<\/span><\/div>\n
\u00a0 \u00a0 \u00a0 \u00a0 {1,1,4}, \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0{2,2,3}}<\/span><\/div>\n
];<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{{1a, 2a, 3a}, {1b, 2b, 3b}}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* First example of majority rule voting, page 39 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3, {134, 341, 413, 222}];<\/span><\/div>\n
u[134]={1,3,4}; u[341]={3,4,1}; u[413]={4,1,3}; u[222]={2,2,2};<\/span><\/div>\n
u2preferences;<\/span><\/div>\n
majorityrule;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{134, 341, 413, 222}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Second example of majority rule voting, page 40 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3, {134, 423, 541, 252, 315}];<\/span><\/div>\n
u[134]={1,3,4}; u[423]={4,2,3}; u[541]={5,4,1};<\/span><\/div>\n
\u00a0 u[252]={2,5,2}; u[315]={3,1,5};<\/span><\/div>\n
u2preferences;<\/span><\/div>\n
majorityrule;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{423, 541, 252}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* Comparative statics examples: player 1 is the kidnapper, *)<\/span><\/div>\n
(* player 2 the relative, player 3 the detective, and \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* player 4 the judge, page 41 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[4, {a,b,c,d}];<\/span><\/div>\n
ord[1]={d,b,a,c};<\/span><\/div>\n
ord[2]={b,c,a,d};<\/span><\/div>\n
ord[3]={b,c,a,d};<\/span><\/div>\n
ord[4]={b,c,d,a};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; b~to[{2}]~c; c~to[{3}]~d; d~to[{4}]~a;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[4, {a,b,c,d}];<\/span><\/div>\n
ord[1]={d,b,a,c};<\/span><\/div>\n
ord[2]={b,c,a,d};<\/span><\/div>\n
ord[3]={b,c,a,d};<\/span><\/div>\n
ord[4]={b,c,d,a};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; b~to[{2}]~c; d~to[{4}]~a;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{c, d}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[4, {a,b,c,d}];<\/span><\/div>\n
ord[1]={d,b,a,c};<\/span><\/div>\n
ord[2]={b,c,a,d};<\/span><\/div>\n
ord[3]={b,c,a,d};<\/span><\/div>\n
ord[4]={b,c,d,a};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; d~to[{4}]~a;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a, b, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Refinements and extensions examples, pages 44–45 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[1, {a,b,c}];<\/span><\/div>\n
ord[1]={a,b,c};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; \u00a0a~to[{1}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{b, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[2, {a,b,c}];<\/span><\/div>\n
ord[1]={c,a,b};<\/span><\/div>\n
ord[2]={a,b,c};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1,2}]~b; \u00a0a~to[{2}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{b, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[2, {a,b,c}];<\/span><\/div>\n
ord[1]={a,b,c};<\/span><\/div>\n
ord[2]={a,b,c};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; \u00a0a~to[{2}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{b, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[2, {a,b,c}];<\/span><\/div>\n
ord[1]={a,c,b};<\/span><\/div>\n
ord[2]={b,c,a};<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
a~to[{1}]~b; \u00a0a~to[{2}]~c;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{b, c}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* Isaac and Plott’s paper *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *)<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3,{a,b,c,d,e,f,g,h,i,j}];<\/span><\/div>\n
ord[1]={f,e,i,d,c,h,a,j,g,b}; \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* each player’s preference ordering *)<\/span><\/div>\n
ord[2]={b,j,a,g,c,h,d,i,e,f};<\/span><\/div>\n
ord[3]={c,a,g,b,i,d,j,h,f,e};<\/span><\/div>\n
\u00a0<\/span><\/div>\n
ord2preferences; \u00a0 \u00a0(* convert order representation to preferences *)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
fromanywhere[{1}, {d}];<\/span><\/div>\n
fromanywhere[{2,3}, {d}];<\/span><\/div>\n
fromanywhere[{1,2}, {a,b,c,d,e,f,g,h,i,j}];<\/span><\/div>\n
fromanywhere[{1,3}, {a,b,c,d,e,f,g,h,i,j}];<\/span><\/div>\n
fromanywhere[{1,2,3}, {a,b,c,d,e,f,g,h,i,j}];<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a, g, h, j}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
inddom[[num[d]]]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{False, False, False, False, False, False, False, True, False, True}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
inddom[[num[j]]]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{False, False, False, False, False, False, True, True, False, False}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
TableForm[inddom[[num[{a,g,h,j}],num[{a,g,h,j}]]]]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
False \u00a0 True \u00a0 \u00a0True \u00a0 \u00a0False<\/span><\/div>\n
\u00a0<\/span><\/div>\n
False \u00a0 False \u00a0 True \u00a0 \u00a0False<\/span><\/div>\n
\u00a0<\/span><\/div>\n
False \u00a0 False \u00a0 False \u00a0 True<\/span><\/div>\n
\u00a0<\/span><\/div>\n
False \u00a0 True \u00a0 \u00a0True \u00a0 \u00a0False<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[3,{a,b,c,d,e,f,g,h,i,j}];<\/span><\/div>\n
ord[1]={f,e,i,d,c,h,a,j,g,b}; \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* each player’s preference ordering *)<\/span><\/div>\n
ord[2]={b,j,a,g,c,h,d,i,e,f};<\/span><\/div>\n
ord[3]={c,a,g,b,i,d,j,h,f,e};<\/span><\/div>\n
\u00a0<\/span><\/div>\n
ord2preferences; \u00a0 \u00a0(* convert order representation to preferences *)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
majorityrule;<\/span><\/div>\n
\u00a0<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{e}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* McKelvey and Ordeshook, Public Choice 1983 *)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
(* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0*)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* Game F1 *)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[5,{a,b,c,d,e,f,g,h,i,j,k,l,m,n,o}];<\/span><\/div>\n
ord[1]={e,l,{a,c},b,{d,m},{g,o,h},k,i,f,j,n};<\/span><\/div>\n
ord[2]={a,{l,n},{h,c},{g,b},{k,d},i,{e,f},m,o,j};<\/span><\/div>\n
ord[3]={o,{l,n},{e,c},g,{k,m,d,j},i,{a,f},h,b};<\/span><\/div>\n
ord[4]={h,{n,j},{f,c},{k,b},i,m,{a,g,o},d,e,l};<\/span><\/div>\n
ord[5]={{f,i},{l,n,j},{o,c},m,d,k,{e,g,h},a,b};<\/span><\/div>\n
\u00a0<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
majorityrule;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a, b, d, e, f, g, h, i, j, k, m, o}<\/span><\/div>\n
\u00a0<\/span><\/div>\n
(* Game *F1A *)<\/span><\/div>\n
\u00a0<\/span><\/div>\n
initialize;<\/span><\/div>\n
setup[5,{a,b,c,d,e,f,g,h,i,j,k,l,m,n,o}];<\/span><\/div>\n
ord[1]={e,l,{a,c},b,{d,m},{o,h},k,i,g,f,j,n};<\/span><\/div>\n
ord[2]={a,{l,n},{h,c},{g,b},{k,d},i,{e,f},m,o,j};<\/span><\/div>\n
ord[3]={o,{l,n},{e,c},g,{k,m,d,j},i,{a,f},h,b};<\/span><\/div>\n
ord[4]={h,{n,j},{f,c},{k,b},i,m,{a,o},d,g,e,l};<\/span><\/div>\n
ord[5]={{f,i},{l,n,j},{o,c},m,d,k,{e,h},g,a,b};<\/span><\/div>\n
\u00a0<\/span><\/div>\n
ord2preferences;<\/span><\/div>\n
majorityrule;<\/span><\/div>\n
name[lcs]<\/span><\/div>\n
\u00a0<\/span><\/div>\n
\u00a0<\/span><\/div>\n
{a, b, d, e, f, g, i, j, k, m, o}<\/span><\/div>\n","protected":false},"excerpt":{"rendered":"

(*************************) (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *) (* preliminary functions *) (* \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 *) (*************************) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (* \u00a0 …<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-386","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/pages\/386","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/comments?post=386"}],"version-history":[{"count":1,"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/pages\/386\/revisions"}],"predecessor-version":[{"id":387,"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/pages\/386\/revisions\/387"}],"wp:attachment":[{"href":"http:\/\/chwe.net\/michael\/index.php\/wp-json\/wp\/v2\/media?parent=386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}