(*Defineparameters*)​​rsah=10;​​rsas=-2;​​rses=0;​​rhch=3;​​rhcs=-2;​​rhds=-2;​​rhbh=1;​​a=0.1;​​b=0.2;​​g=0.8;​​(*Definetheequationsasfunctions*)​​vsEq[vs_,vh_]:=​​Max[a*(rsas+g*vs)+(1-a)*(rsah+g*vh),rses+g*vs]​​vhEq[vs_,vh_]:=​​Max[b*(rhch+g*vh)+(1-b)*(rhcs+g*vs),rhbh+g*vh,rhds+g*vs]​​(*SolvethesystemusingFindRootwithinitialguessesforv_hand\​v_l*)​​solution=​​FindRoot[{vs==vsEq[vs,vh],​​vh==vhEq[vs,vh]},{{vh,0},{vs,0}}];​​(*PrinttheoptimalactionatstateS.1representstheactionaand\​2representstheactione*)​​Ordering[{a*(rsas+g*vs)+(1-a)*(rsah+g*vh),rses+g*vs}/.​​solution,-1]​​(*Printtheoptimalactionatstateh.1representstheactionc,and\​2representstheactionb,and3representstheactiond*)​​Ordering[{b*(rhch+g*vh)+(1-b)*(rhcs+g*vs),rhbh+g*vh,​​rhds+g*vs}/.solution,-1]
Out[]=
{1}
Out[]=
{3}