Appendices A

Weknow 10 > 0becauseotherwise minyU(a, x, y) > maxyU( a, x, y), thereforetheminimialvalueof 10 is maxyU( a, x,1) minyU(a, x, y). If 00 6=0 and 11 6=0 then 00 + 11 10 implies minyU( a, x, y) maxyU(a, x, y)whichviolatesourassumptions, therefore 00+ 11 < 10.