▁resource ▁(" ca ke ") ▁that ▁satisfies ▁the ▁env y - free ▁criter ion , ▁namely , ▁that ▁every ▁partner ▁feels ▁that ▁their ▁allocated ▁share ▁is ▁at ▁least ▁as ▁good ▁as ▁any ▁other ▁share , ▁according ▁to ▁their ▁own ▁subject ive ▁valu ation . ▁ ▁When ▁there ▁are ▁only ▁two ▁partners , ▁the ▁problem ▁is ▁easy ▁and ▁has ▁been ▁solved ▁in ▁Bib lic al ▁times ▁by ▁the ▁divide ▁and ▁choose ▁protocol . ▁When ▁there ▁are ▁three ▁or ▁more ▁partners , ▁the ▁problem ▁becomes ▁much ▁more ▁challeng ing . ▁ ▁Two ▁major ▁variants ▁of ▁the ▁problem ▁have ▁been ▁studied : ▁ ▁Con ne cted ▁pieces , ▁e . g . ▁if ▁the ▁c ake ▁is ▁a ▁ 1 - dimensional ▁interval ▁then ▁each ▁partner ▁must ▁receive ▁a ▁single ▁sub - interval . ▁If ▁there ▁are ▁ ▁partners , ▁only ▁ ▁cut s ▁are ▁needed . ▁ ▁General ▁pieces , ▁e . g . ▁if ▁the ▁c ake ▁is ▁a ▁ 1 - dimensional ▁interval ▁then ▁each ▁partner ▁can ▁receive ▁a ▁union ▁of ▁dis joint ▁sub - interval s . ▁ ▁Short ▁history ▁ ▁The ▁modern ▁research ▁of ▁the ▁fair ▁c ake - cut ting ▁problem ▁has ▁started ▁in ▁the ▁ 1 9 4 0 s . ▁The ▁first ▁fair ness ▁criter ion ▁studied ▁was ▁proportional ▁division , ▁and ▁a ▁procedure ▁for ▁n ▁partners ▁has ▁been ▁found ▁soon . ▁ ▁The ▁stronger ▁criter ion ▁of ▁env y - f reen ess ▁was ▁introduced ▁into ▁the ▁c ake - cut ting ▁problem ▁by ▁George ▁Gam ow