1 8 5 7 ▁establish ments ▁in ▁Indiana ▁Category : Un in cor por ated ▁communities ▁in ▁Indiana <0x0A> </s> ▁In ▁game ▁theory , ▁a ▁prin cess ▁and ▁mon ster ▁game ▁is ▁a ▁purs uit - e vas ion ▁game ▁played ▁by ▁two ▁players ▁in ▁a ▁region . ▁The ▁game ▁was ▁de vised ▁by ▁R uf us ▁Isa acs ▁and ▁published ▁in ▁his ▁book ▁D iffer ential ▁Games ▁( 1 9 6 5 ) ▁as ▁follows : ▁ ▁This ▁game ▁remained ▁a ▁well - known ▁open ▁problem ▁until ▁it ▁was ▁solved ▁by ▁Sh m uel ▁Gal ▁in ▁the ▁late ▁ 1 9 7 0 s . ▁His ▁optimal ▁strategy ▁for ▁the ▁prin cess ▁is ▁to ▁move ▁to ▁a ▁random ▁location ▁in ▁the ▁room ▁and ▁stay ▁still ▁for ▁a ▁time ▁interval ▁which ▁is ▁neither ▁too ▁short ▁nor ▁ ▁too ▁long , ▁before ▁going ▁to ▁another ▁( in dependent ) ▁random ▁location ▁and ▁repeating ▁the ▁procedure . ▁The ▁proposed ▁optimal ▁search ▁strategy , ▁for ▁the ▁mon ster , ▁is ▁based ▁on ▁sub d ivid ing ▁the ▁room ▁into ▁many ▁narrow ▁rect angles , ▁pick ing ▁a ▁rectangle ▁at ▁random ▁and ▁searching ▁it ▁in ▁some ▁specific ▁way , ▁after ▁some ▁time ▁pick ing ▁another ▁rectangle ▁randomly ▁and ▁independently , ▁and ▁so ▁on . ▁ ▁Princess ▁and ▁mon ster ▁games ▁can ▁be ▁played ▁on ▁a ▁pre - selected ▁graph . ▁It ▁can ▁be ▁demonstrated ▁that ▁for ▁any ▁finite ▁graph ▁an ▁optimal ▁mixed ▁search ▁strategy ▁exists ▁that ▁results ▁in ▁a ▁finite ▁pay off . ▁This ▁game ▁has ▁been