The　presence　of　strategic　attackers　has　become　an　important　factor　in　the　security　and　protection　of　systems,　especially　since　the　9/11/2001　attacks,　and　considerable　efforts　have　been　dedicated　to　its　study.　When　defending　against　the　strategic　attacker,　many　existing　studies　assume　that　the　attacker　would　seek　to　minimize　the　defender＇s　utility,　which　implies　that　the　defender　and　attacker　have　symmetric　utilities.　However,　the　attacker＇s　objective　is　determined　by　its　own　valuation　of　the　system　and　target　of　the　attack,　which　is　not　necessarily　consistent　with　the　defender＇s　utility.　If　the　attacker　unexpectedly　targets　a　different　utility,　then　the　defense　strategy　might　no　longer　be　optimal.　In　particular,　the　defense　strategy　could　be　inferior　if　the　attacker＇s　utility　is　not　known　to　the　defender.　This　study　considers　a　situation　where　the　defender＇s　utility　is　the　system　survivability　and　the　attacker＇s　utility　is　the　expected　number　of　destroyed　elements　in　the　system.　We　investigate　possible　attack　strategies　under　these　two　different　utilities　and　compare　(a)　the　conservative　defense　strategy　when　the　attack　utility　is　unknown　to　the　defender　with　(b)　the　optimal　defense　strategy　when　the　attack　utility　is　known　to　the　defender.　We　show　that　the　conservative　protection　strategy　is　still　optimal　under　asymmetric　utilities　when　the　contest　intensity　is　smaller　than　one.