This　paper　is　devoted　to　the　facility　location　games　with　payments,　where　every　agent　plays　a　dual　role　of　facility　and　customer.　In　this　game,　each　selfish　agent　is　located　on　a　publicly　known　location　in　a　metric　space,　and　can　allow　a　facility　to　be　opened　at　his　place.　But　the　opening　cost　is　his　private　information　and　lie　may　strategically　report　this　opening　cost.　Besides,　each　agent　also　bears　a　scrvice　cost　equal　to　the　distance　to　his　nearest　open　facility.　We　are　concerned　with　designing　truthful　mechanisms　for　the　game,　which,　given　agents＇　reports,　output　a　set　of　agents　whose　facilities　could　be　opened,　and　a　payment　to　each　of　these　agents　who　opens　a　facility.　The　objective　is　to　minimize　(exactly　or　approximately)　the　social　cost　(the　total　opening　and　service　costs)　or　the　maximum　agent　cost　of　the　outcome.　We　characterize　the　normalized　truthful　mechanisms　for　this　game.　Concerning　the　minimum　social-cost　objective,　we　give　an　optimal　truthful　mechanism　without　regard　to　time　complexity,　and　show　a　small　gap　between　the　best　known　approximation　ratio　of　polynomial-time　truthful　mechanisms　for　the　game　and　that　of　polynomial-time　approximation　algorithms　for　the　counterpart　of　pure　optimization.　For　the　minimum　maximum-cost　objective,　we　provide　an　optimal　truthful　mechanism　which　runs　in　polynomial　time.　We　also　investigate　mechanism　design　for　the　game　under　a　budget　on　the　total　payment.　©　2019　International　Foundation　for　Autonomous　Agents　and　Multiagent　Systems.　All　rights　reserved.