The　purpose　of　this　paper　is　to　propose　an　effective　linear　programming　technique　for　solving　matrix　games　in　which　the　payoffs　are　expressed　with　intervals　and　the　choice　of　strategies　for　players　is　constrained,　i.e.,　interval-valued　constraint　matrix　games.　Because　the　payoffs　of　the　interval-valued　constraint　matrix　game　are　intervals,　its　value　is　an　interval　as　well.　In　this　methodology,　the　value　of　the　interval-valued　constraint　matrix　game　is　regarded　as　a　function　of　values　in　the　payoff　intervals,　which　is　proven　to　be　monotonous　and　non-decreasing.　By　the　duality　theorem　of　linear　programming,　it　is　proven　that　both　players　always　have　the　identical　interval-type　value　and　hereby　the　interval-valued　constraint　matrix　game　has　an　interval-type　value.　A　pair　of　auxiliary　linear　programming　models　is　derived　to　compute　the　upper　bound　and　the　lower　bound　of　the　value　of　the　interval-valued　constraint　matrix　game　by　using　the　upper　bounds　and　the　lower　bounds　of　the　payoff　intervals,　respectively.　Validity　and　applicability　of　the　linear　programming　technique　proposed　in　this　paper　is　demonstrated　with　a　numerical　example　of　the　market　share　game　problem.