A connector having a socket contact (11, 21, 31, 41) to be electrically connected to a counter-connector contact having a plate shape that is inserted in the socket contact along a fitting plane, wherein the socket contact (11, 21, 31, 41) includes: a main body portion (12, 22, 42) that forms a reception part to accommodate the counter-connector contact and has an inner wall; and a plurality of conduction spring pieces (13, 23, 43) which are bent at upper ends towards an inside of the reception part and which are connected to the main body portion and tip ends of which are disposed inside the reception part, and a plurality of displacement regulators (14, 24, 44) which are connected to the main body portion, tip ends of which being disposed inside the reception part, wherein the displacement regulators (14, 24, 44) are bent at upper central ends towards an inside of the reception part, and the socket contact (11, 21, 31, 41) further includes: one or more pairs of conduction contact points (13A, 43A) provided at the tip ends of the conduction spring pieces (13, 23, 43) and being disposed respectively on both sides of the fitting plane so as to face each other across the fitting plane in an elastically displaceable manner and that come into contact with and are electrically connected to the counter-connector contact; and one or more pairs of displacement regulator contact points (14A, 44A, 48A) being respectively provided near the tip ends of the plurality of displacement regulators and being disposed respectively on both sides of the fitting plane so as to face each other across the fitting plane, the one or more pairs of conduction contact points (13A, 43A) and the one or more pairs of displacement regulator contact points (14A, 44A, 48A) being disposed side by side in a direction along the fitting plane at a substantially same depth in a fitting direction, and each of the pairs of displacement regulator contact points (14A, 44A, 48A) having a gap therebetween larger than a gap between each of the pairs of conduction contact points (13A, 43A), wherein the tip ends of the displacement regulator each are located farther away from the fitting plane than the displacement regulator contact points and are in contact with the inner wall or are close to the inner wall with a small distance therefrom, such that, when the counter-connector contact shifts, the counter-connector contact comes into contact with the displacement regulator contact points (14A, 44A, 48A) and upon the displacement regulators being elastically deformed the tip ends of the displacement regulators abut the facing inner walls so as to prevent the counter-connector contact from further shifting. a main body portion (12, 22, 42) that forms a reception part to accommodate the counter-connector contact and has an inner wall; and a plurality of conduction spring pieces (13, 23, 43) which are bent at upper ends towards an inside of the reception part and which are connected to the main body portion and tip ends of which are disposed inside the reception part, and a plurality of displacement regulators (14, 24, 44) which are connected to the main body portion, tip ends of which being disposed inside the reception part, wherein the displacement regulators (14, 24, 44) are bent at upper central ends towards an inside of the reception part, and the socket contact (11, 21, 31, 41) further includes: one or more pairs of conduction contact points (13A, 43A) provided at the tip ends of the conduction spring pieces (13, 23, 43) and being disposed respectively on both sides of the fitting plane so as to face each other across the fitting plane in an elastically displaceable manner and that come into contact with and are electrically connected to the counter-connector contact; and one or more pairs of displacement regulator contact points (14A, 44A, 48A) being respectively provided near the tip ends of the plurality of displacement regulators and being disposed respectively on both sides of the fitting plane so as to face each other across the fitting plane, the one or more pairs of conduction contact points (13A, 43A) and the one or more pairs of displacement regulator contact points (14A, 44A, 48A) being disposed side by side in a direction along the fitting plane at a substantially same depth in a fitting direction, and each of the pairs of displacement regulator contact points (14A, 44A, 48A) having a gap therebetween larger than a gap between each of the pairs of conduction contact points (13A, 43A), one or more pairs of conduction contact points (13A, 43A) provided at the tip ends of the conduction spring pieces (13, 23, 43) and being disposed respectively on both sides of the fitting plane so as to face each other across the fitting plane in an elastically displaceable manner and that come into contact with and are electrically connected to the counter-connector contact; and one or more pairs of displacement regulator contact points (14A, 44A, 48A) being respectively provided near the tip ends of the plurality of displacement regulators and being disposed respectively on both sides of the fitting plane so as to face each other across the fitting plane, the one or more pairs of conduction contact points (13A, 43A) and the one or more pairs of displacement regulator contact points (14A, 44A, 48A) being disposed side by side in a direction along the fitting plane at a substantially same depth in a fitting direction, and each of the pairs of displacement regulator contact points (14A, 44A, 48A) having a gap therebetween larger than a gap between each of the pairs of conduction contact points (13A, 43A),