This has been identified as a "buffalo stick" of the men's society, the Tomahawk Lodge, by reference to A. Kroeber, The Arapaho, AMNH Bulletin, 1904. James Mooney used the term "Dog soldier" to refer to men's societies in general, but as the Arapaho had a specific society by that name, the catalog term has been changed to prevent confusion.
Listed on page 67 in "The Exhibits of the Smithsonian Institution at the Panama-Pacific International Exposition, San Francisco, California, 1915", in section "Arts of the African Tribes (Bantu)".