This topic has been extensively researched through data analysis of over 200 northern Wisconsin lakes surveyed over a 13 year period. The only gamefish found to strongly interact with walleye populations were largemouth bass, which prey heavily on juvenile walleyes. Musky populations were actually strongly positively correlated with walleye populations - in other words, lakes with high musky populations also had high walleye populations and vice versa, suggesting that both do well in similar environments and there's no significant interaction between them. There was no statistical evidence that either smallmouth bass or northern pike abundance had any relationship to walleye abundance. Look it up:

Fayram, A.H., M.J. Hanson, and T.J. Ehlinger. 2005. Interactions between Walleyes and Four Fish Species with Implications for Walleye Stocking. Journal of the American Fisheries Society 25:1321-1330.