I was asked to have a look at this question so...
Here are some of the reasons certain elements are added to steel:
Carbon- it is what makes iron into steel, from .55% up to .60% you will have a naturally tougher blade that will not hold a really fine edge for long but will do well on beefier edges that can chop. From .70% to .80% the edges will be high hardness and do a wide variety of tasks. From .85% up to 1.2% (or a little higher) the steel is best for fine slicing edges that will have a higher abrasion resistance for edge holding, but will not tolerate chopping of other abuse. This is what carbon will want to do naturally but a skilled heat treater can move the carbon around and use what he wants in different ways, so one could make a 1% C steel behave like a .80% steel if you have good control.
Manganese- in lower levels it is just there to render sulfur contamination harmless, but it can be added in higher levels to increase hardenability. It has a reinforcing mechanism on the structures in the hardened phase of steel that can be good, or bad, depending upon how you look at it. At 1% or higher the steel is a deeper hardening alloy.
Chromium- is the go to for industry for increasing hardenability or, when added in massive amounts lending stain resistance. It will give you some abrasion resistance from its carbide forming properties, so when you have higher carbon levels mixed with it you can have a very fine edge that will wear well. In lesser amount it can refine grain and not form heavy carbides.
Vanadium- a very powerful alloy element, just a pinch ( .2%) will keep grain nice and fine and above that you need to add more carbon because of how hungry V carbides can be, but the abrasion resistance can go through the roof. Blades with vanadium in them take an edge that makes my hair stand on end when I feel it. Great for fine slicers, not so much so for heaver edges on choppers.
Tungsten- great for abrasion resistance, and will raise tempering temperatures as it is often used to increase the life of steel that could get hot in high speed applications, as is the same for molybdenum.
Nickel- the toughener of the bunch. Nickel is the best way to make a steel take a pounding as a large chopper, but it also has some side effects that make you want to keep the carbon levels at around .75% or lower. In higher doses it takes stainless to all new levels for laughing at corrosion but it does so at the expense of hardenability, and is what gives the nonmagnetic quality to austenitic stainless. In simpler steels it will usually be in the range of 1% to 1.4% for excellent toughness.
So for fine slicers- higher carbon, vanadium, chromium, or even tungsten. For heavy choppers- lower carbon levels, chromium at lower levels and nickel, oh and I forgot to mention silicon which is also very good for taking a beating.