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As Poul Anderson fans, we are interested in:

what Larry Niven wrote about the kzinti because this forms the basis of the Man-Kzin Wars series to which Anderson contributed;

Anderson's own Man-Kzin Wars trilogy;

other Man-Kzin Wars stories that might have been influenced by Anderson's;

uninfluenced installments, providing interesting contrasts.

Thus, nothing escapes our sight and we might spend quite some time within Niven's Known Space future history.

As far as I can see at present:

Pournelle's and Niven's trilogy is set during the First Man-Kzin War;

Anderson's trilogy is set shortly after that war;

Niven's Beowulf Shaeffer and his contemporaries live shortly after the Fourth Man-Kzin War.

Shaeffer describes a man who:

"...wore a hellflare tattoo on his shoulder, which meant he'd been in Kzin thirty years back, which meant he'd been trained to kill adult Kzinti with his bare hands, feet, elbows, knees, and whatnot."
-Larry Niven, "Flatlander" IN Niven, Neutron Star (New York, 1971), pp. 129-171 AT p. 129.

Another guy, Jason Papandreou had been:

"...a gunner volunteer on one of Earth's warships during the last stage of the last Kzinti war. The war had been highly unequal in Earth's favor. Kzinti fight gallantly, ferociously, and with no concept of mercy; they always take on several times as much as they can handle."
-Larry Niven, "The Soft Weapon" IN Neutron Star, pp. 73-128 AT p. 73.

In other cases, stories clearly contradict established canon. For example, various MKW stories state that Kzinti did not establish their own interstellar empire nor invent their own spacefaring technology. Instead, primitive Kzinti warriors were hired as mercenaries by the Jotoki, a species of interstellar traders, whom the Kzinti later overthrew and enslaved. Yet, Niven's "The Soft Weapon" states:

There had been a time, between the discoveries of atomic power and the gravity polarizer, when it seemed the Kzinti species would destroy itself in wars. Now the Kzinti held many worlds, and the danger was past.

However, "Jotok" suggests a possible compromise scenario. In that story, primitive Kzinti clans on the Kzin homeworld are being marginalized by advanced Kzinti who use atomic power and gravity polarizer-driven spacecraft. It is the primitives who are hired by the Jotoki, to use as mercenaries against the more advanced Kzinti.
-copied from here.