The main point of "war games" or "joint exercises" is to develop the ability to work together towards a common goal. It is critical that multinational organizations understand the capabilities of their allies' equipment and doctrine. Essentially, they are intended to ensure that all participants can speak a "common military language" so as to ensure that battles can be fought effectively. Getting (as only one example) German Infantry familiar with US tank tactics and capabilities was essential to preparation for the possible defense of the Fulda gap during the cold war-- this was exercised again and again, until the West had a credible force there to attempt to stop any Soviet invasion. Combined arms operations are inherently complex, and adding a component of multinationality to the mix has the great likelihood of really causing confusion and/or failure. Even combined arms activities within a single nation need to be exercised regularly-- for example it was found in some major exercises prior to US entry into WW2 that the radios in Army Air Corps aircraft could not talk to the radios used by the rest of the forces. You'd think that someone would have thought of that, but it is an example of the unexpected things which are found out about and then rectified as a result of "joint military exercises".

Its worth examining just when these giant multi lateral truly multi national exercises began to understand the goals of them.

The answer to the first is pretty straight forward. As we recognize them today the concept arose first in NATO in the late 40's and really got going in the early 50's and were mirrored by the Warsaw Pact.

In that lens early exercises such as the naval events of Exercises Grand Slam and Longstep were held in the Mediterranean in 1952 with large US and allied contributions. But the biggest of them all was in the North Atlantic called Exercise Mainbrace. Roughly 200 warships from 10 different nations participated including a half dozen fleet carriers from the US and Britain and a pair of battleships in Wisconsin and Vanguard!

The Allies in particular the US and UK had developed a high level of interoperability by 1945 and it was desirable to stay as proficient as a joint force as possible as NATO and the WP looked more and more headed to armed conflict at some point. While it allowed for smaller less well equipped or trained forces to catch up or play their more specialized role in the joint force. Sure it was a great opportunity for the other side to get a nice close look but you didnt want the real thing to also be your dress rehearsal as it were. It also allowed for additional dissimilar training, for instance by the 1960's the US Navy was out of the diesel submarine game, so the only way to train against them was by working with allies who still had nonnuclear boats.

Concurrent with similar air and land exercises this trend begun in the 1950's was very different from previous exercises and maneuvers which rarely in the US and most of the West included even more than one service at a time except as exceptions to the rule. Things like the Carolina or Louisiana Maneuvers, or various Fleet Problems were helpful and valuable and continue to be so today when held, but they were anything but joint.