In 1964, Robert Levine, Thomas Schelling, and William Jones circulated a series of drafts through the RAND Corporation internal mail system, discussing the strengths and weaknesses of crisis gaming. In 1991, feeling that the issues laid out remained relevant, Levine republished the entire exchange as a RAND paper: Crisis Games 27 Years Later: Plus C'est Deja Vu. RAND has released this paper (along with some others from their 50 years of research and policy memoranda) for free in pdf form. It's well worth reading in its entirety. Thomas Schelling won the Nobel Prize in economics in 2005, and his defense of crisis gaming as a technique is fascinating.
RAND did a lot of pioneering work in crisis gaming, which seems to have come on the scene during the Cold War as a way of examining the issues surrounding crises between the US and the USSR (I will confirm this at some point in the future, but the earliest references I have seen so far to crisis gaming date to the 1950's). The study of crisis was a priority, given the risks of nuclear war that attended a misstep. The various Berlin crises, the Cuban Missile Crisis, and the surprise attack that began the Korean War were all influential in shaping the view that crisis management was an important skill to develop. Cold War crises had some very appealing features when it comes to gaming: there were two main adversaries whose interactions (due to their superpower status) were much more important than the roles of any other states (whose actions could be devised by the control team), the stakes in any given confrontation were high and the time frames often short (due to the presence of large nuclear arsenals), which ensured that the highest level decision makers would be involved, superseding normal policymaking structures, and the novelty of the nuclear standoff, with unprecedented destructive power involved, which gave a sense to policy theorists that all bets were off and that this type of crisis event needed to be studied outside the context of previous conventional military confrontations. This last point was also a major argument made by the newly ascendant civilian policy analysts in favor of rethinking conflict in ways opposed by the military establishment.