Amazon and Microsoft are battling it out over a $10 billion opportunity to build the U.S. military its first “war cloud” computing system. But Amazon’s early hopes of a shock-and-awe victory may be slipping away. Formally called the Joint Enterprise Defense Infrastructure plan, or JEDI, the military’s computing project would store and process vast amounts of classified data, allowing the Pentagon to use artificial intelligence to speed up its war planning and fighting capabilities. The Defense Department hopes to award the winner-take-all contract as soon as August. Oracle and IBM were eliminated at an earlier round of the contract competition.