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There were three major players in Italy: 1) France 2) Spain/Holy Roman Empire (HRE) (treat them as one unit since one man, Charles V, ruled both, and 3) Venice, the "local bully."
The first stage of the war started when the other Italian states asked two large, outside powers, France and Spain/HRE to help them against Venice. That's why it was the League of Cambrai. In the second stage of the war, France was seen as the bully, and first the Papal states, then Spain/HRE allied with Venice against France. Henry VIII"s England also joined the anti-French alliance.
In the final stage, Venice decided that Spain/HRE was the greater bully, and defected to the side of France, its former enemy. This was the way things stood when the war ended in 1516.
Venice was vindicated over a decade later, Rome was sacked by HRE troops in 1527, which induced the Papal States, and even Henry VIII to side with France against Spain/HRE.
But all this illustrated a rule that every boy learns on the playground: "You don't want to be the odd man out in a three way fight." At times, each of the three main parties was the "odd man out," and each strove hard not to be. The description from Machiavelli as "the least comprehensible war Iβve ever studied," refers to domestic and political issues in which he specialized. But it may best be understood in the context of a schoolyard brawl.