What is the best way to describe a progressive, advancing cycle?

Commonly, individuals talk about how two opposing interests will invent "game changing," technology that renders the other interest useless until that interest, in turn, invents a new technology. The best example I can give is with weapons and armor:

[with some simplification]

• Simple weapons resulted in Leather Armor
• Metal Weapons outmoded Leather Armor
• Metal Armor outmoded Metal Weapons
• Simple Firearms outmoded Metal Armor
• Tanks outmoded Simple Firearms

I'm looking for a term similar to "a vicious cycle," but that I can use to describe how a business could play increasingly complex games with income reporting, forcing 3rd party auditors to spend more time checking their work.

Alternatively, a less pejorative phrase similar to "If you make something idiot-proof, God designs a better idiot." would work.

You could metaphorically broaden arms race without much fear of misinterpretation (although it applies literally to your example, of course). In fact, the following definition allows for such a broadening:

Arms race [Sam Perlo-Freeman; Contributor to International Encyclopedia of Political Science ... Britannica]

Arms race: a pattern of competitive acquisition of military capability between two or more countries. The term is often used quite loosely to refer to any military buildup or spending increases by a group of countries. The competitive nature of this buildup often reflects an adversarial relationship. The arms race concept is also used in other fields....

Metaphorical examples include

• The evolutionary arms race [see ThoughtCo]

  • Viruses up their game in arms race with immune system. ... In a classic example of the evolutionary arms race between a host and a pathogen, the myxoma virus – introduced to control the rabbit population in Australia in 1950 – has developed a novel and deadly ability to suppress the immune response of its host rabbits. [Science Daily; Aug 2017]

• The medical arms race (!): A popular term for escalating health care costs due to proliferation of expensive medical technology and devices [Segen's Medical Dictionary]

• The first two usages are fixed-phrase, possibly compounds. The term is also used in a less fixed-phrase way in other spheres of competition:

  • In Formula One, the focus of the technological arms race is always the cars. [Formula One Dictionary]

  • The Arms Race Of Industrial Companies Buying Software ... [Forbes]