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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.

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    Sounds like an escalation. – Yosef Baskin Mar 29 '20 at 19:01
  • A repeating cycle which tends to move in one direction is generally described as a "spiral". Most often it's a spiral downward, getting worse and worse, but if one explicitly calls it a "spiral upward" then it implies continuous improvement. (Whether more and more complex weapons is "upward" or "downward" is a value judgement.) – Hot Licks Apr 28 '20 at 22:20
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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]

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You will want to look into descriptions of schemes that are tactical vs strategic. This is the level of gamesmanship you are describing.

With regard to escalating armaments you might consider the idea of the Axe maker's Gift. This is the notion that as technology develops, say to feed more people the population increases to outstrip the new technologies abilities. Such escalations are common thought history.

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From https://searchitchannel.techtarget.com/definition/feedback-loop

A feedback loop is the part of a system in which some portion (or all) of the system's output is used as input for future operations. Each feedback loop has a minimum of four stages. During the first stage, input is created. During the second stage, input is captured and stored. During the third stage, input is analyzed and during the fourth stage, the insight gained from analysis is used to make decisions.

Feedback loops can be either negative or positive. [...]

In contrast, positive feedback loops simply repeat actions that have been effective in the past. The intention of a positive feedback loop is to amplify a desired variable and naturally move the system away from its starting state to a desired state. Problems can occur, however, when the positive feedback loop grows exponentially without any checks or balances. In such a scenario, a runaway positive feedback loop can make a system become unstable.

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