Eg - Some people think that education / the cosmetics industry benefit some individuals but hurt other individuals at the same time because job markets / dating markets involve zero-sum games, so education / the cosmetic industry don’t provide any benefit to society overall. In other words, they change who succeeds but don’t cause more success.

I’d also like to find a term / nicer way of phrasing how individuals involved are incentivised to invest more resources to these things as others do the same, leading to a vicious cycle and increasing amounts of resources being dedicated to something that does not benefit society.

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That is perfect, exactly what I was looking for, thank you!

“Pareto efficiency“ - Pareto efficiency, or Pareto optimality, is an economic state where resources cannot be reallocated to make one individual better off without making at least one individual worse off (from https://www.investopedia.com/terms/p/pareto-efficiency.asp)

and “arms race”, if that counts as a nicer way, or some allusion to the Red Queen (https://en.wikipedia.org/wiki/Red_Queen%27s_race)

These are also perfect, thank you!

Maybe rent seeking

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I think the two answers so far, Positional Goods and Arms Race, are pretty solid.  But I'd like to challenge the underlying statement - there are no truly fixed-sum games in the real world.  Utility is highly-dimensional and highly variable across time and individuals, and every legible interaction is actually a sub-game in a much more complex set of known and unknown future decisions.

I think I agree with you, but I also think it's very useful to think of games as fixed-sum when making decisions relating to them.

It's very often worth noticing these features in interpersonal, small-scale decisions.  Whether you frame it as "look for the win-win", "avoid zero-sum sub-games", or "prefer kindness over winning", it's good advice.

I don't know many cases where it's useful on the general topics you give as examples (industries, education as a whole, dating).  

I should probably admit that I actually do care about myself and those close to me more than strangers, and I acknowledge that there is some amount of zero-sum outcomes in our current perceptions of individual identity.  The overall game of individual existence is a mix of many games, and winning some of the zero-sum components lets me get higher sums on other components.