There're some studies looking at the role of testosterone in anonymous social interactions (like one-shot trust games) but nothing I'm finding related to the winners effect in anonymous competitions, sadly.

I found those studies with a "testosterone+anonymous+competition" boolean search

https://pubmed.ncbi.nlm.nih.gov/29222722/

Thanks for notifying me.

Weird that happened.

Czerwinski, M., Smith, G., Regan, T., Meyers, B., Robertson, G. G., & Starkweather, G. K. (2003, September). Toward characterizing the productivity benefits of very large displays. In Interact (Vol. 3, pp. 9-16).

https://d1wqtxts1xzle7.cloudfront.net/43905284/INTERACT2003-ProductivityLargeDisplays-libre.pdf?1458438509=&response-content-disposition=inline%3B+filename%3DToward_characterizing_the_productivity_b.pdf&Expires=1671213310&Signature=gTZRut7BZYV1Cq3IntvuB53Ww2WSdlEWQ6ikPPz1E448OG-T9-YeEWoGgjsHgmsyuyKZdYZxL~Ww5sBBZ6ghhxWnRgfeuTNoFJh347Pyk5VrUKE6QZeH8ZchapvfONq5ZPn4XCZ8jrPMhe8tAsxZ~Kz9b7aYecMQTg0sp4TFyUYLSyP~fD~i4mZzaH1bh1Y2ZOete45xvGwOsS76cXhoy9enzK1psHA5YwRMS4jr-hINHCxvoLKBid51yaXr2zf9CTLgwaJpEL6hb-KARH0iH1~6hheGU1GxEmTP10v5VPKg6CjoHtNXXRXEyIZb8kl-521-WgO~7STAhVcUB5qo-w__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA

And another:

Colvin, J., Tobler, N., & Anderson, J. A. (2004). Productivity and multi-screen computer displays. Rocky Mountain Communication Review, 2(1), 31-53.

Found this one - didn't read it but seems up the alley.

Here's a lay article that summarizes historical findings.

Tl;dr: a long time ago - I think someone else noted that in the Epic of Gilgamesh, he goes through some significant bereavement after his friend's death.

Not my field, but can queue you into ways to optimize searching?

Insight learning is the "aha" moment we arrive at when the solution isn't nec. something we can deduce from our past experiences. It's a specific extreme of a novel problem, as that term can be used for things we can deduce solutions to.

Here're the three most-relevant studies that came up for a boolean search for fMRI + "insight learning" https://d1wqtxts1xzle7.cloudfront.net/44317146/Neural_correlates_of_the_Aha_experiences20160401-21193-1spnnjf-with-cover-page-v2.pdf?Expires=1665970463&Signature=Th~81e18UNi4YyTdBPH74al0VYAohwD9pw8rVs-z1lSXekdLayAcud6adesF-RumDXysyadlO8N92GsPWFZT4J2psbypDhlT43jl2QVRo~NNgO~yHJ44l5Bo1IIP-r1AUIWzv62fnJ7qHjC1PpboPr4DGj-92VuHZPZZuFoyd1upd6K6gtdrYqKM1FDp3fjRZlMmVS2Xdcea3a7lnMbEAoka7ENn7RE69hP-s99MtSbVOrrboBrhNFpn~QfgnapWzfzAgYhGjK~3VeN547Is83P6~jnsyBPoIXiwS1GFdjoHmIyLCmSoTpoBwS8rYS05Hwzi2j5a9dYy8HICyipsjQ__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA

https://onlinelibrary.wiley.com/doi/pdf/10.1002/hbm.24073

https://www.frontiersin.org/articles/10.3389/fnsys.2016.00046/full

As far as I can throw them =D

EDIT - less tongue in check of an answer: yes, but I recognize that what I remember might not be how it happened, but a lot of times, what matters is how I remember it, if that makes sense. Like a meal with a friend: I don't need to know the specifics, just need to know how it felt, etc., and even if it wasn't how I felt then, it's how I think I felt back then now, and that's cool with me.

1. Theoretically possible? Sure. Practical, in any sense? No. We perceive reality in a biased way, so, from inception, all memories are faulty.

2. Impossible to know. Generally, again, our memories are not 100% accurate after they leave our short-term memory -- if not before that when sensory memory (which is pretty accurate and vast, but fleeting) is encoded into short-term memory. They're good enough to serve our personal agendas (not being pejorative, just recognizing the inherent self-focused bias of memory formation), whatever that may be. I'd argue that we all have a good gist of what happened to us and when and a good deal of details, but there are lots of details that we have woven in to fit the naturally occurring gaps to make us seem more sure of a memory/detail than we actually are. It's all relative and probabilistic.

If you're using the term "memories" strictly, I'd garner it's too late to distinguish between "true" and "false" ones.

There are some activation differences in the brain. Here's a good read-up from Elizabeth Loftus, who did some of the original work on inducing false memories by suggestion.

This question is also predicated upon the idea that memories can be inherently true, which we know isn't quite accurate. Memory is inherently faulty. At best, what we remember is what we remembered the last time we remembered it, and not the actual event itself.