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I'm a 3rd year undergrad in mathematics who has recently developed a burgeoning interest in differential geometry. I'm also quite interested in dynamical systems and game theory, both of which are heavily employed in my research.

Are there any meaningful connections between game theory and differential geometry? (hopefully beyond formulating differential games as mechanics problems but I'd love to learn more about that too). Anything to add would be greatly appreciated.

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  • $\begingroup$ @RodrigodeAzevedo that sounds cool $\endgroup$
    – green frog
    Commented Aug 23, 2019 at 21:25
  • $\begingroup$ I was thinking of Parrilo, who works on both fields. However, his papers on game theory do not seem to be as algebro-geometric as I thought. Apologies for the false alarm. $\endgroup$
    – Rodrigo de Azevedo
    Commented Aug 23, 2019 at 21:35
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    $\begingroup$ There are connections between control theory and differential systems (and differential geometry), but I'm not sure that's truly anything game theoretic. $\endgroup$
    – Ted Shifrin
    Commented Aug 23, 2019 at 22:45

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Perhaps it will help to look at Nash equilibria and the surrounding literature. For example,

Swenson, Brian, Ryan Murray, and Soummya Kar. "On best-response dynamics in potential games." SIAM Journal on Control and Optimization 56, no. 4 (2018): 2734-2767.

         
          Fig.3c.

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