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I am curious about the geometry of these sets (assuming compact, convex action space and concave utility function, so the nash must exist). Is there any general argument about when will any solution set be convex?

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  • $\begingroup$ Welcome to Math.SE, ZUN LI!. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. $\endgroup$ – Brian Mar 25 at 23:09
  • $\begingroup$ You will usually have $3$ nash equilibria for a $2$ person game where everybody has $2$ choices. $3$ points are never a convex set. I'm not sure what you mean with "correlated equilibria". $\endgroup$ – s.harp Mar 26 at 14:02

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