Construction of a 3x3 simultaneous game How could I construct a 3x3 simultaneous game with 2 players with no equilibrium in pure strategies but 1 is mixed strategies .
I am able to write down one with no pure strategy Nash equilibrium but how would I then know if only one mixed strategy would show not more?

I was thinking if I could eliminate one row and one column ,I.e they are strictly dominated in mixed strategies then I would only get 1 MSNE otherwise I get a continuum of mixed strategy Nash  equilibria’s is that right?
Eliminating a column and a row strategy is a nice idea. If the remaining 2x2 game has no pure strategy Nash equilibria (PSNE) than Nash's theorem guarantues you exactly one MSNE.

However there are also very trivial 3x3 games with zero PSNE and exactly one MSNE, e.g. rock-paper-scissors.