我的想法
One of the most important fact of Mixed-Strategy Nash Equilibrium is that it is about possibility
Sometimes a game could not have Pure-Strategy Nash Equilibrium, but it is always possible to get MSNE in a well-defined game (from lecture note by Professor Sun)
And during the class, we have a very interesting but complicated example see here: Complicated NE question
Also noted that the number of Mixed-Strategy Nash Equilibrium is always odd-number
Example
In this case:
| Heads | Tails | |
|---|---|---|
| Heads | 1,-1 | -1,1 |
| Tails | -1,1 | 1,-1 |
We found that there is no such Pure-Strategy Nash Equilibrium . So we assume the player randomly chooses heads or tails, so the probability would be 1/2 heads and 1/2 tails.
Simple Conclusion
The Mixed-Strategy Nash Equilibrium is always come with the probability.