It refers to a no-win/no-lose situation. It does not require three participants; two is enough.
There's a 19th Century story in Mexico that illustrates the Mexican Standoff very well. Two horse carriages going in the opposite direction entered a narrow street and met halfway through. Neither could move forward, and each insisted that the other back his horse carriage up. Each sent servants for foor and water, and both stayed firm for several days, until the authorities made both of them back up.