Multiple equilibria exist in this case. If the Egyptian rioters "enjoy" their experience and grow more confident and gain in numbers, then there could be a peaceful regime change as the Mubarak government chooses to quit without a fight. Dora Costa and I studied a similar issue in this U.S Civil War desertion paper. We used a large sample of Union Army soldiers and their choice of deserting or not to document that both "Macro Factors" (i.e was the Union Winning recent battles) and "co-ordination factors" (i.e were men in your unit deserting) both influenced the probability that any individual deserted in a given month. So, the math is tricky here; your probability of deserting is a function of whether all the men around you are deserting. This is like a bank run. Returning to Egypt, it is cheaper to protest if you know that everyone else will protest with you. There is strength in numbers.
But, the Mubarak government may have learned the wrong lessons from China's 1989 hard line at Tiananmen
Square. If Mubarak plays "fight", then people will die and rational free riders such as Nasser al-Sherif will quit the fight and "the people" are likely to lose. The good news for Nasser is that in this age of Twitter and the Internet, the world will know that this unfair fight is playing out and Egypt would risk suffering greatly on the world stage.
The Military represents a 3rd player in this complicated game. Who do they work for? Who is the leader of the military in the middle of a riot?
If there is a revolution in Egypt, what nation is next in the domino chain? The United States?