Modelling Pay what you want I have been trying to model a Pay What you Want scheme. Now, for a monopoly it is clear that monopoly will have more profit by setting monopoly pricing assuming all players are selfish. But consider a scenario of 2 sellers one posting a fix price and other a PWYW strategy. In a market of selfish players the PWYW will make huge losses and market would move on to the fix price seller who can now act as a monopoly. So does this imply that there is an incentive for the selfish players to keep PWYW firm in market ? Also, how do I extend this idea to more than 2 firms ?
So does this imply that there is an incentive for the selfish players
  to keep PWYW firm in market ?


No, unfortunately not. In general equilibrium models (as @FooBar already mentioned) buyer's do not think about the influence of their actions on the seller. Therefore, they would just buy at the lowest possible price.

However, if you have a game theoretic model including uncertainty about profits of the PWYW firm and risk-averse consumers who prefer the PWYW firm for some reason you might get Nash-equilibria in which PWYW firms have positive profits.

Another way to model PWYW firms is to include non-monetary benefits from paying. For example a disutility for being seen as a cheapskate or for exploiting the firm or a positive utility from "doing the right thing" (i.e., paying the price that they think is appropriate). The selfish, rational players will pay a positive price and will generate profits for the firm.

I think in reality the impact of non-monetary benefits is much higher than the impact of asymmetric information with risk-aversion.


  Also, how do I extend this idea to more than 2 firms ?


I don't really think it is really interesting to extend this to more than two firms (especially without having solved this for 2 firms), but for both modeling options presented it should be "easy enough".