These models are different games, i.e., price vs. quality competition, but we do not need different solution concepts.
The single solution concept (Nash equilibrium) can explain different market outcomes depending on the situations. In other words, we do not need different assumptions about firms’ behaviors. Once a model is specified, then Nash equilibrium gives us the result of the game.
Review of Lecture 5
Indifference property in mixed strategy NE.
If a player chooses more than one strategy with positive
probability, she must be indifferent among such pure strategies: choosing any of them generate same expected payoff.