In which market structures does the producer employ price discrimination? I was recently reading up on the Price Discrimination, first second and third degree. Although the author has laid out the concept neatly, there are no connections established between this concept and the market structures. Therefore, I came up with the above-mentioned question. 

In my opinion, the key criteria to exercise price discrimination is that the firms must have some price setting abilities. So Perfect Competition is definitely out. In Monopolistic Competition prices tend to be sticky so I think that this might be one market form where Price Discrimination is not heavily practiced. In a Monopoly, though the situation is quite different as the sole producer can charge as much as he likes and could therefore engage in Price Discrimination. I am not sure as to what would happen in Oligopolisitc Market Forms.
Market power required for price-discrimination?

In my understanding, no. I'm pretty sure that one can show this mathematically, but I'll just give you the intuition. Price-discrimination (PD) increases profits, because it incorporates different price-elasticities by having different prices. Therefore, a firm that incorporates PD should make, c.p. more profits than a firm that does not.

Perfect competition means that less profitable firms are forced out of the market. In this case, perfect competition will lead to firms that act with price-discrimination whenever they can.

Think about restaurants, where there is a lot of price-discrimination going on, either via lunch offers or menu pricing. Restaurants really shouldn't have market power, should they?