The proper response to 'Thank you,' is not 'Thank you,' but 'You're welcome.' The latter response, however, appears to be falling into desuetude. Similarly, the proper response to being applauded is not to applaud, but to graciously accept the applause of the audience. For if one applauds when being applauded, one is either applauding oneself, or applauding one's audience. Either way, one displays an unacceptable level of egotism. This is obvious in the case of applauding oneself. To applaud one's audience, however, is to applaud their applauding -- which is again a form of egotism.
Why then are people increasingly responding to 'Thank you' with 'Thank you' and to applause with applause? Why this simian symmetry? Perhaps it is a form of social oneupsmanship predicated on a lack of graciousness. Rather than accept your thanks graciously, I try to get the social upper hand by thanking you in return. Rather than accept the audience's applause with gratitude, I try to put them in my debt by applauding them. It is similar to the charade often seen in restaurants: 'I'll pay'; 'No, I'll pay.' Each wants to prove how generous he is, but each only succeeds in proving how ungracious he is.