Let's assume that everyone has a fixed budget of attention and empathy.

This is a bad assumption. I could spend more time empathizing than I do -- for example, when I chose to read a nonfiction book, I am likely to emphasize less than when I read a fictional tear-jerker. Moreover, the media spends a lot of time trying to increase your attention and empathy budget, getting you very engaged (attentive and empathetic) to their characters, whether these be fictional or political personages or whatever. Anytime that you stay up late watching Football (rather than go to sleep) you have increased your attention and empathy for that day.

However, it is true that TV and internet have strong money-making incentives for gaming your attention and empathy, and your neighbors probably don't. So on the A&E market, it is reasonable to expect that large powerful players will often outperform small local players. The fact that the market is flexible rather than fixed is probably a factor that makes it worse.