…competitive conduct changes quickly as the number of incumbents increases. In markets with five or fewer incumbents, almost all variation in competitive conduct occurs with the entry of the second or third firm…once the market has between three and five firms, the next entrant has little effect on competitive conduct.
That is from Bresnahan and Reiss, “Entry and Competition in Concentrated Markets.”
Part of their method is to compare doctor and dentist pricing practices across towns of different size, and thus across different numbers of providers. Then they see where bigger numbers makes a difference in terms of pricing. Plumbers and tire dealers are considered too. One lesson seems to be that market concentration has to rise to very high levels to make a big difference in outcomes.
If you are wondering, the “sweet spot” for a town to have a single dentist or doctor is population between 700 and 900, at least circa the early 1990s.