The relationship between ADR and yield is a fine one and there is a cut off point. Balance is the focus to drive yield and understanding the elasticity of your demand and market conditions.
Lowering rates does not guarantee an increase in demand just as maintaining rate does not guarantee optimal revenue.
A lower yield than the competitive set can still mean higher revenue for the individual property depending on what strategy they chose at that time.
Measurement, analysis, accurate forecasting & price positioning, understanding market drivers, reviewing agreements and pricing that bring in the bulk of your base business and ensuring your product on the market makes sense across channels including your direct channel all impact the rate/yield relationship. As does online presence and reviews.