General aviation Instructor pilot reported a near miss with another aircraft while in the traffic pattern at a non-towered airport. The Instructor performed an evasive descent maneuver to avoid a collision.

Narrative

I was flying Aircraft X during an instructional flight on a right-hand downwind leg for Runway 16 established at approximately 5600 feet MSL. Another aircraft; Aircraft Y; entered the pattern on a left-hand downwind. The pilot was advised by someone on CTAF that it was a right-hand pattern. He responded by stating he would overfly the field at 5900 for a tear-drop entry. However; while continuing on downwind; I noticed Aircraft Y descending from 5900. I asked on CTAF if Aircraft Y had me in sight and he advised that he did. I realized if he descended further; he would end up directly above my aircraft at 5700; approximately 100 feet above. To avoid a potential mid-air collision; I had to take evasive action; diving from 5600 feet down to 5300 feet. After diving to 5300 he was located above my aircraft at 5700.If I had not descended; I believe there would have been a mid-air collision; given Aircraft Y's proximity and descent path. The incident caused significant concern about airspace and pattern awareness in this instance. Cause: Inadequate altitude separation due to Aircraft Y's descent into the pattern below their announced altitude. Potential misunderstanding of traffic pattern procedures by Aircraft Y.Suggestions: Re-emphasize the importance of maintaining announced altitudes when overflying a field and ensuring traffic separation in the pattern. Encourage pilots to review traffic patterns and procedures before arriving at non-towered airports. Consider additional education on Class B airspace boundaries and altitude restrictions to avoid confusion in the traffic pattern.