How do you handle accepting an offer then receiving. Better one?

[Steve S.]

let me provide more details. 

I've been showing to several people and haggling back and forth. Nobody has submitted an app yet but I've agreed via text to accept someone's offer pending the application and verification 

The very next day, someone comes along and offers $200 more per month. 

What is legal here?  What is ethical? 

My personal thought is I should honor the price I agreed to with the other prospect.