First of all, a stalemate is a specific type of draw where the player who has the move has no legal move to make.
What you are talking about, a draw by threefold repetition, is in the rules. However, one of the players must claim the draw. If neither player claims it, then play continues.
I have a question pertaining to a statelmate caused by stubborness, not an inability to move.
Here is the scenario - please tell me if Chess or Chess.com has a rule that governs it: Two players, neither in check and both with plenty of options to move. However, they keep repeating (over and over) the same 1-2 step moves, because neither wants to sacrifice position. Move 1 invites response 1. Move 2 and response 2 puts the game board right back where it began.
Can this go on forever? Or is there a 3-repeat-and-your-out rule? [In playing against the Chess.com computer, I actually have had the computer declare a stalemate in this exact situation, stating that I've repeated the same exact move pattern three times.] In actual human-to-human chess play, does any such rule exist to prevent a vicious cycle from continuing forever?