After taking a break from serious competitive chess for a year and a half, I've begun studying and playing in tournaments again. Two recent games come to mind. One was against a master rated about 2230 (I'm rated about 1840). In a G/30 tournament against him, I was up an exchange in a simple endgame. By simple, I mean that there was no "funny stuff"-- I had a King, Rook, and five pawns, he had a King, Bishop, and five pawns, all the pawns were connect (no passers or anything like that). Simply put, there was no way to lose short of dropping the Rook. I had 2 minutes (with 5 second time delay) on my clock. The position was probably winning for me, but I couldn't see an easy way through to his position and knew I wouldn't figure it out in those two minutes. I offered a draw, and to my surprise, he declined. In the end, I hung the rook and lost the game.
Another recent game was against a 1900 player. I had a slightly worse position the entire game, but managed to simplify down to a Bishops of opposite color endgame. We both had 4 minutes on our clock and I offered a draw. He declined, and I subsequently won a pawn, dropped that pawn,and eventually lost an easily drawn Rook and pawn endgame.
In both cases, I was certain my opponent would accept my draw offer and shaken that he did not. I think there was almost this psychological need to prove the position was a draw when my opponent declined, and this state of mind contributed to horrible blunders. This has made me wonder whether I should accept draw offers in positions that are clearly drawn but not trivially so, if by rejecting the offer I put my opponent at a psychological disadvantage. If not that, at least wait for my opponent to offer the draw instead of offering it myself. I think Nigel Short once said, "If you're opponent offers a draw, take a moment and try to figure out why he thinks your position is better."
Anyone else have any similar experiences or thoughts on the subject?