How much does resolve matter in international relations? There are some who argue that resolve is unimportant. Dr. Farley argued that one's enemies will interpret one's actions however they wish. While this is true to some extent, I have to dispute it. Stalin closed off Berlin in an attempt to force the West to surrender it. Instead, the US initiated the legendary Berlin Airlift. After it became clear to Stalin that the US was determined to keep Berlin, Stalin called off the blockade.
There are other examples as well. An Iranian frigate attacked two American military aircraft. In response, US fighters sunk the frigate. If memory serves, Kenneth Pollack argues in The Persian Puzzle that the Iranian government took a lesson from this incident, namely that they could only push the US before the US would respond.
Finally, I feel obliged to bring an example in from World War II. Yes, I'm going to talk about Munich. I know that's the most cited example of the need for resolve, but it's a good one. Hitler was having problems at home, so he did what he always did. He went looking for trouble abroad. He demanded the Sudetenland, and he got it. Some experts argue that, had the British and the French stood up to him, the military would have initiated a coup and removed Hitler from power. Instead, Hitler got a strategically vital section of Czechoslovakia, and the German military stayed loyal.
Now, does that mean standing fast is always a wise idea? Of course not. Quite simply, some things aren't worth fighting over. Mexico disputed a small section of the Texas border (the Rio Grande had moved since the border was drawn); eventually, the US agreed to give it up in return for increased oil sales from Mexico. Attempting to hold onto that land would have simply been stupid.
What I'm saying is that resolve matters. It's not everything, but it does matter.