It depends on what you mean by competition. In the beginning when I am meeting people and talking I am not obligated or committed. Dating is meant for you to get to know many people. How else will you know what you like? I don't consider that competition but normal. When a person is chatting with me or we have gone on a "date" it is the period of let me see if we mesh as human beings. Who you talk to and what you do is none of my business at that point as long as we have not decided to be exclusive. If we decide we like each other enough after some time ;and we decide to take things further and focus our energy and interest ONLY on each other to see if we can build something then there should be no "competition".
Either you have decided to be serious or not. If you have it is disrespectful for either the man OR the woman to put someone in "competition" with another. Here it really just boils down to honesty. People jump into relationships too fast when they should see people for a while before they commit to one person.
It has been my experience that people put to much pressure on themselves and others to be locked down with one person immediately. Then two or three months in they realize basic things that they would have known hd they not been so quick to label things. In the past I have had a man pressure me to tell him that I was his girlfriend after one week. Mind you in that one week we only saw each other once. And to be honest I have done the same when I was younger and when I was older during times of my life when I was using relationships to fullfill parts of my life that required more growth on my part. I am learning to slow down and really "meet and greet" people, feel them out by really talking and listening, and yes it may mean that I am in "competition" at the beginning. But I don't focus on that. I focus on getting to know the person. At some point you choose each other or move on.
i'm not sure about the 'indirectly inviting to compete' comment, but i would say a fair few women who back down when they know they have competition do so because they feel they are not good enough, something which is then confirmed when they are left to walk away. If we are indeed good enough then you would continue to pursue the person who is cautiously protecting her heart.